A 1990 kg car moving at 20.0 m/s collides and locks together with a 1540 kg car at rest at a stop sign. Show that momentum is conserved in a reference frame moving at 10.0 m/s in the direction of the moving car.

Answers

Answer 1

Answer:

The momentum before collision and momentum after collision is equal in a frame of reference moving at 10.0 m/s in the direction of the moving car.

Explanation:

[tex]m_1[/tex] = Mass of moving car = 1990 kg

[tex]u_1[/tex] = Velocity of moving car in stationary frame = 20 m/s

[tex]m_2[/tex] = Mass of stationary car = 1540 kg

[tex]u_2[/tex] = Velocity of stationary car in stationary frame = 0 m/s

v = Combined velocity in stationary frame

Momentum conservation for stationary frame

[tex]m_1u_1+m_2u_2=(m_1+m_2)v\\\Rightarrow v=\dfrac{m_1u_1+m_2u_2}{m_1+m_2}\\\Rightarrow v=\dfrac{1990\times 20+0}{1990+1540}\\\Rightarrow v=\dfrac{3980}{353}\ \text{m/s}[/tex]

In frame moving at 10 m/s the velocities change in the following ways

[tex]u_1=20-10\\\Rightarrow u_1=10\ \text{m/s}[/tex]

[tex]u_2=0-10\\\Rightarrow u_1=-10\ \text{m/s}[/tex]

[tex]v=\dfrac{3980}{353}-10\\\Rightarrow v=\dfrac{450}{353}\ \text{m/s}[/tex]

Momentum before collision

[tex]m_1u_1+m_2u_2=1990\times 10+1540\times -10\\\Rightarrow m_1u_1+m_2u_2=4500\ \text{kg m/s}[/tex]

Momentum after collision

[tex](m_1+m_2)v=(1990+1540)\times \dfrac{450}{353}\\\Rightarrow (m_1+m_2)v=4500\ \text{kg m/s}[/tex]

The momentum before collision and momentum after collision is equal. So, the momentum is conserved in a reference frame moving at 10.0 m/s in the direction of the moving car.


Related Questions

If you had to choose one device to use with the battery, what would it be? Do you think such a battery could be invented
someday? Explain

Answers

Answer:

I would choose refrigerator.

Explanation:

In my opinion, such a battery could be invented by changing the device as a low power mode. Plus, it is a must in order to decrease the CFC gas spreading through the atmosphere. That's all, thank you.

as water warms on the stove, what is happening to the molecules in the liquid?​

Answers

Answer:

The water molecules start moving faster.

Explanation:

As the water is heated, the water molecules absorb heat and moves faster. The longer the water is kept on the stove, the more heat and kinetic energy the molecules gain. Soon, the hydrogen bonds break down completely because of the high kinetic energy and the water molecules escape into the air as gas.

The temperature that causes this to happen is known as the boiling point.

What is Newton 2nd law

Answers

Answer:

Newton's second law states that the acceleration of an object is directly related to the net force and inversely related to its mass.

Please help which letter goes where ?

Answers

Answer:

See list below

Explanation:

5. positively charged particles : D

6. dense center of the atom: C

7. negatively charged particles: A

8. articles with NO charge: B

For what absolute value of the phase angle does a source deliver 71 % of the maximum possible power to an RLC circuit

Answers

Answer: the absolute value of the phase angle is 28°

Explanation:

taking a look at expression for the instantaneous electric power in an AC circuit;

P = VI -------let this be equation 1

p is power, v is voltage and I is current;

for maximum power

P_max = V_rms × I_rms --------let this be equ 2

where P_max is the maximum power, V_rms is the rms value of voltage and I_rms is the rms value of current.

