Inclined Planes with Friction Practice Problems

A small metallic box is projected up along a smooth inclined plane with a speed of 2.0 m/s. The length of the incline is 20 cm, and its height is 5.0 cm. Calculate the box's speed at the summit of the incline.

A 13.0 kg wooden block rests on a ramp. The block slides down the incline when the minimum incline plane angle is θ. The friction coefficients are static friction coefficient = 0.41 and kinetic friction coefficient = 0.29. Determine the value of θ, then compute the acceleration at this angle once the block begins moving.

The students in a physics laboratory class have an experiment on the motion of objects on inclined planes. They considered a crate as their object. It was released from rest at the top of a smooth ramp. The crate is subject to constant acceleration as it moves down, and the speed after it has traveled 3.40 m to the bottom of the ramp is 2.25 m/s. Calculate the speed of the crate when it has reached 1.70 m from the top of the ramp.

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.

In an experiment, a student holds a stationary wooden block of mass 5.80 kg at the top of a 1.80 m long frictionless incline. The student releases the block and measures its speed at the bottom of the ramp to be 3.30 m/s. In a repeat experiment, determine the speed of the block at the bottom of the incline if a constant 4.60 N friction force parallel to the incline's surface opposes the motion.

A skateboard released with an initial speed of 10.0 m/s moves up an inclined plane. The inclined plane makes an angle of 15.0° with the horizontal. Determine the distance traveled before the skateboard changes its direction of motion.

A 30 kg ice slab slides on a snowy plane inclined at 18° with the horizontal. Determine the acceleration of the ice slab if there is friction on the snowy plane. Consider μ_k = 0.03 (for ice on ice).

A box initially moving on a flat and smooth surface with a speed of 1.00 m/s is projected downward along a frictionless inclined plane. The incline makes an angle of 5.00° with the horizontal. At the end of the incline, the box's speed is increased to 5.00 m/s. Calculate the distance traveled by the box along the incline.

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.

A toy car track consists successively of a 30 cm straight inclined downhill section making an angle of 10° with the horizontal, a 70 cm horizontal section, and a 50 cm uphill section making an angle of 20° with the horizontal. All the sections are frictionless. A car is released from rest at the top of the 30 cm downhill. What is the distance traveled by the car along the 20° uphill?

One end of a frictionless board of length L is raised to an elevation of E above the ground. The other end is in contact with the ground. The setup forms a ramp. The ramp makes an angle of α with the horizontal. An object at the top of the ramp is released from rest. Write the formula that describes the speed of the object when it touches the ground.

A steel cart weighing 25.0 kg is pushed upwards on a 20° inclined steel slope at a speed of 12 m/s. Calculate the vertical height reached by the cart with respect to its starting point.

A block of ice slides down an inclined plane at a constant speed. The plane is inclined at an angle θ to the horizontal. Given that the ice experiences a kinetic friction due to the roughness of the surface, determine the coefficient of kinetic friction between the ice and the plane. 

A bicycle starts rolling down an inclined plane. The incline of the plane can be called a 2-in-5 incline. '2-in-5' refers to the fact that for every 5.0 m traveled along the incline, the height changes by 2.0 m. Given the effective coefficient of rolling friction to be 0.0080, calculate the speed of the bicycle after it travels a distance of 15 m along the incline.

A sled is resting at the top of a snowy slope that descends at an angle of 30°. As the sun rises and slightly melts the snow, the coefficient of static friction decreases, causing the sled to begin sliding. Assuming the distance from the sled to the bottom of the slope is 8.0 m and the coefficient of kinetic friction between the sled and the snow is 0.15, calculate the speed of the sled when it reaches the bottom of the slope.

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.

A 1370-kg coupe towing a 355-kg trolley accelerates horizontally with a 3.80 x 10³ N force against the ground. If the trolley's friction coefficient is 0.17, determine the force the coupe applies to the trolley.

Calculate the coefficient of kinetic friction for a skier descending a slope inclined at 29°. The skier’s final speed at the slope’s base is half of the expected speed if friction is ignored.