Two ice skaters are holding hands at the center of a frozen pond when an argument ensues. Skater A shoves skater $\mathrm{B}$ along a horizontal direction. Identify (b) those acting on $\mathrm{B}$.

A roller coaster car with mass $640 \mathrm{~kg}$ moves along the track shown in Figure 8. Assume all friction is negligible. (a) Is the mechanical energy of the roller coaster conserved? Explain your answer. (b) If the roller coaster starts from rest at point $\mathrm{A}$, what is its total mechanical energy at point $A$ ? (c) What is the total mechanical energy at point $\mathrm{B}$ ? (d) Calculate the speed of the roller coaster when it reaches points $\mathrm{B}$ and $\mathrm{C}$. (e) If the car starts with a speed of $12 \mathrm{~m} / \mathrm{s}$ at point $\mathrm{A}$, calculate the speed of the roller coaster when it reaches points $\mathrm{B}$ and $\mathrm{C}$.

In Section 6.2, we implied that the kinetic energy of the Earth can be ignored when considering the energy of a system consisting of the Earth and a dropped ball of mass $m_b$. Verify this statement by first setting up a ratio of the kinetic energy of the Earth to that of the ball as they collide. Then use conservation of momentum to show that

$$\frac{v_E}{v_b}=-\frac{m_b}{m_E} \quad \text { and } \quad \frac{K E_E}{K E_b}=\frac{m_b}{m_E}$$

Find the order of magnitude of the ratio of the kinetic energies, based on data that you specify.

A 4.60-kg sled is pulled across a smooth ice surface. The force acting on the sled has a magnitude of 6.20 N and points in a direction $35.0^{\circ}$ above the horizontal. If the sled starts from rest, how fast is it going after being pulled for 1.15 s?

A 5.0-kg box has an acceleration of 2.0 m/s² when it is pulled by a horizontal force across a surface with

$$μ_K = 0.50.$$

Find the work done over a distance of 10 cm by (a) the horizontal force, (b) the frictional force, and (c) the net force. (d) What is the change in kinetic energy of the box?

A box has a weight of 150 N and is being pulled across a horizontal floor by a force that has a magnitude of 110 N. The pulling force can point horizontally, or it can point above the horizontal at an angle $\theta$. When the pulling force points horizontally, the kinetic frictional force acting on the box is twice as large as when the pulling force points at the angle $\theta$. Find $\theta$.

A 20.0-kg sled is being pulled across a horizontal surface at a constant velocity. The pulling force has a magnitude of $80.0 \mathrm{~N}$ and is directed at an angle of $30.0^{\circ}$ above the horizontal. Determine the coefficient of kinetic friction.

A box with a mass of 5.24 kg is sliding along a horizontal surface at constant velocity. It is pulled by a horizontal force and the coefficient of kinetic friction between the box and the surface is 0.225.

a) What is the work done, in joules, by the pulling force as the box moves a distance of 0.29 m?

b) What is the work done, in joules, by the force of friction on the box as the box moves a distance of 0.29 m?

c) What is the work done, in joules, by the net force on the box?

A $25 \mathrm{~kg}$ box sliding to the left across a horizontal surface is brought to a halt in a distance of $35 \mathrm{~cm}$ by a horizontal rope pulling to the right with $15 \mathrm{~N}$ tension. How much work is done by (a) tension and (b) gravity?

A 20.0-kg sled is being pulled across a horizontal surface at a constant velocity. The pulling force has a magnitude of 80.0 N and is directed at an angle of

$$30.0^\circ$$

above the horizontal. Determine the coefficient of kinetic friction.

An object has a speed of 3.5 m/s and a kinetic energy of 14 J at t = 0. At t = 5.0 s the object has a speed of 4.7 m/s. (a) What is the mass of the object? (b) What is the kinetic energy of the object at t = 5.0 s? (c) How much work was done on the object between t = 0 and t = 5.0 s?

An object has a kinetic energy of 275 J and a momentum of magnitude 25.0 $\mathrm { kg } \cdot \mathrm { m } / \mathrm { s }$. Find the (a) speed and (b) mass of the object.

If the object starts at the origin moving to the right with a kinetic energy of $25.0 \mathrm{~J}$, how much kinetic energy does it have at $x=4.00 \mathrm{~m}$.

How much work does gravity do on a 0.150-kg ball falling from a height of 10.0 m? (Forget about air resistance.)