1.926kg is the maximum book mass you can hold this way and keep from slipping.
This book with 27 N, so Normal rection force N = 27N.
let mass of brook = m Kg
here gravitational force acting downwards which tend book to more downwards and frictional force moving is acting vertically upwards to held
frictional force a must be equal to gravitational force here frictional force
fr = μN
so for body to be rest fr = mg
μN = mx 9.81
m = μN / 9.81
here maximum value of coefficient static friction μ = 0.70
m = 0.70x 27/9.81
m = 1.926kg
What is frictional force?
Friction is the force that opposes motion when the surface of one object comes into contact with the surface of another. The mechanical advantage of the machine is reduced by friction, in other words, the ratio of power to input decreases due to friction. A car uses a quarter of its energy to limit friction. However, the friction of the tires also allows the car to stay on the road, and the friction of the clutch allows it to drive. From matches to machines and molecular structures, friction is one of the most important phenomena in the physical world.
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which body has more internal energy - a piece of ice at a temperature of 0 degrees or from the melting of this ice at the same temperature?
The melting ice at the same temperature will have greater internal energy as compared to the ice at 0° C.
What is internal energy?
In thermodynamics, the internal energy is a quantity or state function that characterizes a substance's energy when capillary effects and other external fields, such as electric and magnetic forces, are absent. The value of the energy depends on the substance's state, not the nature of the processes that brought it to that condition, just like any other state function.
The melting ice at the same temperature will have more internal energy as compared to the ice at 0° C because during the melting of ice the intermolecular particles will absorb energy while breaking their bond and because of this, the melting ice has greater kinetic energy as well.
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In the diagram below, two of the three rays used to find the image position are shown. Which of the following best describes the third (missing) ray?A.A ray incident parallel to the axis refracts outward, as if it came from the focus on the left hand side.B.A ray incident through the vertex continues through the lens without refracting.C.A ray incident parallel to the axis refracts so that it passes through the focus on the right hand side.D.A ray incident on a path that would take it through the right focus refracts parallel to the axis.
Answer:
C. A ray incident parallel to the axis refracts so that it passes through the focus on the right hand side
Explanation:
The third ray is the blue ray in the following figure
Therefore, the third ray is a ray parallel to the axis that refracts and passes through the focus of the right side.
So, the answer is:
C. A ray incident parallel to the axis refracts so that it passes through the focus on the right hand side
in a simple electric circuit, ohm's law states that , where v is the voltage in volts, i is the current in amperes, and r is the resistance in ohms. assume that, as the battery wears out, the voltage decreases at 0.03 volts per second and, as the resistor heats up, the resistance is increasing at 0.03 ohms per second. when the resistance is 400 ohms and the current is 0.04 amperes, at what rate is the current changing?
Current is dwindling at 0.125 , where v is the voltage in volts, i is the current in amperes, and r is the resistance in ohms
Voltage = Current * Resistance ,
The Ohm's law is given by
V = IR eq. 1
Where V is the voltage across Resistance R and I is the current flowing through the Resistance R
Taking outgrowth of eq. 1 with respect to time t yields
dV/ dt = I * dR/ dt dI/ dt * R
dI/ dt * R = - I * dR/ dt dV/ dt
dI/ dt = (- I * dR/ dt dV/ dt)/ R eq. 2
Now substitute the given values into eq. 2
dI/ dt = (-0.02 *0.04(-0.02)) 300
dI/ dt = (-0.0008-0.02)/ 300
dI/ dt = -0.0208/ 300
Charge will go via the external circuit if the two conditions of an electrical circuit are satisfied. Flow of charge is appertained to as a current. In this case, the word" current" simply means that" charge is moving," indicating that commodity is taking place in the cables. The physical property of current, still, may be measured and quantified. The quantum of charge that moves past a point on a circuit at a given time is called current as a physical volume. The quantum of charge Q travelling through a line's cross section in a given quantum of time, as shown in the illustration below, can be measured to determine the current in a circuit.