Also for average electric power in an AC circuit

P_avg = V_rms × I_rms × cos²∅ -------let this be equ 3

where P_avg is the average power and cos∅ is the power factor

now from equation 2;  P_max = V_rms × I_rms

so p_max replaces V_rms × I_rms in equation 3

we now have

P_avg = P_max × cos²∅

so we substitute

expression for the given value of the average power is

P_avg = P_max × 75%

p_avg = P_max.78/100

for the expression of the average electricity in an AC circuit

P_max.78/100 = P_max × cos²∅

78/100 = cos²∅

to get the absolute value of phase angle

∅ = cos⁻¹ ( √(78/100))

∅ =  cos⁻¹ ( 0.8832)

∅ = 27.969 ≈ 28°

Therefore the absolute value of the phase angle is 28°

We have that for the Question "For what absolute value of the phase angle does a source deliver 71 % of the maximum possible power to an RLC circuit"

It can be said that

[tex]45^o[/tex] of the phase angle is required to deliver 71 % of the maximum possible power

Power delivered to RLC circuit is given by

[tex]P = \frac{V^2}{Z}cos\theta\\\\P = I^2Zcos\theta[/tex]

Therefore,

[tex]Z = \sqrt{R^2 + (X_L-X_C)^2}[/tex]

Power delivered is maximum, therefore,

[tex]P_{max} = cos\theta\\\\71\% = cos\theta\\\\cos\theta = 0.71\\\\\theta = cos^{-1}0.71\\\\\theta = 44.76^o\\\\approximately 45^o[/tex]

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a car drives under a bridge. as it passes underneath a man jumps down onto the top of the car. the man and the car continue moving together. what type of collision is this?

Answers

Answer:

Inelastic collision.

Explanation:

Because both the momentum of the man and that of the car, is conserved because they are both moving with the same velocity.

Also kinetic energy is not conserved because the car moved with different kinetic energy, as well as the man.

When they came into contact, the final kinetic energy is different from the initial kinetic energy.

Answer:

perfectly inelastic

Explanation:

Why the tyres are in circular shape?

Answers

The circular shape allows the tire to roll easily with the least amount of bumps or jolts

Waves that hit a fixed boundary return to the starting point on the____
side that it began

A.Opposite

B.same

Answers

Answer:

A: Opposite

Explanation:

From Newton's third law of motion, to every action there is an equal an opposite reaction. Thus, when the wave hits a fixed boundary, it is returned as a reflected wave to the starting point albeit on the other side.

A spring with a spring constant value of 2500 StartFraction N over m EndFraction is compressed 32 cm. A 1.5-kg rock is placed on top of it, then the spring is released. Approximately how high will the rock rise? 9 m 17 m 27 m 85 m

Answers

Answer:

it's 9m

Explanation:

Answer:

9m

Explanation:

edge2o2o

You are planning a bicycle trip for which you want to average 24 km/h. You cover the first half of the trip at an average speed of 21 km/h. What must your average speed be in the second half of the trip to meet your goal?

Answers

Answer:

27km/h that's the answer

Define the Element of Art, value. If you were using a pencil, how would you create a darker value?

Answers

Elements of art are stylistic features that are included within an art piece to help the artist communicate. The seven most common elements include line, shape, texture, form, space, colour and value, with the additions of mark making, and materiality.

You would create a darker value if you shaded it, shading it makes it darker.

A block slides at constant speed down a ramp while acted on by three forces: its weight, the normal force, and kinetic friction. Respond to each statement, true or false.

Answers

Answer:

a) True

b)False

c)False

• Had to complete the question first.

A block slides at constant speed down a ramp while acted on by three forces: its weight, the normal force, and kinetic friction. Respond to each statement, true or false.

(a) The combined net work done by all three forces on the block equals zero.

(b) Each force does zero work on the block as it slides.

(c) Each force does negative work on the block as it slides.

