A small sphere of mass m is launched horizontally over a body of water from a he

Question

A small sphere of mass m is launched horizontally over a body of water from a height h above the water and with a launch speed Vo- Determine expressions for the following in terms of m, v_0. h, and g. Air resistance is negligibly small. W is the amount work done by the force of gravity on the projectile during its flight. W =___. Delta KE is the change in kinetic energy AKE of the projectile from the time it was fired until it hits the water. AKE =___. KE_f is the final kinetic energy delta KE of the projectile as it hits the water. KE_f =__. Are any of the answers changed if the initial angle is changed? Yes No

Explanation / Answer

(a) For a conservative force, the work done by the force acting over a distance is the negative of the change in potential energy associated with that force. This allows us to write

Wg = PEg = (mgy) = mg(h) = mgh.

(b) According to the workenergy theorem, the net work done on an object is equal to the change in its kinetic energy. This allows us to write

K = Wnet = Wg = mgh.

(c) Since energy is conserved,

K = PE,

or

Kf Ki = (mgh)

or

Kf = Ki + mgh = 1/2mv0^2 + mgh

(d) Notice that the answer to parts (a) and (b) depend on the change in gravitational potential energy. The answer to part (c) depends on the initial kinetic energy and also the change in gravitational potential energy. Since neither the launch speed or the change in potential energy depend on the launch angle, none of the answers are changed if the initial angle is changed.

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