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three solid, uniform, cylindrical flywheels, each of mass 65.0 kg and radius 1.47 m rotate independently around a common axis. two of the flywheels rotate in one direction at the other rotates in the opposite direction at 3.42 rad/s. calculate the magnitude of the net angular momentum of the system.
Three solid, uniform, cylindrical flywheels with a radius of 1.47 m and a mass of 65.0 kg each rotate. The system's net angular momentum is 297.77 298 kg m2 / s in size.
I is the moment of inertia.
W = angular momentum L = angular velocity
I = 1/2 MR^2
I = 1/2 (65)(1.47^2)
I = 70.23
Moment of Inertia times Angular Velocity equals L.
In the same direction, two of the fly wheels turn.
L = 2I(W1) - I(W2) (W2)
L = 2*70.23(3.83) - 70.23(3.42) (3.42)
L = 297.77 ≈ 298 kg m^2 / s
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An electrified rod attracts pieces of paper. After a while these pieces fly away! Why?
Answer: The paper prices fall off due to repulsive forces.
Explanation: When an electrified or charged object is brought near an uncharged object, it causes the electrons of the uncharged object to move as electrons are free movable particles. The electron leave behind the atoms. The uncharged object becomes ionized.
Here the pieces of paper may fall off because it becomes de-ionized by surrounding air particles. While the pieces are attached to the rod, surrounding air particles may provide or take away electrons and make the pieces become neutral again
a boy pushes his little sister on a sled. the sled accelerates from 0 to 3.2 m/s . if the combined mass of his sister and the sled is 40.0 kg and 18 w of power were generated, how long did the boy push the sled?
The boy pushed the sled for 15 seconds. The Work-Energy theorem can be applied in circumstances when a rigid body must move while being subjected to several forces.
What is Energy Theorem?The Work - Energy theorem states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle.
The Work-Energy theorem can be applied in circumstances when a rigid body must move while being subjected to several forces. A rigid body can only have kinetic energy because of its rigid structure, which prevents it from storing potential energy in its lattice.
The sled is initially at rest → initial velocity (u) = 0.
Final velocity (v) = 3.2 m/s
Mass of boy and sled (M) = 40 kg
Power developed (P) = 18 W = 18 Joules/sec
According to work - energy theorem -
Work done (W) = Δ E(K) = E(f) - E(i)
Therefore -
W=[tex](1/2*40*3.2*3.2-1/2*40*0)[/tex]=204 joule
Now, Power is defined as the rate of doing work -
P =[tex]pw/dt[/tex]= [tex]w/t[/tex]
18 = 204/t
t = 15 seconds
Hence, the boy pushed the sled for 15 seconds.
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The boy pushed the sled for 15 seconds.
What is Energy Theorem?The Work - Energy theorem states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle.The Work-Energy theorem can be applied in circumstances when a rigid body must move while being subjected to several forces. A rigid body can only have kinetic energy because of its rigid structure, which prevents it from storing potential energy in its lattice.The sled is initially at rest → initial velocity (u) = 0.
Final velocity (v) = 3.2 m/s
Mass of boy and sled (M) = 40 kg
Power developed (P) = 18 W = 18 Joules/sec
According to work - energy theorem -
Work done (W) = Δ E(K) = E(f) - E(i)
Therefore -
[tex]$$\mathrm{W}=(1 / 2 * 40 * 3.2 * 3.2-1 / 2 * 40 * 0)=204 \text { joule }$$[/tex]
Now, Power is defined as the rate of doing work -
[tex]&\mathrm{P}=p w / d t=w / t \\[/tex]
[tex]&18=204 / \mathrm{t} \\[/tex]
[tex]&\mathbf{t}=15 \text { seconds }[/tex]
Hence, the boy pushed the sled for 15 seconds.
