A father (mass $M$ ) and his son (mass $m$ ) begin walking out toward opposite ends of a balanced see-saw. As they walk, the see-saw stays exactly horizontal. What can be said about the relationship between the father's speed $V$ and the son's speed $v$?

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?

In bowling, usually the bowling ball will initially slide down the lane without spinning. Partway down the lane, however, the ball begins to roll. What happens to the velocity of the ball when it begins to roll?

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.

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 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.

An airplane flying due north has an air speed of 500 m/h. There is a northwesterly wind of 60 km/h. Find the true speed and direction of the plane relative to the ground.

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.

Figure shows a claw hammer as it is being used to pull a nail out of a horizontal board. If a force of $150 \mathrm{~N}$ is exerted horizontally as shown, find (a) the force exerted by the hammer claws on the nail and (b) the force exerted by the surface on the point of contact with the hammer head. Assume that the force the hammer exerts on the nail is parallel to the nail.

At the end of a delivery ramp, a skid pad exerts a constant force on a package so that the package comes to rest in a distance d. When the pad is replaced by one that requires a distance of 2d to stop the same package, what happens to the length of time it takes for the package to stop?

A science-fiction author asks for your help. He wants to write about a newly discovered spherically symmetric planet that has the same average density as the earth but with a 25% larger radius. What is g on this planet?

An archer needs to hit a bull's eye on a target at eye level $60.0 \mathrm{ft}$ away. Will the arrow hit the target, If the archer fires the arrow from eye level with a speed of $47.0 \mathrm{ft} / \mathrm{s}$ at an angle of $25.0^{\circ}$ above the horizontal?