A bowling ball that originally is not spinning is thrown down a bowling lane; by the time the ball strikes the pins it is rolling without slipping. Is the total mechanical energy cons- erved?

Can the translational kinetic energy of a system change into rotational kinetic energy of the system in the absence of ex- ternal forces? If so, give an example; if not, explain why not.

A uniform, hollow, cylindrical spool has inside radius R/2, outside radius R, and mass M. It is mounted so that it rotates on a fixed, horizontal axle. A counterweight of mass m is connected to the end of a string wound around the spool. The counterweight falls from rest at t = 0 to a position y at time. Show that the torque due to the friction forces between spool and axle is

$$\tau_{f}=R\left[m\left(g-\frac{2 y}{t^{2}}\right)-M \frac{5 y}{4 t^{2}}\right]$$

The central radius of gyration of the spool is k, and its inner radius is R. If the spool is released from rest, determine the velocity of the spool as a function of its displacement x. Neglect the friction between the spool and the vertical wall.

_ states that every action force creates a reaction force that is equal in strength and opposite in direction.

To every action there is always an equal and opposite reaction" is a statement of

According to _ , for every action force, there is a reaction force equal in strength and opposite in direction.

Discuss the words “energy conservation” as used $(a)$ in this chapter and $(b)$ in connection with an “energy crisis” (for ex- ample, turning off lights). How do these two usages differ?

The coefficient of static friction between the tires of a car and a dry road is $0.62$. The mass of the car is $1500$ kg. What max- imum braking force is obtainable $(a)$ on a level road and $(b)$ on an $8.6\degree$ downgrade?

A person bending forward to lift a load "with his back" rather than "with his knees" can be injured by large forces exerted on the muscles and vertebrae. The spine pivots mainly at the fifth lumbar vertebra, with the principal supporting force provided by the erector spinalis muscle in the back. To see the magnitude of the forces involved, and to understand why back problems are common among humans, consider the model shown in the figure for a person bending forward to lift a 200-N object. The spine and upper body are represented as a uniform horizontal rod of weight $350 \mathrm{~N}$, pivoted at the base of the spine. The erector spinalis muscle, attached at a point two thirds of the way up the spine, maintains the position of the back. The angle between the spine and this muscle is $12.0^{\circ}$. Find the tension in the back muscle and the compressional force in the spine.

Explain, using work and energy ideas, how a child pumps a swing up to large amplitudes from a rest position. (See “How to Make a Swing Go,” by R. V. Hesheth, $\it{Physics~ Education,}$ July $1975$, p. $367$.)

When a person stands on tiptoe (a strenuous position), The total gravitational force on the body $\overrightarrow{\mathbf{F}}_g$ is supported by the force $\overrightarrow{\mathbf{n}}$ exerted by the floor on the toes of one foot, where $\overrightarrow{\mathbf{T}}$ is the force exerted by the Achilles tendon on the foot and $\overrightarrow{\mathbf{R}}$ is the force exerted by the tibia on the foot. Find the values of $T, R$, and $\theta$ when $F_g=700 \mathrm{~N}$.

The arm weighs $41.5 \mathrm{~N}$. The gravitational force on the arm acts through point $A$. Determine the magnitudes of the tension force $\overrightarrow{\mathbf{F}}_t$ in the deltoid muscle and the force $\overrightarrow{\mathbf{F}}_s$ exerted by the shoulder on the humerus (upper-arm bone) to hold the arm in the position shown.

In earlier Sample Problem (see earlier Fig.) we concluded that the speed of the roller coaster at the bottom does not depend at all on the shape of the track. Would this still be true if fric- tion were present?