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according to modern ideas and observations, what can be said about the location of the center of our expanding universe? according to modern ideas and observations, what can be said about the location of the center of our expanding universe? the milky way galaxy is at the center. the universe does not have a center. earth is at the center. the sun is at the center.
The correct answer is option C:
According to modern ideas and observations, the location of the center of our expanding universe explains that the universe does not have a center.
Our universe is composed of three kinds of substances that are dark matter, normal matter, and dark energy.
Everything in the universe is made of normal matter i.e. planets, stars, human beings, and all other visible objects.
Astronomers have theorized that the universe is expanding at a faster rate. Between any two given points, the distance of the universe is increasing and so we can predict that the universe will be 2x in size after ten billion years.
In general, the universe has no central point and it is expanding continuously because of a dark, mysterious force that is pulling the universe apart.
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What is the speed of a rocket that starts with a speed of 120m/s and slows down at a rate of 22m/s2 for 4 seconds?
The final speed of the rocket, given it started with a speed of 120 m/s and slows down at a rate of 22 m/s² for 4 seconds is 208 m/s
How do I determine the final speed?From the question given above, the following parameters were obtained:
Initial speed (u) = 120 m/sAcceleration (a) = 22 m/s²Time (t) = 4 secondsFinal speed (v) =?The final speed of the rocket can be obtained as follow:
v = u + at
v = 120 + (22 × 4)
Clear bracket
v = 120 + 88
v = 208 m/s
Thus, we can conclude from the calculation above that the final speed of the rocket is 208 m/s
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HELP!
Emily is riding her skateboard down the sidewalk at 2 m/s when she suddenly hits a rock, causing the skateboard to stop. According to Newton's first law of motion, what happens to Emily?
a
Emily accelerates forward.
b
Emily moves forward at 2 m/s.
c
Emily moves forward at less than 2 m/s.
d
Emily stops with her skateboard.
Answer: (b)
Explanation:
According to the law of conservation of momentum.
B. Emily moves forward at 2 m/s.
32. heavy rain reduces your ability to see and be seen; in daytime turn on your a. windshield wipers. b. low beam headlights. c. windshield defroster. d. all of the above
Heavy rain reduces your ability to see and be seen. So in daytime turn on all of the above ( d ) mentioned options.
Windshield wipers and windshield defroster are for the ability to see and the low beam headlights are for the ability to be seen by others. If it is night time drive below the speed limit because it is extremely hard to maneuver under those conditions.
Windshield wipers wipes the water off your windshield consistently. Low beam headlights indicate the presence of your car. Windshield defroster condenses the frosted windshield.
Therefore, in daytime turn on your windshield wipers, low beam headlights and windshield defroster.
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As shown in the diagram below, a soccer player kicks a ball directly toward the goal along a displacement vector r, which has a length of 7.7 m and a direction 30 degrees east of south. Alternatively, she could have kicked it to a second player standing directly in front of the goal along a displacement ry, who could have then kicked it to the goal along a displacement vector rx, as shown. Find the magnitudes (in m) and directions of rx and ry
Given that, the soccer player makes a displacement r = 7.7 m from the goal.
The distance between this player and the second player is [tex]r_{y}[/tex], and the distance between the second player and the goal is [tex]r_{x}[/tex]. The angle made by the first player with the goal is θ = [tex]30^{0}[/tex] east of south.
The magnitudes of [tex]r_{x}[/tex] and [tex]r_{y}[/tex] can be determined using the trigonometric rules.
r is the hypotenuse of the triangle formed (as shown in figure in the question), and [tex]r_{x}[/tex] is the side of triangle which is opposite to the angle θ = [tex]30^{0}[/tex]. So, [tex]r_{x}[/tex] = r sinθ = 7.7m × sin(30°) = 3.85 m.
[tex]r_{y}[/tex] is the side of triangle adjacent to the angle θ = [tex]30^{0}[/tex]. So, [tex]r_{y}[/tex] = r cosθ = 7.7m × cos(30°) = 5.445 m.
