A $1250-\mathrm{~kg}$ car rounds a curve of radius $72 \mathrm{~m}$ banked at an angle of $14^{\circ}$. If the car is traveling at $85 \mathrm{~km} / \mathrm{~h}$, will a friction force be required? If so, how much and in what direction?

Around a fixed vertical axis, a sizable turntable rotates. making one revolution in $6.00 \mathrm{~s}$. The moment of inertia of the turntable about this axis is $1200 \mathrm{~kg} \cdot \mathrm{m}^2$. A child of mass $40.0 \mathrm{~kg}$, initially standing at the center of the turntable, runs out along a radius. What is the angular speed of the turntable when the child is $2.00 \mathrm{~m}$ from the center? (Assume that you can treat the child as a particle.)

A large turntable rotates about a fixed vertical axis, making one revolution in $6.00 \mathrm{~s}$. The moment of inertia of the turntable about this axis is $1200 \mathrm{~kg} \cdot \mathrm{m}^2$. A child of mass $40.0 \mathrm{~kg}$, initially standing at the center of the turntable, runs out along a radius. What is the angular speed of the turntable when the child is $2.00 \mathrm{~m}$ from the center, assuming that you can treat the child as a particle?

Suppose you are riding on a roller coaster, which moves through a vertical circular loop. Show that your apparent weight at the bottom of the loop is six times your weight when you experience weightlessness at the top, independent of the size of the loop. Assume that friction is negligible.

A roller coaster has a vertical loop with radius 29.5 m. With what minimum speed should the roller coaster car be moving at the top of the loop so that the passengers do not lose contact with the seats?

A Nordic jumper goes off a ski jump at an angle of 10.0 $^ { \circ }$ below the horizontal, traveling 108 m horizontally and 55.0 m vertically before landing. Olympic Nordic jumpers can make such jumps with a jump speed of 23.0 m/s, which is considerably less than. Explain how that is possible.

The blade of a windshield wiper moves through an angle of

$$90.0 ^ { \circ } \text { in } 0.40 \mathrm { s }$$

The tip of the blade moves on the arc of a circle that has a radius of 0.45 m. What is the magnitude of the centripetal acceleration of the tip of the blade?

A satellite has a mass of 5850 kg and is in a circular orbit

$$4.1 \times 10 ^ { 5 } \mathrm { m }$$

m above the surface of a planet. The period of the orbit is two hours. The radius of the planet is

$$4.15 \times 10 ^ { 6 } \mathrm { m }.$$

What is the true weight of the satellite when it is at rest on the planet's surface?

A disk rotates with constant angular acceleration. The initial angular speed of the disk is 2.0

$$\pi \mathrm { rad } / \mathrm { s }$$

. After the disk rotates through

$$10.0 \pi$$

radians, the angular speed is

$$7.0 \pi$$

rad/s. (a) What is the magnitude of the angular acceleration? (b) How much time did it take for the disk to rotate through

$$10.0 \pi$$

radians? (c) What is the tangential acceleration of a point located at a distance of 5.0 cm from the center of the disk?

A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N. How fast must the bucket move at the top of the circle so that the rope does not go slack?

Two forces, $\quad \overrightarrow{\mathbf{~F}}_1=(1.50 \hat{\mathbf{~i}}-0.80 \hat{\mathbf{~j}}+0.70 \hat{\mathbf{~k}}) \mathbf{~N}$ and $\overrightarrow{\mathbf{~F}}_2=$ $(-0.70 \hat{\mathbf{~i}}+1.20 \hat{\mathbf{~j}}) \mathbf{~N}$, are applied on a moving object of mass $0.20 \mathrm{~kg}$. The displacement vector produced by the two forces is $\overrightarrow{\mathbf{~d}}=(8.0 \hat{\mathbf{~i}}+6.0 \hat{\mathbf{~j}}+5.0 \hat{\mathbf{~k}}) \mathrm{m}$. What is the work done by the two forces?

A $36.0-\mathrm{kg}$ crate, starting from rest, is pulled across a floor with a constant horizontal force of $225 \mathrm{~N}$. For the first $11.0 \mathrm{~m}$ the floor is frictionless, and for the next $15.0 \mathrm{~m}$ the coefficient of friction is $0.20$. What is the final speed of the crate after being pulled these $26.0 \mathrm{~m}$?

A $36.0 \mathrm{~kg}$ crate, starting from rest, is pulled across a floor with a constant horizontal force of $225 \mathrm{~N}$. For the first $11.0 \mathrm{~m}$ the floor is frictionless, and for the next $10.0 \mathrm{~m}$ the coefficient of friction is $0.20$. What is the final speed of the crate after being pulled these $21.0 \mathrm{~m}$ ?

A $28.0\,\text{kg}$ block is connected to an empty $2.00\,\mathrm{kg}$ bucket by a cord running over a frictionless pulley (Fig. 5-56). The coefficient of static friction between the table and the block is $0.42$ and the coefficient of kinetic friction between the table and the block is $0.34$. Sand is gradually added to the bucket until the system just begins to move. Estimate the mass of sand added to the bucket.