The kinetic energy of a rolling billiard ball is given by KE=1/2mv2. Suppose a 0.17-kg billiard ball is rolling down a pool table with an initial speed of 4.7m/s . As it travels, it loses some of its energy as heat. The ball slows down to 3.8m/s and then collides straight-on with a second billiard ball of equal mass. The first billiard ball completely stops and the second one rolls away with a velocity of 3.8m/s . Assume the first billiard ball is the system

Calculate w Q and change in energy in j?

To calculate the work done (Q) and the change in energy in joules, we need to consider the principles of conservation of energy and the work-energy theorem.

The initial kinetic energy (KE) of the first billiard ball can be calculated using the formula KE = (1/2)mv^2, where m is the mass of the ball and v is its initial velocity. Therefore, the initial kinetic energy is KE = (1/2)(0.17 kg)(4.7 m/s)^2.

Next, we need to calculate the final kinetic energy of the first ball. Since the ball completely stops, its final velocity is 0 m/s. Therefore, the final kinetic energy is KE = (1/2)(0.17 kg)(0 m/s)^2 = 0 joules.

The work done on the first ball can be determined using the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. Therefore, Q (work done) is given by Q = KE(final) - KE(initial).

Substituting the values into the equation, we get Q = (0 joules) - [(1/2)(0.17 kg)(4.7 m/s)^2].

Calculating Q, we have Q = 0 - [(1/2)(0.17 kg)(4.7 m/s)^2].

Finally, to find the change in energy (ΔE) in joules, we use the formula ΔE = -Q (since the first ball lost energy). Thus, ΔE = -[0 - (1/2)(0.17 kg)(4.7 m/s)^2].

Evaluating this expression, we find ΔE = -[0 - (1/2)(0.17 kg)(4.7 m/s)^2].