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The deepest section of ocean in the world is the Mariana Trench, located in the Pacific Ocean. Here,the ocean floor is as low as 10,918m below the surface. If the index of refraction of water is 1.33, howlong would it take a laser beam to reach the bottom of the treach?
Given:
The depth of the trench, d=10,918 m
The refractive index of the water, n=1.33
To find:
The time it takes for the laser beam to reach the bottom of the ocean.
Explanation:
The refractive index of water is given by,
[tex]n=\frac{c}{v}[/tex]Where c is the velocity of the laser in vacuum and v is the velocity of the laser in water.
On substituting the known values,
[tex]\begin{gathered} 1.33=\frac{3\times10^8}{v} \\ \implies v=\frac{3\times10^8}{1.33} \\ =2.3\times10^9\text{ m/s} \end{gathered}[/tex]The velocity is given by the equation,
[tex]v=\frac{d}{t}[/tex]Where t is the time it takes for the laser to reach the bottom of the trench.
On substituting the known values,
[tex]\begin{gathered} 2.3\times10^8=\frac{10,918}{t} \\ \implies t=\frac{10,918}{2.3\times10^8} \\ =47.5\times10^{-6}\text{ s} \\ =47.5\text{ }\mu\text{s} \end{gathered}[/tex]Final answer:
The laser beam would reach the bottom in 47.5 μs
the combination of crumple zones and air bags and seat belts might increase the distance over which a person stops in a collision to as much as 1.00 mm . what is the force exerted on a 65.0- kgkg driver who decelerates from 18.0 m/sm/s to rest over a distance of 1.00 mm ?
From Newton's second law of motion,
F = ma
We know m = 65 kg. Next, we have to find a through this formula:
v² = v₀² + 2ad
0² = (18 m/s)² + 2(a)(1 m)
Solving for a,
a = -162 m/s²
So,
F = (65 kg)(-162 m/s²) = -10,530 Newtons.
A crumpled zone in the front of the car gradually slows the car down and increases the braking time. A safety cell is a rigid cage that prevents passengers from becoming trapped. Inside the car seat belts and airbags prevent the driver from hitting the windshield steering wheel and dashboard.
Crumple zones are typically found in the front and rear of a vehicle and are designed to crumple and crush under high-force impacts. The Crumple Zone transfers a portion of the vehicle's kinetic energy during impact to a controlled crash while maintaining the integrity of the occupant cell.
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If net force acting on object is 0, then the force is considered to be..
a. balanced
b. equal in direction
c. unbalanced
d. distance/time
If net force acting on object is 0, then the force is considered to be balanced (option A).
What is net force?A net force refers to the sum of all the forces acting on an object.
The net force can accelerate a mass. Some other force acts on a body either at rest or motion. The net force is a term used in a system when there is a significant number of forces.
Fnet = F₁ + F₂ + F₃.............+ Fn
When the net force of an object is zero (0), this means that the sum of forces acting on the object is balanced. A balanced forces are forces that are opposite in direction and equal in size.
Therefore, a net force of 0 is a balanced force.
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There is a ball of fresh fruit at the top of a small cliff that is 45 m high. The fresh fruit baskets mass is 10kg's. Identify the energy (PE or KE) and calculate the it.
Given,
The mass of the fruit basket, m=10 kg
The height of the cliff, h=45 m
Kinetic energy is the energy possessed by an object due to its motion. Kinetic energy is directly proportional to the square of the velocity of the object.
Potential energy is the energy possessed by an object due to its position. The gravitational potential energy is directly proportional to the height at which the object is situated.
As the basket is at rest, its velocity is zero and hence it does not have kinetic energy.
Thus the energy possessed by the fruit basket is the potential energy.
The potential energy is given by,
[tex]E_P=\text{mgh}[/tex]Where g is the acceleration due to gravity.