Explanation:

Net work is the change in kinetic energy, which leads to final kinetic energy - our initial kinetic energy this is the formula for net work. This is the working energy theorem, a theorem that states that the net work on an object induces a change in the object's kinetic energy.

what type of energy is kinetic energy? A nuclear energy B chemical energy C potential energy D mechanical energy

Answers

Answer:

I believe it is C, Potential

Explanation:

Google, since all types are either kinetic or potential, so it wouldn't make sense if kinetic was itself. I also know for a fact it isn't Chemical

Car A rear ends Car B, which has twice the mass of A, on an icy road at a speed low enough so that the collision is essentially elastic. Car B is stopped at a light when it is struck. Car A has mass m and speed v before the collision. After the collision:______

a. each car has half the momentum.
b. car A stops and car B has momentum m v.
c. car A stops and car B has momentum 3m v.
d. the momentum of car B is three times as great in magnitude as that of car A.
e. each car has half of the kinetic energy.

Answers

Answer:

D. The momentum of Car B is three times as great in magnitude as that of car A.

Explanation:

I majored in Physics

A cooling fan is turned off when it is running at 850 rev/min . It turns 1350 revolutions before it comes to a stop. What was the fan's angular acceleration, assumed constant

Answers

Answer:

α = -0.47 rad/sec²

Explanation:

Assuming that the angular acceleration is constant, we can apply the following kinematic equation:

        [tex]\omega^{2}_{f} - \omega^{2}_o} = 2* \alpha* \Delta \theta (1)[/tex]

Since the fan comes to an stop, ωf = 0.In order to get the value of the angular acceleration in rad/sec2, we neeed to convert first ω₀ to rad/sec, and Δθ, to rad, as follows:

       [tex]\omega_{o} = 850 rev/min * \frac{2*\pi rad}{rev} * \frac{1min}{60 sec} = 89 rad/sec (2)[/tex]

      [tex]\Delta \theta = 1350 rev *\frac{2*\pi rad}{1rev} = 8482.3 rad (3)[/tex]

Solving for α in (1):

       [tex]\alpha = \frac{-\omega_{o}^{2} }{2*\Delta\theta} = -0.47 rad/sec2 (4)[/tex]

True or False: An acid is a solution that has an excess of H+ ions.

Answers

Answer:

true

Explanation:

A block has two strings attached to it on opposite ends. One string has a force of 5 N,

the other string a force of 15 N. The block is accelerating at 1 m/s2 on a horizontal surface.

A) What is the mass of the block if the friction force is 3 N?


B) What is the coefficient of friction?

Answers

Unless you have a diagram to include or any other additional info, I'll assume the block is being pulled by two opposing forces along the horizontal surface.

Horizontally, the block is under the influence of

• one rope pulling in one direction with magnitude 15 N,

• the other rope pulling in the opposite direction with mag. 5 N, and

• friction, opposing the direction of the block's motion, with mag. 3 N.

It stands to reason that the block is accelerating in the direction of the larger pulling force.

(A) By Newton's second law, we have

15 N + (-5 N) + (-3 N) = m (1 m/s²)

where m is the mass of the block. Solve for m :

7 N = m (1 m/s²)

m = (7 N) / (1 m/s²)

m = 7 kg

(B) The friction force is proportional to the normal force, so that if f is the mag. of friction and n is the mag. of the normal force, then f = µ n where µ is the coefficient of friction.

The block does not bounce up and down, so its vertical forces are balanced, which means the normal force and the block's weight (mag. w) cancel out:

n + (-w) = 0

n = w

n = m g

where g = 9.8 m/s² is the mag. of the acceleration due to gravity.

n = (7 kg) (9.8 m/s²)

n = 68.6 N

Then

3 N = µ (68.6 N)

µ = (3 N) / (68.6 N)

µ ≈ 0.044

Waves that hit a fixed boundary return to the starting point on the ____
side that it began


opposite
same

Answers

Answer:

Opposite

Explanation:

Waves that hit a fixed boundary return to the starting point on the opposite side that it began.

After striking, the wave gets reflected and it moves in the direction opposite to the initial direction.

Hence, it would mean that waves that hit a fixed boundary return to the starting point on the opposite direction.

