As shown in the figure below, a 2.25 kg block is released from rest on a ramp of height h = 0.650 m.  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 μ = 0.800. Find the block’s kinetic energy after crossing the rough patch.

The Super Sled travels with an initial kinetic energy of 3369 J horizontally and to the right along a frictionless flat surface, initially at a height of zero (initial gravitational potential energy = 0). The driver briefly engages the rocket over a distance (Ax) of 2.000 m, pushing the sled with a force of 400.0 N over that distance. The rocket is then turned off. The sled then goes up an inclined surface with a rough surface. The coefficient of kinetic friction on the incline is uk. At the top of the incline, the sled reaches a height h = 1.500 m above the ground where the surface becomes flat and frictionless again. The sled (including the rocket and driver) has a total mass of 87.00 kg. (Notes: assume that g = 9.810 m/s² , and that the mass of fuel used by the rocket is negligible. Do not use scientific notation). After &, rocket rocket Before propulsion propulsion starts ends rough inclined surface rocket frictionless engaged coefficient of kinetic friction = H surface h = 1.500 m…

A 69.0-kg athlete leaps straight up into the air from a trampoline with an initial speed of 8.9 m/s. The goal of this problem is to find the maximum height she attains and her speed at half maximum height. Write the general equation for energy conservation and solve for the velocity at half the maximum height. Substitute and obtain a numerical answer.

A 5.40-kg block is set into motion up an inclined plane with an initial speed of v; = 8.20 m/s (see figure below). The block comes to rest after traveling d = 3.00 m along the plane, which is inclined at an angle of 0 = 30.0° to the horizontal. (a) For this motion, determine the change in the block's kinetic energy. J (b) For this motion, determine the change in potential energy of the block-Earth system. J (c) Determine the friction force exerted on the block (assumed to be constant). N (d) What is the coefficient of kinetic friction?

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

A child starts at rest and slides down a frictionless slide as in picture. The bottom of the track is a height h above the ground. The child then leaves the track horizontally, striking the ground at a distance d as shown. (a) Using conservation of energy, find the speed of the child at the end of the slide (b) Using your answer to part (a) and equations related to a projectile, determine the initial height H of the child above the ground in terms of h and d. Н d

A 50.6 g golf ball is driven from the tee with an initial speed of 55.4 m/s and roses to a height of 23.8 m (a) Neglect air resistance and determine the kinetic energy of the ball at its highest point. (b) what is it speed when it is 5.63 m below its highest point ?

In the figure here, a block of ice slides down a frictionless ramp at angle 0=51.0 the ramp. As the block slides down through distance d = 0.580 m along the ramp, its kinetic energy increases by 83.0 J. How much greater would its kinetic energy have been if the rope had not been attached to the block? while an ice worker pulls on the block (via a rope) with a force that has a magnitude of 51.0N and is directed up F, Number Unit