On substituting the known values,
[tex]\begin{gathered} E_P=10\times9.8\times45 \\ =4410\text{ J} \end{gathered}[/tex]The potential energy of the fruit basket is 4410 J
Please help meee I really need help on this one. 30 points! And brainliest
a. the amount of work done is __________(equal to, greater than, less than) the amount of energy used
b. power is the rate of __________ (energy use, work done, force)
c. the greater the work done. the _________(equal, greater, smaller) power needed
d. The two factors that affect the amount of work done are _________ and ______________(mass, force, power, length, with, displacement)
choose the correct answer from the parentheses for each sentence
a) The amount of work done is equal to the amount of energy used.
b) Power is the rate of energy use/work done .
c) The greater the work done. The greater the power needed.
d) The two factors that affect the amount of work done are force and displacement .
Energy is the ability to perform work. Work and energy are related in that an increase in work results in an increase in energy, and vice versa. Power is defined as the rate at which work is completed or the amount of work completed per unit of time. Power is also defined as the rate at which energy is supplied to the system.
Power depends mainly on the amount of work done as well as the time taken by the body to perform the work.
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Compare the interaction between light and two different materials: a reflective glass mirror and a transparent glass block. How did the light behave differently
When a material is reflective, it would cause the light that meets it to bounce off while a transparent material would make the light to pass through it.
What is light?Light is a form of energy that produces a sensation that is visible to the optical eye. We know that a material is said to be transparent if the material can allow light to pass through it. A material is said to be reflective when it bounces off the rays of light that fall on it.
We can see that when light interacts with the transparent material, the light can pass through the material. If the light interacts with the reflective material then the light rays are seen to bounce off the light rays.
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an electron accelerated from rest through a voltage of 790 v enters a region of constant magnetic field. part a if the electron follows a circular path with a radius of 21 cm , what is the magnitude of the magnetic field? express your answer using two significant figures. b
The electron is accelerated through a potential difference of , so the kinetic energy gained by the electron is equal to its variation of electrical potential energy:
1/2mv²=eΔV
where
m is the electron mass
v is the final speed of the electron
e is the electron charge
is the potential difference
Re-arranging this equation, we can find the speed of the electron before entering the magnetic field:
v=√2eΔv/m=√2(1.6-10-19c)(790v)/9.1-10-31=1.66.10 m/s
Now the electron enters the magnetic field. The Lorentz force provides the centripetal force that keeps the electron in circular orbit:
evb=mv²/r
where B is the intensity of the magnetic field and r is the orbital radius. Since the radius is r=25 cm=0.25 m, we can re-arrange this equation to find B:
b=m/er =3.8.10 t
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From the bob’s frame while it is in uniform circular motion what is the direction and magnitude of the inertial force it feels?.
Radially outward is both the direction and magnitude of the inertial force. as it is moving uniformly in a circle, from the bob's frame. Radially emanating from the source of the charge is an electric field that is positively charged.
Radially outward means This is so because an electric field is produced when a positive charge is forced by the field. The electric field pulls the positive charge with a force that is directed away from the charge's origin. It is called Radially outward.
In physics, magnitude is referred to as an object's maximal size and direction. Both vector and scalar values use magnitude as a common factor. We know that scalar quantities are those that have magnitude and nothing else by definition.
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if an aircraft is in sluf and we know the weight of the aircraft, w, the wing area, s, the density and velocity, what else must we know to determine the coefficient of lift of the aircraft?
To determine the coefficient of lift of an aircraft in sluf, we must also know the angle of attack.
What is aircraft?
A vehicle that can fly by gaining support from of the air is called an aircraft. It uses either static lift, dynamic lift from an airfoil, or, in a few rare instances, the downward thrust from jet engines to counteract the force of gravity. Aeroplanes, helicopters, airships (including blimps), gliders, paramotors, as well as hot air balloons are a few examples of common types of aircraft. Aviation refers to the human activity which surrounds aircraft. Aeronautics is the study of aviation, which includes creating and building aircraft. Unmanned aerial vehicles may well be remotely controlled as well as self-controlled by onboard computers, unlike crewed aircraft that have an onboard pilot. Different factors, including lift type, aircraft propellant, usage, and others, can be used to categorise aircraft.