An irrigation system supplies water at a pressure of 0.5 MPa and flow rate of 5,000 liter per hour. If both the pump and motor are 100% efficient, what is the current required of a 220 volt service. Give your answer as a bare number in amps, with no units attached.

Answers

Answer:

3.16 A

Explanation:

The irrigation system has a motor which is used to drive the pump. The efficiency of the system is the ratio of the power output to power input. It is given as:

Efficiency = Power output / Power input

Given that efficiency = 100%  = 1, flow rate = 5000 liter / hour = 0.00139 m³/s, pressure = 0.5 MPa = 0.5 * 10⁶ Pa, voltage = 220 V.

Power output = supply of the pump = flow rate * pressure

Power output = 695 W

Efficiency = Power output / Power input

1 = 695 / power input

Power input = 695 / 1

Power input = 695 W

Also, Power input = input of motor = voltage * current

Power input = voltage * current

695 = 220 * current

current = 695 / 220

current = 3.16 A

WHO WANts TO HAVE SOME GLIZZY ACTION

Answers

bruh huh.............

When does a battery give off the most gas, when charging has just begun or when the battery is almost fully charged?

Answers

Answer:

When the battery is almost fully charged.

Explanation:

A battery is a term used to describe any device that has the capability to convert chemical energy through an oxidation-reduction(redox) reaction taking place within the electrical circuit.

A battery usually have two ends, named as a cathode electrode(Positive) and an anode(negative) electrode. Batteries usually give off the most gas when they are almost fully charged, that is while it is advisable not to over charge a battery.

as speed increases, what happens to potential energy ?

Answers

Answer:

As the Speed increases , the potential energy decreases

Answer:

Since the object only has so much total internal energy, and the faster an object moves the larger the kinetic energy is, hence the potential energy will decrease as a result of speed increasing.

Explanation:

Hope this helped!

A rocky meteoroid is on a collision course with planet Earth. The meteoroid is only 0.10 m in diameter.

The meteoroid will most likely not reach the surface of the Earth because
A.
it will be struck by lightning.
B.
it will collide with a shooting star.
C.
it will be intercepted by a space vehicle.
D.
it will burn up in the Earth's atmosphere.

Answers

it will burn up in earth's atmosphere

Answer:

it will burn up in the Earth's atmosphere.

Explanation:

The structure of the Earth's atmosphere protects the surface from frequent meteoroid strikes. As a meteoroid enters the atmosphere from outer space, it moves at very high speeds. At such speeds, intense amounts of friction and heat result. This process usually causes small meteoroids to burn up in the Earth's atmosphere before ever reaching the surface.

Difference between compressions and rarefactions

Answers

Answer:

Compression- a region in a longitudinal (sound) wave where the particles are closest together. Rarefaction- a region in a longitudinal (sound) wave where the particles are furthest apart.

Answer:

please mark as brainliest!!!!

Explanation:

Compression- a region in a longitudinal (sound) wave where the particles are closest together.

Rarefaction- a region in a longitudinal (sound) wave where the particles are furthest apart.

Points P and Q are located at (0, 2, 4) and (-3, 1,5). Calculate

a) The position vector of P

b) The distance vector from P to Q

c) The distance between P and Q

d) A vector parallel to PQ with magnitude of 10​

Answers

Answer:

a) The position vector of P is [tex]\vec P =(0, 2,4)[/tex].

b) The distance vector from P to Q is [tex]\overrightarrow{PQ} = (-3,-1,1)[/tex].

c) The distance between P and Q is [tex]\|\overrightarrow{PQ}\|=\sqrt{11}[/tex].

d) A vector parallel to PQ with magnitude of 10 is [tex]\vec v = \left(-\frac{30\sqrt{11}}{11},-\frac{10\sqrt{11}}{11}, \frac{10\sqrt{11}}{11} \right)[/tex].

