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.

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.

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?

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 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.