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Instructions:Draw a speed graph in the box that matches thefollowing scenario:A runner jogged 40m at a slow pace for 40seconds. She then stopped for 40 seconds to gea drink of water. After that, she sped up and ran60m more in 20 seconds.Tip:y axis - total of 100 mx axis - total of 100 s
Given data:
1) Runner jogged 40 m at a slow pace for 40 sec.
2) Stopped for 40 sec.
3) Again funs for 60 m in 20 sec.
Match the engines in the following list with their drawbacks. Place your answer in the blank space given. i. gunpowder engine ii. Savery engine iii. Newcomen engine iv. Watt engine a.____ The boiler could not withstand the steam pressure needed to lift water beyond 6 m. b.____ The engine had no mechanism to move the piston back to complete a cycle. c.____ The continual reheating needed after each cooling of the engine cylinder required a tremendous amount of thermal energy. d.____ This engine was large and massive and less efficient than thought possible.
a. (ii) Savery engine - The boiler could not withstand the steam pressure needed to lift water beyond 6 m.
b. (i) Gun powder engine - The engine had no mechanism to move the piston back to complete a cycle.
c. (iii) Newcomen engine - The continual reheating needed after each cooling of the engine cylinder required a tremendous amount of thermal energy.
d. (iv) Watt engine - This engine was large and massive and less efficient than thought possible.
Explanation:
a. Creating a lower vacuum in Savery engine causes more water to evaporate and limits the pressure differential. Practically, Savery's device was limited to 20-25 feet of suction (20 feet = 6 m).
b. The explosion of gun powder, in the gunpowder engine, forces the piston upwards for the gas to escape from the tube. Gravity and air pressure then pull the piston back. It then lifts another weight when it reaches the bottom, it explodes again and the cycle restarts.
c. The Newcomen engine operates by condensing steam drawn into the cylinder, thereby creating a partial vacuum which requires continual reheating after each cooling and a tremendous amount of thermal energy.
d. Watt's engine was able to convert around 2% of the thermal energy in steam to work. Later, the efficiency of this engine was increased to approximately 17%.
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p3. a double-convex lens is to be made of glass with an index of refraction of 1.5. one surface is to have twice the radius of curvature of the other and the focal length is to be 60 mm. what is the (a) smaller and (b) larger radius?
The magnitude of smaller and larger radius is 45mm and 90mm respectively.
Using lens makers formula:
1/f = (n-1) (1/ [tex]r_{1}[/tex] - 1/ [tex]r_{2}[/tex])
where n is the index of refraction, [tex]r_{1}[/tex] and f is the focal length and the curvature's radius of the first surface the light touches, and [tex]r_{2}[/tex] is the second's radius of curvature. The radius of one surface is two times that of the other, such that one is concave to the incoming light and the other is convex.
Plugging in the values we get:
1/f = (n-1) (1/ [tex]r_{1}[/tex] + 1/ [tex]2r_{1}[/tex]) = 3(n-1) / 2[tex]r_{1[/tex]
(a) For magnitude of smaller radius:
3(n-1)f / 2 = 3(1.5-1)(60) / 2 = 45mm
(b) For larger radius:
[tex]r_{2} = 2r_{1}[/tex] = 90mm
Therefore, the magnitude of smaller and larger radius is 45mm and 90mm respectively.
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What is the magnitude of the velocity of the plane
We will have the following:
First, we are told that the wind accelerates directly northwest, that means that the angle of inclination is 45°, so the following is true:
[tex]\begin{gathered} \sum F_x=115-75cos(45) \\ \\ \sum F_y=75sin(45) \end{gathered}[/tex]Then:
[tex]\begin{gathered} v_f=\sqrt{(115-75cos(45))^2+(75sin(45))^2}\Rightarrow v_f=81.56229536... \\ \\ \Rightarrow v_f\approx81.6 \end{gathered}[/tex]So, the magnitude of the final velocity is approximately 81.6 m/s.