Explanation:

a) The position vector of a point is the vector displacement from the origin to the location of the point. That is:

[tex]\vec P = (0,2,4)-(0,0,0)[/tex]

[tex]\vec P = (0-0, 2-0, 4-0)[/tex]

[tex]\vec P =(0, 2,4)[/tex]

The position vector of P is [tex]\vec P =(0, 2,4)[/tex].

b) First, we calculate the position vector of point Q:

[tex]\vec Q = (-3,1,5)-(0,0,0)[/tex]

[tex]\vec Q = (-3-0,1-0,5-0)[/tex]

[tex]\vec Q =(-3,1,5)[/tex]

The distance vector from P to Q is define by the following vectorial expression:

[tex]\overrightarrow{PQ} = \vec Q - \vec P[/tex] (1)

[tex]\overrightarrow{PQ} = (-3,1,5)-(0,2,4)[/tex]

[tex]\overrightarrow{PQ} =(-3-0,1-2,5-4)[/tex]

[tex]\overrightarrow{PQ} = (-3,-1,1)[/tex]

The distance vector from P to Q is [tex]\overrightarrow{PQ} = (-3,-1,1)[/tex].

c) There are two approaches to calculate the distance between P and Q:

First Method - Pythagorean Theorem:

[tex]\|\overrightarrow{PQ}\| = \sqrt{(-3)^{2}+(-1)^{2}+1^{2}}[/tex]

[tex]\|\overrightarrow{PQ}\|=\sqrt{11}[/tex]

Second Method - Dot Product:

[tex]\|\overrightarrow{PQ}\| = \sqrt{\overrightarrow{PQ}\,\bullet\,\overrightarrow{PQ}}[/tex] (2)

[tex]\|\overrightarrow{PQ}\| = \sqrt{(-3,-1,1)\,\bullet (-3,-1,1)}[/tex]

[tex]\|\overrightarrow{PQ}\|=\sqrt{11}[/tex]

The distance between P and Q is [tex]\|\overrightarrow{PQ}\|=\sqrt{11}[/tex].

d) To determine a vector parallel to PQ with a given magnitude is determined by the following expression:

[tex]\vec v = \frac{k}{\|\overrightarrow{PQ}\|} \cdot \overrightarrow{PQ}[/tex] (3)

Where [tex]k[/tex] is the scale factor.

If we know that [tex]\overrightarrow{PQ} = (-3,-1,1)[/tex], [tex]\|\overrightarrow{PQ}\|=\sqrt{11}[/tex] and [tex]k = 10[/tex], then the vector is:

[tex]\vec v = \frac{10}{\sqrt{11}}\cdot (-3,-1,1)[/tex]

[tex]\vec v = \left(-\frac{30}{\sqrt{11}},-\frac{10}{\sqrt{11}},\frac{10}{\sqrt{11}}\right)[/tex]

[tex]\vec v = \left(-\frac{30\sqrt{11}}{11},-\frac{10\sqrt{11}}{11}, \frac{10\sqrt{11}}{11} \right)[/tex]

A vector parallel to PQ with magnitude of 10 is [tex]\vec v = \left(-\frac{30\sqrt{11}}{11},-\frac{10\sqrt{11}}{11}, \frac{10\sqrt{11}}{11} \right)[/tex].

Determine the force P required to maintain the 200-kg engine in the position for which θ = 30°. The diameter of the pulley at B is negligible.

Answers

Answer:

The force P required  is 1759.22 N

Explanation:

The missing diagram is seen in the first image below.

From the second image, we can see the schematic diagram of the engine hanging over the pulley.

