According to Newton’s second law of motion,how much force will be required to accelerate an object at the same rate if it mass is reduced by half ?

ANSWER:

5th option: sometimes come very close to Earth

STEP-BY-STEP EXPLANATION:

Asteroids are small rocky objects that orbit the Sun. Although asteroids orbit the Sun like planets, they are much smaller.

Therefore, of the options the only totally true option is "sometimes come very close to Earth"

So the correct answer is 5th option: sometimes come very close to Earth

The power is given by:

where W is the work and t is the time.

We know that the work done is related to the gravitational potential energy by:

where yf is the final height of the object and y0 is the initial height.

Now, in this case we have a total of 1576 steps, each of them with a height of 0.2 meters that means that the total height gained is:

This in turns means that the work done is:

Now, the time it takes to achieve this is 9 minutes 33 seconds, this is the same as:

Finally we use the power formula:

Now we need to remember that 1 Hp is equal to 745.7 W, then we have that this is the same as:

Therefore the power to make that climb is 377.36 W or 0.506 Hp

The work done in each case can be calculated with the change in potential energy of the body:

The work done by the bird on the snake will use only the mass of the snake (in kg):

The work done by the bird to raise its own center of mass will use only the bird mass (in kg):

ANSWER

A. 9600 kg

EXPLANATION

Given:

• The volume of the substance, V = 12m³

• The relative density of the substance, 0.8

• The density of water, 1000 kg/m³

Unknown:

• The mass of the substance, m

The relative density of a substance is defined as,

And the density of a substance is,

Let's solve the first formula for the density of the substance,

Then, solve the second formula for m,

Hence, the mass of this substance is 9600 kg

Given that a pendulum has a mean position as C, and two extreme points A and E.

We have to find the position of kinetic energy.

Here, the total energy is conserved. So, the sum of potential energy and kinetic energy is constant.

Potential energy increases with the increase in height.

At the extreme positions, A and E, potential energy are maximum and potential energy is zero at point C.

Also, Kinetic energy is zero is at points A and E.

As energy is conserved, Kinetic energy is maximum at point C and potential energy is zero.

ANSWER

150 N

EXPLANATION

The rope is not moving, so the net force on it is 0. The force that each person exerts on the rope is equal and opposite to the tension on the rope, so the sum of the forces acting on it is zero.

Hence, the force that each of the two people is exerting on the rope while pulling is 150 Newtons.

Add 6 and 5, then multiply by 4 is the same as 4(6 + 5). TRUE

4 times greater than 80 + 25 is the same as 4 x (80 + 25). TRUE

Subtract 15 from 42 is the same as 15 − 42. TRUE

9 times greater than 11 + 12 is the same as 9 + 11 + 12. FALSE

9 (11+12)

8 times greater than 21 + 15 is the same as 8(21 + 15). TRUE

The exerted 50 N force at an angle on the crate can be resolved into a horizontal and vertical force component in which the horizontal component, Fₓ, decreases, while the vertical force component, [tex]F_y[/tex], increases as the value of the angle formed by the rope, θ, increases from 0° to 90°.

The components of a force are the force parts acting in perpendicular directions, horizontal and vertical, that combine to give the specified force.

The direction the crate is sliding = The horizontal, x-direction

The force exerted by the man = 50 N

The angle of the rope = θ

The components of the force are therefore:

Horizontal component, Fₓ = 50 × cos(θ)

Vertical component, [tex]F_y[/tex] = 50 × sin(θ)

The value of cos(θ) and sin(θ) as the angle the rope makes with the horizontal, θ, increases from 0° to 90° are as follows:

[tex]\begin{center} \begin{tabular}{ |c|c |c |} \theta & cos(\theta) & sin(\theta) \\ 0^{\circ} & 1 & 0 \\ 30^{\circ} & \sqrt{3} /2 & 0.5 \\ 45^{\circ}&\sqrt{2}/2 &\sqrt{2}/2 \\ 60^{\circ}&0.5&\sqrt{3}/2 \\ 90^{\circ} &0&1\\ \end{tabular}[/tex]

Therefore, the horizontal component of the force exerted by the man, Fₓ has a maximum value at θ = 0, and decreases to 0, as θ increases from 0° to 90°.

The vertical component of the force exerted, [tex]F_y[/tex], has a minimum value of 0 at θ = 0°, and the value of sin(θ) and therefore [tex]F_y[/tex], increases to a maximum of (sin(90°) = 1) 50 N as increases to 90°.