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A football player kicks a football off a tee with a speed of 21 m/s at an angle of 51°.
a. What is the horizontal component of the velocity?
b. What is the vertical component of the velocity?
c. How long does it take the ball to reach its highest point?
d. What is the maximum height of the ball?
e. What is the total amount of time that the ball is in the air?
f. How far is the ball from the football player when it lands?
A football player kicks a football off a tee with a speed of 21 m/s at an angle of 51°, then the horizontal component of the velocity would be 15.58 m/s and the vertical component of the velocity would be 14.07 m/s.
What is a projectile motion?
It can be defined as the motion of any object or body when thrown from the earth's surface and follows any curved path under the effect of the gravitational force of the earth.
The horizontal component of the velocity = 21 × cos51 = 15.58 m/s
The vertical component of the velocity = 21 × sin51 = 14.07 m/s
Thus, the horizontal component of the velocity would be 15.58 m/s and the vertical component of the velocity would be 14.07 m/s.
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The separation distance between two 2.0 kg masses is decreased by two-thirds. How is the gravitational force between them affected?
Given:
The mass of two objects is: m1 = m2 = m = 2 kg
The distance between the object is decreased by two-thirds
To find:
How on reducing the distance, the gravitational force between them affects them.
Explanation:
Let the distance between two objects each having mass "m" be "r". The gravitational force between them is given as:
[tex]F_1=G\frac{m_1\times m_2}{r^2}[/tex]Here, G is the universal gravitational constant.
Substituting the values in the above equation, we get:
[tex]\begin{gathered} F_1=G\times\frac{2\text{ kg}\times2\text{ kg}}{r^2} \\ \\ F_1=G\times\frac{4\text{ kg}^2}{r^2}..........(1) \end{gathered}[/tex]Now, the distance between the mass is reduced by two-thirds. Thus, the new distance between them will be "R" which is given as:
[tex]R=r-\frac{2}{3}r=r(1-\frac{2}{3})=\frac{r}{3}[/tex]Now, the gravitational force between two masses with their distance of separation reduced by two-thirds is given as:
[tex]F_2=G\frac{m_1\times m_2}{R^2}[/tex]Substituting the values in the above equation, we get:
[tex]\begin{gathered} F_2=G\times\frac{2\text{ kg}\times2\text{ kg}}{(\frac{r}{3})^2} \\ \\ F_2=G\times\frac{4\text{ kg}^2}{\frac{r^2}{9}} \\ \\ \begin{equation*} F_2=G\times\frac{9\times4\text{ kg}^2}{r^2} \end{equation*} \\ \\ F_2=9\times(G\times\frac{4\text{ kg}^2}{r^2})..........(2) \end{gathered}[/tex]Substituting equation (1) in equation (2), we get:
[tex]\begin{gathered} F_2=9\times(G\times\frac{4\text{ kg}^2}{r^2}) \\ \\ F_2=9F_1 \end{gathered}[/tex]From the above equation, we observe that the new gravitational force F2 between two masses when their distance of separation is reduced by two-thirds will be nine times that of the original value of gravitational force F1.
Final answer:
The new gravitational force F2 between two masses when their distance of separation is reduced by two-thirds will be nine times that of the original value of gravitational force F1.
Equal masses are suspended from two separate wires made of the same material. The wires have identical lengths. The first wire has a larger cross-sectional area than the second wire. Which wire will stretch the least?.
The original lengths of both wires are equal, the thicker wire will stretch less as a result since Young's Modulus predicts that its original length will change less.
Young's modulus is a measurement of a material's capacity to endure changes in length when subjected to compression or tension along its length. Young's modulus, also known as the modulus of elasticity, is determined by dividing the longitudinal stress by the strain. i.e.Young's modulus = stress/strain
We can assume that the thicker wire must have less strain if it suffers less stress than the thinner wire because strain is defined as the percentage change in length.
