The package of mass M = 5 kg is released from rest at A which is h = 3 m above B.  It slides down the frictionless plane which is inclined at an angle θ = 30o onto the rough surface having a coefficient of kinetic friction μK = 0.2.  Neglect the size of the package. Considering only the motion along the incline, what will happen to the change in kinetic energy of the block if friction is present?

As shown in the figure below, a 2.25-kg block is released from rest on a ramp of height h. When the block is released, it slides without friction to the bottom of the ramp, and then continues across a surface that is frictionless except for a rough patch of width 15.0 cm that has a coefficient of kinetic friction u, = 0.730. Find h such that the block's speed after crossing the rough patch is 3.70 m/s. rough patch 15.0 cm

A 1.50-kg block at rest on a ramp of height h. When the block is released, it slides without friction to the bottom of the ramp, and then continues across a surface that is frictionless except for a rough patch of width 10.0 cm that has a coefficient of kinetic friction µk = 0.60. Using conservation of energy, find h such that the block’s speed after crossing the rough patch is 3.50 m/s.

A 42.0-kg projectile is fired at an angle of 30.0° above the horizontal with an initial speed of 136 m/s from the top of a cliff 154 m above level ground, where the ground is taken to be y = 0. (a) What is the initial total mechanical energy of the projectile? (Give your answer to at least three significant figures.) (b) Suppose the projectile is traveling 96.4 m/s at its maximum height of y = 347 m. How much work has been done on the projectile by air friction? (c) What is the speed of the projectile immediately before it hits the ground if air friction does one and a half times as much work on the projectile when it is going down as it did when it was going up? TA m/s