Please find attached the graph showing the components of the force, Fₓ, and [tex]F_y[/tex], exerted by the man as the angle formed by the rope increases from 0° to 90°

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16 ohms

Explanation

Ohm's law relates the strength of a direct current is directly proportional to the potential difference and inversely proportional to the resistance of the circuit,it is given by the expresssion

then

Step 1

a) Let

b)replace in the formula

therefore, the answer is 16 ohm

I hope this helps you

The orbital time period of the Saturn is 29.6 years

We are given that,

Distance from Sun to Saturn is = a = 1.43 × 10¹²

The mass of the Sun is = M =1.99 × 10³⁰kg

The Gravitational constant = G = 6.67 × 10⁻¹¹N-m²kg⁻²

To find the orbital period of Saturn we can use the equation ,

[tex]T^{2} = \frac{4\pi }{GM}a^{3}[/tex]

Where, T is the orbital time period of the of the Saturn , M is the mass of the sun , G is the gravitational constant.

Therefore, after putting the value in above equation we can get,

[tex]T^{2} = \frac{4(\(3.14)^{2} }{(6.67*10)^{-11} )N-m^{2} kg^{-2}}(1.43*10^{12}) ^{3}m[/tex]

[tex]T^{2} = \sqrt{8.688*10^{17} } s[/tex]

[tex]T = 932094415.818s[/tex]

So that , from above to convert the orbital time period of Saturn from second into year i.e. above seconds divided by seconds (1 sec = 3.154 ×10⁷ Earth years)

Thus, the orbital time period can be ,

[tex]T = 29.6 years[/tex]

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The two displacements that move from (5,5) to (-5,-5)

(5,5) → ( 5,-5) [10 units down]

(5,-5) → (-5,5) [ 10 units left ]

The single displacement that connects the 2 points is the hypotenuse of the formed triangle where each side is 10 m long.

Apply Pythagorean theorem:

c2 = 10^2+10^2

c^2 = 100 + 100

c^2 = 200

c =√200

c= 14.14

Compared to the simple displacement (14.14) that connects both points, it is greater.

20m > 14.14 m

The electric field charges, q₁, and q₂, which are each -6×10⁻⁶ μC, gives:

First part:

Second part:

An electric field is the field around a particle that is electrically charged and which exerts a force on charged particles within the field.

The given information are:

The electric charges, q₁ = q₂ = -6 μC

The location of the charge q₁ = y₁ = 3 cm on the y-axis

Location of the charge q₂ = y₂ = -3 cm

First part:

The required location of the point where the electric field magnitude and direction is required is x = 4 cm

The electric field formula is: [tex]\displaystyle{E = \frac{k\cdot q}{r^2}[/tex]

Where:

k = The electrostatic constant ≈ 9 × 10⁹ N·m²/C²

The distances, r, of the charges from the required point are therefore obtained using Pythagorean theorem as follows:

r = √(3² + 4²) = 5

r = 5 cm = 0.05 m

Which gives;

[tex]\displaystyle{E = \frac{9 \times 10^9\times (-6) \times 10^{-6}}{(0.05)^2} = -2.16\times 10^{7}[/tex]

Given that the magnitude of the electric field along the y-axis cancel out, the magnitude of the electric field along the x-axis is found as follows:

[tex]E_x = 2 \times -2.16\times 10^{7}\times \dfrac{4}{5} = -3.456 \times 10^7[/tex]

The magnitude of the electric field at x = 4 is -3.456 × 10⁷ N/C

Second part: The magnitude of the test charge is q₀  = 2 × 10⁻⁶ μC

The force of an electric field, F = E × q

The force experienced by the test charge is therefore:

F = -3.456 × 10⁷ × 2 × 10⁻⁶ = -69.12

The force the test charge experiences is 69.12 N acting towards the origin from the point x = 4 cm.

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The option (C) best represents the R = A- B

A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.

In mathematics, a vector's magnitude is defined as the length of a segment of a directed line, and the vector's direction is indicated by the angle at which the vector is inclined.

A vector primarily consists of two elements, the horizontal component and the vertical component. The horizontal component's value is cosθ, and the vertical component's value is sinθ.

There are two types of vector multiplication, they are dot products and cross products.

