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Chapter 4: Problem 125

Two blocks lie side by side on a frictionless table. The block on the left is of mass \(m\); the one on the right is of mass \(2 m .\) The block on the right is pushed to the left with a force of magnitude \(F,\) pushing the other block in turn. What force does the block on the left exert on the block to its right?

Short Answer

Expert verified
Answer: The force exerted by the left block on the block to its right is \(\dfrac{F}{3}\).

Step by step solution

01

Define the System

Let's consider the whole system of the two blocks together.
02

Apply Newton's Second Law to the System

According to Newton's Second Law, the net force acting on the system is equal to the total mass of the system multiplied by its acceleration. The net force acting on the system is F and the total mass of the system is m + 2m = 3m. So, we can write: \(F = (3m)a\) Where F is the force exerted on the right block and a is the acceleration of the system.
03

Calculate the Acceleration of the System

We can calculate the acceleration a of the system by solving the equation from Step 2: \(a = \frac{F}{3m}\)
04

Apply Newton's Second Law to the Left Block

Now we will consider the left block separately. Let's denote the force exerted by the left block on the right block as \(F_1\). According to Newton's Second Law, \(F_1\) must be equal to the left block's mass multiplied by its acceleration: \(F_1 = m \cdot a\)
05

Calculate the Force Exerted by the Left Block

We can calculate the force exerted by the left block on the right block by substituting the acceleration of the system that we found in Step 3: \(F_1 = m \cdot \frac{F}{3m}\) Simplifying the equation and canceling the mass m: \(F_1 = \frac{F}{3}\) So the force exerted by the left block on the block to its right is \(\dfrac{F}{3}\).

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Most popular questions from this chapter

A crate of oranges weighing \(180 \mathrm{N}\) rests on a flatbed truck $2.0 \mathrm{m}$ from the back of the truck. The coefficients of friction between the crate and the bed are \(\mu_{\mathrm{s}}=0.30\) and $\mu_{\mathrm{k}}=0.20 .\( The truck drives on a straight, level highway at a constant \)8.0 \mathrm{m} / \mathrm{s} .$ (a) What is the force of friction acting on the crate? (b) If the truck speeds up with an acceleration of \(1.0 \mathrm{m} / \mathrm{s}^{2},\) what is the force of the friction on the crate? (c) What is the maximum acceleration the truck can have without the crate starting to slide?
In the physics laboratory, a glider is released from rest on a frictionless air track inclined at an angle. If the glider has gained a speed of $25.0 \mathrm{cm} / \mathrm{s}\( in traveling \)50.0 \mathrm{cm}$ from the starting point, what was the angle of inclination of the track? Draw a graph of \(v_{x}(t)\) when the positive \(x\) -axis points down the track.
Before hanging new William Morris wallpaper in her bedroom, Brenda sanded the walls lightly to smooth out some irregularities on the surface. The sanding block weighs \(2.0 \mathrm{N}\) and Brenda pushes on it with a force of $3.0 \mathrm{N}\( at an angle of \)30.0^{\circ}$ with respect to the vertical, and angled toward the wall. Draw an FBD for the sanding block as it moves straight up the wall at a constant speed. What is the coefficient of kinetic friction between the wall and the block?
An \(80.0-\mathrm{N}\) crate of apples sits at rest on a ramp that runs from the ground to the bed of a truck. The ramp is inclined at \(20.0^{\circ}\) to the ground. (a) What is the normal force exerted on the crate by the ramp? (b) The interaction partner of this normal force has what magnitude and direction? It is exerted by what object on what object? Is it a contact or a long-range force? (c) What is the static frictional force exerted on the crate by the ramp? (d) What is the minimum possible value of the coefficient of static friction? (e) The normal and frictional forces are perpendicular components of the contact force exerted on the crate by the ramp. Find the magnitude and direction of the contact force.
In a movie, a stuntman places himself on the front of a truck as the truck accelerates. The coefficient of friction between the stuntman and the truck is \(0.65 .\) The stuntman is not standing on anything but can "stick" to the front of the truck as long as the truck continues to accelerate. What minimum forward acceleration will keep the stuntman on the front of the truck?
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