Find an expression for the acceleration a of the red block after it is released. Use mr for the mass of the red block, mg for the mass of the gray block, and μk for the coefficient of kinetic friction between the table and the red block. Express your answer in terms of mr, mg, μk, and g.

An 1150-kg car pulls a 450-kg trailer. The car exerts a horizontal force of $3.8 \times 10^{3} \mathrm{N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.

The rope and pulley have negligible mass, and the pulley is frictionless. Initially the 6.00-kg block is moving downward and the 8.00-kg block is moving to the right, both with a speed of 0.900 m/s. The blocks come to rest after moving 2.00 m. Use the work–energy theorem to calculate the coefficient of kinetic friction between the 8.00-kg block and the tabletop.

The upward normal force exerted by the floor is 620 N on an elevator passenger who weighs 650 N. What are the reaction forces to these two forces? Is the passenger accelerating? If so, what are the magnitude and direction of the acceleration?

A coffee mug slides down an incline starting from rest.

The incline makes an angle θ with respect to the horizontal. The mass of the mug is m and the acceleration due to gravity is g. Assume that the friction force is well modeled by a coefficient of kinetic friction μk.

Determine:

a. The magnitude of the normal force on the cart
b. The magnitude of the frictional force on the cart
c. The magnitude of the component of the weight parallel to the incline
d. The magnitude of the acceleration of the mug

A box with mass $m$ is dragged across a level floor with coefficient of kinetic friction $\mu_{\mathrm{k}}$ by a rope that is pulled upward at an angle $\theta$ above the horizontal with a force of magnitude $F$.
(b) Knowing that you are studying physics, a CPR instructor asks you how much force it would take to slide a $90$-$\mathrm{kg}$ patient across a floor at constant speed by pulling on him at an angle of $25\degree$ above the horizontal. By dragging weights wrapped in an old pair of pants down the hall with a spring balance, you find that $\mu_{\mathrm{k}}=0.35$. Use the result of part (a) to answer the instructor's question.

A dockworker applies a constant horizontal force of 80.0 N to a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves 11.0 m in 5.00 s. (a) What is the mass of the block of ice? (b) If the worker stops pushing at the end of 5.00 s, how far does the block move in the next 5.00 s?

A woman rides on a Ferris wheel of radius 16 m that maintains the same speed throughout its motion. She sits on a bathroom scale (with memory) and sits on it. When she gets off the ride, she uploads the scale readings to a computer. It showed that the minimum value that the scale read was 510 N and the maximum was 666 N. What is the woman's mass?

A flat (unbanked) curve on a highway has a radius of 170.0 m. A car rounds the curve at a speed of 25.0 m/s. (a) What is the minimum coefficient of static friction that will prevent sliding? (b) Suppose that the highway is icy and the coefficient of static friction between the tires and pavement is only one-third of what you found in part (a). What should be the maximum speed of the car so that it can round the curve safely?

A flat (unbanked) curve on a highway has a radius of $220.0 \mathrm{~m}$. A car rounds the curve at a speed of $25.0 \mathrm{~m} / \mathrm{s}$. $(a)$ What is the minimum coefficient of friction that will prevent sliding? $(b)$ Suppose the highway is icy and the coefficient of friction between the tires and pavement is only one-third what you found in part $(a)$. What should be the maximum speed of the car so it can round the curve safely?

Listed below are six crates at rest on level surfaces. The crates have different masses and the frictional coefficients (given as $\mu_s$, $\mu_k$) between the crates and the surfaces differ. The same external force is applied to each crate, but none of the crates move.

Rank the crates on the basis of the frictional force acting on them.

Rank from largest to smallest.

Items: (mass in kg, $\mu_s$, $\mu_k$)

A. 250, 0.2, 0.1

B. 1500, 0.3, 0.1

C. 500, 0.6, 0.3

D. 750, 0.6, 0.5

E. 600, 0.8, 0.5

F. 750, 0.4, 0.3

In the situation shown in the given figure, let $\theta$ be the angle of the slope and suppose there is friction between the cart and the track. You find that if the cart and bucket each have the same weight $w$, they remain at rest when released. In this case, what is the magnitude of the friction force on the cart? Is it less than, greater than, or equal to $w$?

A system is shown in the figure.

Determine G(s) and H(s) of the block diagram shown in the figure that are equivalent to those of the block diagram of the figure.

A flat (unbanked) curve on a highway has a radius of $220 \mathrm{~m}$. A car rounds the curve at a speed of $25.0 \mathrm{~m} / \mathrm{s}$.
(a) Make a free-body diagram of the car as it rounds this curve.
(b) What is the minimum coefficient of friction that will prevent sliding?