A flatbed truck is carrying a crate up a 10.0° hill, as the figure illustrates. The coefficient of static friction between the truck bed and the crate is 0.350. Find the maximum acceleration that the truck can attain before the crate begins to slip backward relative to the truck.

A box is sliding up an incline that makes an angle of

$$15.0^\circ$$

with respect to the horizontal. The coefficient of kinetic friction between the box and the surface of the incline is 0.180. The initial speed of the box at the bottom of the incline is 1.50 m/s. How far does the box travel along the incline before coming to rest?

A cup of coffee is on a table in an airplane flying at a constant altitude and a constant velocity . The coefficient of static friction between the cup and the table is 0.30. Suddenly, the plane accelerates forward, its altitude remaining constant. What is the maximum acceleration that the plane can have without the cup sliding backward on the table?

Three objects have mass $80.0 \mathrm{~kg}$ , $10.0 \mathrm{~kg}$ and $25.0 \mathrm{~kg}$. They are connected by strings that pass over massless and friction free pulleys. Masses $10.0 \mathrm{~kg}$ and $25.0 \mathrm{~kg}$ connected by string besides the mass $80.0 \mathrm{~kg}$ .The objects move, and the coefficient of kinetic friction between the middle object and the surface of the table is 0.100. (a) What is the acceleration of the three objects? (b) Find the tension in each of the two strings.

A car is towing a boat on a trailer. The driver starts from rest and accelerates to a velocity of + 11 m/s in a time of 28 s. The combined mass of the boat and trailer is 410 kg. The frictional force acting on the trailer can be ignored. What is the tension in the hitch that connects the trailer to the car?

Three objects are connected on a table. The coefficient of kinetic friction between the block of mass $m_{2}$ and the table is 0.350. The objects have masses of $m_{1}=4.00 \mathrm{kg},$ $m_{2}=1.00 \mathrm{kg},$ and $m_{3}=2.00 \mathrm{kg},$ and the pulleys are frictionless. (a) Draw a free-body diagram of each object. (b) Determine the acceleration of each object, including its direction. (c) Determine the tensions in the two cords. (d) If the tabletop were smooth, would the tensions increase, decrease, or remain the same? Explain.

A person with a black belt in karate has a fist that has a mass of 0.70 kg. Starting from rest, this fist attains a velocity of 8.0 m/s in 0.15 s. What is the magnitude of the average net force applied to the fist to achieve this level of performance?

A toboggan slides down a hill and has a constant velocity. The angle of the hill is

$$8.00 ^ { \circ }$$

with respect to the horizontal. What is the coefficient of kinetic friction between the surface of the hill and the toboggan?

Newton’s law of gravity and Coulomb’s law are both inverse-square laws. Consequently, there should be a “Gauss’s law for gravity.” a. The electric field was defined as $\vec{E}=\vec{F}_{\mathrm{on} q} / q$, and we used this to find the electric field of a point charge. Using analogous reasoning, what is the gravitational field $\vec{g}$ of a point mass?

A train consists of 50 cars, each of which has a mass of $6.8 \times 10 ^ { 3 } \mathrm { kg }$ The train has an acceleration of $+ 8.0 \times 10 ^ { - 2 } \mathrm { m } / \mathrm { s } ^ { 2 }$ Ignore friction and determine the tension in the coup ling

between the 30th and 31st cars

To hoist himself into a tree, a 72.0-kg man ties one end of a nylon rope around his waist and throws the other end over a branch of the tree. He then pulls downward on the free end of the rope with a force of 358 N. Neglect any friction between the rope and the branch, and determine the man's upward acceleration.

A man seeking to set a world record wants to tow a 109 000-kg airplane along a runway by pulling horizontally on a cable attached to the airplane. The mass of the man is 85 kg, and the coefficient of static friction between his shoes and the runway is 0.77. What is the greatest acceleration the man can give the airplane? Assume that the airplane is on wheels that turn without any frictional resistance.

A 95.0-kg person stands on a scale in an elevator. What is the apparent weight when the elevator is (a) accelerating upward with an acceleration of

$$1.80 m/s^2,$$

(b) moving upward at a constant speed, and (c) accelerating downward with an acceleration of

$$1.30 m/s^2?$$

A 205-kg log is pulled up a ramp by means of a rope that is parallel to the surface of the ramp. The ramp is inclined at

$$30.0^\circ$$

with respect to the horizontal. The coefficient of kinetic friction between the log and the ramp is 0.900, and the log has an acceleration of

$$0.800 m/s^2.$$

Find the tension in the rope.