To start with determining the value of the angle ∝;

[tex]tan \ \alpha = \dfrac{CD}{BD}[/tex]

where;

BD = AB-AD

Then;

[tex]tan \ \alpha = \dfrac{CD}{AB-AD}[/tex]

[tex]\alpha = tan^{-1} \bigg(\dfrac{CD}{AB-AD} \bigg )[/tex]

replacing their respective values, where;

CD = 2 sin 30° m,  AB = 2m and AD = 2 cos 30° m

[tex]\alpha = tan^{-1} \bigg(\dfrac{2 \ sin \ 30^0}{2-2 \ cos \ 30^0} \bigg )[/tex]

[tex]\alpha = tan^{-1} \bigg(\dfrac{1}{2-1.732} \bigg )[/tex]

[tex]\alpha = tan^{-1} \bigg(\dfrac{1}{0.268} \bigg )[/tex]

[tex]\alpha = tan^{-1} \bigg(3.73\bigg )[/tex]

[tex]\alpha \simeq 75^0[/tex]

From the third diagram attached below:

The tension occurring in the thread BC is equal to force P

[tex]T_{BC} = P[/tex]

Using the force equilibrium expression along the horizontal direction.

[tex]\sum F_x = 0\\\\ -T_{AC} \ cos \ 30^0 + Pcos \alpha = 0[/tex]

replacing the value of [tex]\alpha \simeq 75^0[/tex]

[tex]-T_{AC} \ cos 30^0 + P cos 75^0 = 0[/tex]

[tex]P \ cos \ 75^0 = T_{AC} \ cos \ 30^0[/tex]

[tex]P =\dfrac{ T_{AC} \ cos \ 30^0}{\ cos \ 75^0} \ \ \ - - - (1)[/tex]

Along the vertical direction, the force equilibrium equation can be expressed as:

[tex]\sum F_y =0[/tex]

[tex]-W + P \ sin \alpha + T_{AC} \ sin \ 30^0 = 0[/tex]

[tex]W = P \ sin \ \alpha + T_{AC} \ sin \ 30^0[/tex]

replacing [tex]\alpha \simeq 75^0[/tex] and [tex]P =\dfrac{ T_{AC} \ cos \ 30^0}{\ cos \ 75^0}[/tex]

[tex]W =\dfrac{T_{AC} \ cos \ 30^0}{cos \ 75^0}\times sin \ 75^0 + T_{AC} \ sin \ 30^0[/tex]

Also, replacing W for (200 × 9.81) N

[tex]200 \times 9.81 =\dfrac{T_{AC} \ cos \ 30^0}{cos \ 75^0}\times sin \ 75^0 + T_{AC} \ sin \ 30^0[/tex]

[tex]200 \times 9.81 = T_{AC} \ cos \ 30^0 \ tan \ 75^0 + T_{AC} \ sin \ 30^0[/tex]

[tex]1962= T_{AC} \ ( cos \ 30^0 \ tan \ 75^0 + \ sin \ 30^0)[/tex]

[tex]1962= T_{AC} \ (0.8660\times 3.732 + 0.5)[/tex]

[tex]1962= T_{AC} \ (3.231912 + 0.5)[/tex]

[tex]1962= T_{AC} \ (3.731912)[/tex]

[tex]T_{AC} = \dfrac{1962}{ \ (3.731912)}[/tex]

[tex]T_{AC} = 525.736 \ N[/tex]

From [tex]P =\dfrac{ T_{AC} \ cos \ 30^0}{\ cos \ 75^0}[/tex]

[tex]P =\dfrac{ 525.736 \ cos \ 30^0}{\ cos \ 75^0}[/tex]

[tex]P =\dfrac{ 525.736 \times0.866}{0.2588}[/tex]

P = 1759.22 N

Thus, the force P required  is 1759.22 N

A marble rolls off of a table that is 0.97 meters tall with a velocity of 1.87 m/s. How long
does it take the marble to hit the floor?
O 0.44 seconds
O 0.98 seconds
O 0.39 seconds
O 0.52 seconds

Answers

It’s the last one
Good luck
God bless you

describe the relationship between the direction of the velocity vector and the direction of the acceleration for a body moving in a circle at coinstant speed

Answers

Answer:

a = v²/r

Explanation:

The acceleration of a body moving in a circular path is known as the centripetal acceleration. This is the acceleration of a body that keeps the body within the circular path. It is written in terms of the linear velocity v and the radius of the circle of rotation as shown;

a = v²/r where

v is the linear velocity

r is the radius

a is the centripetal acceleration

What is the conflict in this passage?
Tony worries about how to fight Felix without hurting him.
Tony cannot figure out how to get down from the roof.
Tony no longer wants to be friends with Felix.
Tony wants to figure out a way for both of them to win.

