A 1000 kg block is resting on a plane inclined at 20°. Calculate the force of friction experienced by the block if μ_s between the block and the surface of the slope is 0.87.

Organizers of a bicycle race want to include a challenging hill climb in the course. They need to determine the steepness of the hill to ensure that it is challenging yet achievable for most cyclists. A test with a cyclist on a bicycle with a total mass of 90 kg shows that the cyclist can accelerate from rest to 11.0 m/s in 12.6 s on a flat surface. Using this data, calculate the maximum incline angle of the hill that the cyclist should be able to ascend without deceleration.

A guardian drags a 36 kg cart containing their baby, with the handle inclined horizontally at 56°. Given the cart accelerates at 0.44 m/s² on smooth wheels, what force does the guardian exert on the handle?

An interior decorator is rearranging furniture and needs to move a 75-kg bookcase across a hardwood floor. The coefficient of kinetic friction between the bookcase and the hardwood floor is μₖ = 0.3. The decorator applies a force of 250N by dragging to slide the bookcase. Calculate the bookcase's acceleration given that the force is applied at an angle θ = 5° to the horizontal.

A box with mass m falls vertically onto a moving belt feeder with a velocity of v=4.0 m/s, and the kinetic friction coefficient between the box and the belt is μ_k=0.90. The box slides for some time before coming to a complete stop. Calculate the distance the box travels on the belt feeder.

A 50.0 N animal salt block is at rest on a horizontal floor. The coefficients of static and kinetic friction between the block and the floor are 0.54 and 0.36 respectively. A goat pushes on the block applying a horizontal force of magnitude 12.0 N. Determine the magnitude of the friction force if the block is at rest when the push is applied.

A block is on the floor of a bus moving at an acceleration of 0.50 g. Calculate the required minimum value of the coefficient of static friction between the block and the bus floor to keep it from sliding. 

A robot weighing 50 kg is deployed inside a vertical shaft as shown in the figure below. As it descends, it eventually comes to a halt due to friction forces exerted by the walls of the shaft. The coefficient of static friction between the robot and the shaft's left wall is 0.70, and it's 0.50 for the right wall. Assuming the friction forces are at their maximum, what is the minimum normal force exerted by the walls to prevent further descent of the robot?

During a film shoot, there is a stunt scene where the hero drives his car up a 25° inclined slope leading to a 4.0 m high cliff. The car then jumps off the cliff and has to cross the fire area of 9.0 m on the ground below and safely reach the ground part without fire. As soon as the hero starts up the slope at a speed of 12 m/s, his car's engine gets locked. The coefficient of rolling friction for tires is 0.025. Determine whether he lands safely on the ground or falls in the fire given its flight time is 1.3 s.

As shown in the figure, a bar is welded to a vertical hoop of diameter 0.50 m between points A and B located on the rim. B is the lowest point of the rim. The bar makes an angle θ with the line joining the center of the hoop O and B. A small box placed on A can slide from rest on this frictionless bar. Determine the time required for the box to slide from point A to point B.

If a skateboarder can decelerate at a_x=3.90 m/s² on flat ground without sliding to a halt, what is its deceleration when moving uphill on a 9.5° incline? Assuming the same coefficient of static friction.