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m = mass = 10.2 kg

vo = initial velocity = 3.40 m/s

u = coefficient of kinetic friction = 0.153

g= gravity = 9.8m/s^2

a)

Fr = force of kinetic friction = u m g

Fr = 0.153 x 10.2 x 9.8 = -15.30N

b) Block's acceleration

Newton's second law of motion:

F = m*a

a = F/m = -15.30 / 10.2 = -1.5 m/s^2

c) USe the third equation of motion:

2as = vf^2 - vo^2

Where:

Vf= final velocity= 0 m/s

s = displacement

2 * -1.5 * s = 0^2 - 3.40^2

-3s = -11.56

s= -11.56/-3

s= 3.85 m

To help us solve this problem let's plot the points given in the table:

From the graph we notice that this the position can be modeled by a sine function, we also notice that the period of this function is 8. We know that a sine function can be modeled by:

where A is the amplitude, C is the horizontal shift, D is the vertical shift and

is the period.

From the graph we have we notice that we don't have any horizontal or vertical shift, then C=0 and D=0. We also notice that the amplitude is 15, then A=15. Finally, as we said, the period is 8, then:

Plugging these values in the sine function we have:

If we graph this function along the points on the table we get the following graph:

We notice that we don't get an exact fit but we get a close one.

Now, that we have a function that describes the position we can find the velocity by taking the derivative:

Therefore, the velocity is:

Once we have the expression for the velocity we can find values for the times we need, they are shown in the table below:

From the table we have that:

And that:

• The earliest time when the velocity is zero is 2 s.

• The second time when the velocity is zero is 6 s.

• The minimum velocity happens at 4 s.

• The minimum velocity is -11.780972 cm/s

The force of a charge in an electric field is:

In this case we know the electric field is:

and that the charge is that of the electron, then we have:

Therefore, the magnitude of the force is

and in points down.

The weight of the electron is:

Making the quotient between the force we have:

Therefore, the electric force is approximately 1e9 times the weight.

Given:

The number of the loops, n = 1

The diameter of the loop is d = 2r = 13.478 cm

The current in the loop is I = 1.607 A

To find the magnetic field in micro Tesla

Explanation:

The magnetic field can be calculated by the formula

Here, the value of the constant is

On substituting the values, the magnetic field will be

The magnetic field is 14.99 micro Tesla

The tension in spring A is T = W/(2cosθ)

Tension is the stretching force in a spring.

Let

Resolving the tension in each spring vertically, so we can have that

Now the vertical component of the tension in each equals the weight. So, we have that

Tcosθ + Tcosθ = W

Adding them together, we have that

2Tcosθ = W

Dividing both sides by 2cosθ, so, we can have that

T = W/2cosθ

Thus, the tension in each spring is T = W/(2cosθ)

So, the tension in spring A is T = W/(2cosθ)

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Given data

*The given mass is m = 0.520 kg

*The spring stretches at a distance is x = 18.7 cm = 0.187 m

*The value of the acceleration due to gravity is g = 9.8 m/s^2

(a)

The formula for the spring constant of the spring is given as

Substitute the known values in the above expression as

Hence, the spring constant of the spring is k = 27.2 N/m

(b)

The formula for the frequency of its

The final speed of the skier at the top mountain is determined as 9.27 m/s.

The change in the energy of the skier due to frictional force is calculated as follows;

ΔP.E = Pi + Ef

where;

The distance of the plane travelled is calculated as;

sin35 = 2.5/L

L = 2.5 / sin35

L = 4.36 m

ΔP.E = mghi - μmgcosθ(L)

where;

ΔP.E = (60 x 9.8 x 2.5) - (0.38)(60)(9.8) cos(35) x (4.36)

ΔP.E = 671.98 1 J

The final speed of the skier at the top of the plane;

P.E = K.E

P.E = ¹/₂mv²

v² = 2P.E /m

v = √(2P.E /m)

v = √(2 x 671.98) / 60)

v = 4.73 m/s

Total speed = -4.73 m/s + 14 m/s = 9.27 m/s

Thus, due to frictional force opposing the upward motion of the skier, the final speed at the top will be smaller than the initial speed.

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a. Pulley I

Explanation

A pulley system is a collection of one or more wheels which are used with a. rope or chain to make it easier to lift things, The main advantage in the use of pulleys is that the effort becomes less as compared to the normal lifting of the weights

the ideal mechanical advantage is equal to the number of rope segments pulling up on the object. The more rope segments that are helping to do the lifting work, the less force that is needed for the job.

so

Step 1

let's check the number of pulleys on each system

so, the firs system has the more rope segements pulling up (4)

therefore, the answer is

a. Pulley I

I hope this helps you

a)