Therefore we can said that, For the Young's modulus to remain constant, which it does, it must also drop correspondingly as strain rises. The thicker wire will stretch less as a result since its original length will change less because both wires started off the same length.
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Galileo’s pendulum theory stated that the time taken to swing through one complete cycle of a pendulum depends on what?
Italian astronomer, physicist, and engineer Galileo di Vincenzo Bonaiuti de' Galilei was sometimes referred to be a polymath.
Galileo asserted that the length of a pendulum affects how long it takes to swing through a full cycle.
A weight suspended from a pivot such that it can freely swing is called a pendulum. Gravity exerts a restoring force on a pendulum that causes it to accelerate back toward its equilibrium position when it is sideways from its resting position.
A pendulum is a tool for tracking periodic motion. It is made out of a string that is fastened to a sturdy structure. Typically, a pendulum swings from side to side when it is shifted through a tiny angle.
The length of the pendulum determines how long it takes for it to swing through one full cycle. The "period of the pendulum" is when things happen.
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a lighthouse is located on a small island 4 km away from the nearest point p on a straight shoreline and its light makes two revolutions per minute. how fast is the beam of light moving along the shoreline when it is 1 km from p? (round your answer to one decimal place.)
The speed of the beam of light moving along the shoreline when it is 1 km from p 62.83 km/min revolution.
A revolution is the motion of 1 object around a center or some other object, a forceful overthrow of a government by using the people, or any sudden or grand trade. An example of revolution is the movement of the earth around the solar.
dθ/dt = 3 rev/min
= 3×2π = 6π rad/min
tanθ = x/3
[tex]\frac{d}{dt}[/tex] tanθ = [tex]\frac{d}{dt}[/tex] (x/3)
sec²θ dθ/dt = 1/3 dx/dt
dx/dt = 3sec²θdθ/dt
At x = 1km; tanθ =x/3 =1/3
sec²θ = 1 + tan²θ = 1+(1/3)²
sec²θ =10/9
dx/dt = 3sec²θ dθ/dt
dx/dt = 3×10/9×6π
dx/dt = 62.83 km/min
Hence, the beam of light along the shoreline when it is 1 km away from point P is 62.83 km/min
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a car with a mass of 1,060.0 kg accelerates from 0 to 88.0 km/h in 10.0 s. the driver applies the brakes when the car is moving at 88.0 km/h, and the car comes to rest after traveling 46.0 m. what is the net force (in n) on the car during its deceleration? (assume the car is traveling in the positive direction. indicate the direction with the sign of your answer.)
A car with a mass of 1,060.0 kg accelerates from 0 to 88.0 km/h in 10.0 sec .The net force (in n) on the car during its deceleration is F = 7812.5 N.
Given
m= 1000 kg
u= 0 m/s
V = 90 km/h = 25m/s
t = 10 sec
a)by equation of motion :
v = u+at
25 = 0+ ax10
a = 2.5 m/c2
( b )By newton's law;
F= m*a
F=100X 2.5
F =2500N
( C )
u= 25m/s
V = 0
S = 40m
by equation of motion ;
v² = u²+2as
0=25²+80a
a=-7.8125 m/s²
by newton's law
F= m*a
F= 1000X 7.8125
F = 7812. 5N
A higher level motion control operation than velocity control is the control of acceleration and deceleration. Given that torque is the result of inertia and rate of altered speed, the system's forces will be affected by the rate of acceleration or deceleration. Any force calculation of this kind must take into account the actuator's or motor's inertia because it can significantly affect the torque needed. Control performance will also be impacted by the acceleration or deceleration profiles used. A motor needs linear acceleration in order to transition smoothly from one velocity to the next until the desired speed is reached. The rates of change, on the other hand, depend on both position and velocity when acceleration follows a non-linear, curved profile.
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