Answers

Answer:

the conflict in this passage is

Tony worries about how to fight Felix without hurting him.

it right i just took the test

The conflict sentence in the passage is, Tony worries about how to fight Felix without hurting him.

What is meant by conflict?

    Conflict can be meant as clash happened between one another of different individuals and they used to arise out for one's own process, their way of understanding and their interests and also it depends upon everyone's perception. Also, conflicts leads to physical abuse.

In the given sentences,

A. Tony worries about how to fight Felix without hurting him.

    Here, there is a point to thinking  about no physical abuses and loss of peace and harmony.

B. Tony cannot figure out how to get down from the roof.

   In the above sentence Tony was just thinking an idea about how to come down from the roof. There will not be any clashes.

C. Tony no longer wants to be friends with Felix.

    The above sentence was only about the relationship of Tony and Felix.

D. Tony wants to figure out a way for both of them to win.

    This sentence is completely in the positive approach to attain success.

So, the correct answer is option A.

Learn more about conflicts,

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A rock is attached to the left end of a uniform meter stick that has the same mass as the rock. How far from the left end of the stick should the triangular object be placed so that the combination of meter stick and rock is in balance

Answers

Answer:

M₂ = M  then L₂ = L

M₂> M  then L₂ = \frac{M}{M_{2}} L

Explanation:

This is a static equilibrium exercise, to solve it we must fix a reference system at the turning point, generally in the center of the rod. By convention counterclockwise turns are considered positive

          ∑ τ = 0

           

The mass of the rock is M and placed at a distance, L the mass of the rod M₁, is considered to be placed in its center of mass, which by uniform e is in its geometric center (x = 0) and the triangular mass M₂, with a distance L₂

The triangular shape of the second object determines that its mass can be considered concentrated in its geometric center (median) that tapers with a vertical line if the triangle is equilateral, the most used shape in measurements.

         M L + M₁ 0 - m₂ L₂ = 0

         M L - m₂ L₂ = 0

         L₂ = [tex]\frac{M}{M_{2}}[/tex] L

From this answer we have several possibilities

* if the two masses are equal then L₂ = L

* If the masses are different, with M₂> M then L₂ = \frac{M}{M_{2}} L

The triangular object should be placed at the distance of   [tex]\dfrac{M}{M_{2}} \times L[/tex]  from the left end of the stick.

The given problem can be resolved using the concept of static equilibrium. We must consider a reference system at the turning point, generally in the center of the rod. By convention counterclockwise turns are considered positive. So, static equilibrium says,

[tex]\sum \tau = 0[/tex]

Here, [tex]\tau[/tex] is the torque.

Let the  mass of the rock is M and it is placed at a distance L. Such that the mass of the rod is [tex]M_{1}[/tex] which is considered to be placed in its center of mass.  By uniformity in its geometric center (x = 0) and the triangular mass [tex]M_{2}[/tex] lies at the distance [tex]L_{2}[/tex].

Also, triangular shape of the second object determines that its mass can be considered concentrated in its geometric center (median) that tapers with a vertical line if the triangle is equilateral, the most used shape in measurements.

Then,

[tex]ML+M_{1} \times 0 -M_{2} \times L_{2}=0\\\\ML=M_{2}L_{2}\\\\L_{2}=\dfrac{M}{M_{2}} \times L[/tex]

Thus, we can conclude that triangular object should be placed at the distance of  [tex]\dfrac{M}{M_{2}} \times L[/tex]  from the left end of the stick.

Learn more about the equilibrium of forces here:

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