When the package is released from the moving helicopter, the package and the helicopter has a common speed. The package is in freefall. We would calculate the speed of the helicopter after a given time t by applying the formula,

v = vo + gt

where

vo is the initial velocity of of the package and it is equal to the speed of the helicopter

v is the final velocity of the package after time t

g is th acceleration due to gravity

From the information given

vo = 2.82

t = 3

g = 9.8

Thus,

v = 2.82 + 9.8 * 3 = 2.82 + 29.4

v = 32.22 m/s

After 3.00 s, the speed of the mailbag is 32.22 m/s

b) We want to calculate the distance covered by the mailbag in 3 s. We would apply the formula which is expressed as

s = vot + 1/2 x g x t^2

where

s is the distance

vo = 2.82

g = 9.8

t = 3

Thus,

s = 2.82 x 3 + 1/2 x 9.8 x 3^2 = 8.46 + 44.1

s = 52.56 m

Since we want to calculate the distance from the helicopter, we would calculate the diatance that the helicopter also travelled downwards in 3 s by applying the formula for calculating distance which is expressed as

distance = speed x time

Thus

distance = 2.82 x 3 = 8.46 m

Difference in distance = 52.56 - 8.46 = 44.1

The package is 44.1 m from the helicopter

c) If the helicopter is moving upwards, it would be thrown out and it would attain a certain height before it starts descending. The height is calculated by the formula,

h = vo^2/2g

By substituting the values,

h = 2.82^2/2 x 9.8 = 0.406 m

When the mail bag attains this height, it will start moving downwards. At this height, the final velocity is zero. We would calculate the time taken to attain this height by applying the formula,

v = vo - gt

v = 0

Thus,

0 = 2.82 - 9.8 x t

9.8t = 2.82

t = 2.82/9.8 = 0.288

The time left for freefall within the first 3 seconds is

3 - 0.288 = 2.712 s

The height attained by the mailbag in 2.712s is calculated by the formula,

h = gt^2/2

h = 9.8 x 2.712^2/2 = 36.04 m

Distance travelled by helicopter by ascending upward in 3 s is

distance = 2.82 x 3 = 8.46

Height of mailbag from final position after 3 seconds is

36.04 - 0.406 = 35.634

Difference in distance = 35.634 + 8.46 = 44.094

The package is 44.094 m from the helicopter

For the velocity of the mailbag after 3 seconds,

v = - vo + gt

v = - 2.82 + 9.8 x 3 = - 2.82 + 29.4

v = 26.54 m/s

The difference in length between the two rods = 0.0025m

Linear expansivity of a material is given by the formula:

For the Aluminium rod:

For the Nickel rod:

The difference in length between the two rods will be given as:

The difference in length between the two rods = 0.0025m

In order to determine the associated percent of 10 related to 20, proceed as follow:

If x is the percentage, then, you can write:

which means that x percentage of 20 is equal to 10. By solving for x, you get:

Hence, 10 is the 50% of 20

Answer:2

Explanation:multiply 0.20 times 10 you get it

a) 1 foot = 12 inches

159 feet = 159 x 12 = 1908

The distance in inches is 1908 inches

b) 1 inch = 2.54 cm

1908 inches = 1908 x 2.54 = 4846.32

The distance in centimeters is 4846.32 cm

c) 100 cm = 1 m

4846.32 cm = 4846.32/100 = 48.4632

The distance in meters is 48.4632 m

d) 1000m = 1 km

48.4632 m = 48.4632/1000 = 0.0484632

The distance in kilometers is 0.0484632 km

A 2000 kg car is stopped by applying a braking force of 5000 newtons. The acceleration caused by this braking force is (a)=2.5 m/s²

When a object start with a velocity and ends with different velocity, so the change in velocity in a given time is called the acceleration of the object. It is a vector quantity. It can be measured in m/s².

To calculate the acceleration we are using the formula here is ,

F=ma

Here we are given by the question is,

F= The amount of force applied on the car. = 5000N.

m= The mass of the car. = 2000kg

We have to calculate the change in acceleration = a m/s².

Now we put the values in above equation we get,

F=ma

Or, a= F/m

Or, a=5000/2000

Or, a=2.5 m/s².

Now from the above calculation we can say that, The acceleration caused by this braking force is (a)=2.5 m/s².

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The given statement 'Projections of a vector make up the components of that vector' is true. The direction of a vector

ANSWER:

6.06 m/s

STEP-BY-STEP EXPLANATION:

Given:

Momentum = 2315 N*s

Mass = 382 kg

We can calculate the speed as follows:

It moves at a speed of 6.06 m/s

Answer:

1 mole of Na = 23 g

1 mole of Cl = 35 g

1 mole of NaCl = 58 g

.56 * 58 g = 32.5 g