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?

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.

A typical running track is an oval with 74-m-diameter half circles at each end. A runner going once around the track covers a distance of 400 m. Suppose a runner, moving at a constant speed, goes once around the track in 1 min 40 s. What is her centripetal acceleration during the turn at each end of the track?

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.

The equation for a demand curve is P = 48 – 3Q. What is the elasticity in moving from a quantity of 5 to a quantity of 6?

Suppose that only the rear wheels of an automobile can accel- erate it, and that half the total weight of the automobile is supported by those wheels. $(a)$ What is the maximum acceler- ation attainable if the coefficient of static friction between tires and road is $\mu_s?$ $(b)$ Take $\mu_s=0.56$ and get a numerical value for this acceleration.

A machine can operate for an average of 10 weeks before it needs to be overhauled, a process which takes two days. The machine is operated five days a week. Compute the availability of this machine. ( Hint: All times must be in the same units.)

Suppose that you need to measure whether a tabletop in a train is truly horizontal. If you use a spirit level, can you de- termine this when the train is moving down or up a grade? When the train is moving along a curve? (Hint: There are two horizontal components.)

As a roller coaster car crosses the top of a 40-m-diameter loop-the-loop, its apparent weight is the same as its true weight. What is the car's speed at the top?

A car of weight $w$ travels on a curve of radius 200 m banked at $10^{\circ}$. At what speed is no friction required?

A 0.30-kg puck, initially at rest on a frictionless horizontal surface, is struck by a 0.20-kg puck that is initially moving along the x-axis with a velocity of 2.0 m/s. After the collision, the 0.20-kg puck has a speed of 1.0 m/s at an angle of $\theta = 53 ^ { \circ }$ to the positive x-axis. Determine the velocity of the 0.30-kg puck after the collision.

The $0.20 \mathrm{~kg}$ puck on the NT frictionless, the horizontal table in as we discussed earlier is connected by a string through a hole in the table to a hanging $1.20 \mathrm{~kg}$ block. With what speed must the puck rotate in a circle of radius $0.50$ $\mathrm{m}$ if the block is to remain hanging at rest?

In the Wall of Death carnival attraction, stunt motorcyclists ride around the inside of a large, $10$-m-diameter wooden cylinder that has vertical walls. The coefficient of static friction between the riders' tires and the wall is $0.90$. What is the minimum speed at which the motorcyclists can ride without slipping down the wall?

A fast-pitch softball player does a "windmill" pitch, illustrated BD in as we discussed earlier, moving her hand through a circular arc to pitch a ball at $70 \mathrm{mph}$. The $0.19 \mathrm{~kg}$ ball is $50 \mathrm{~cm}$ from the pivot point at her shoulder. At the lowest point of the circle, the ball has reached its maximum speed.
a. At the bottom of the circle, just before the ball leaves her hand, what is its centripetal acceleration?
b. What are the magnitude and direction of the force her hand exerts on the ball at this point?