Question

a 2-kg bowling ball is 2.5 meters off the ground on a post when it falls. Just before it reaches the ground, it is traveling 7 m/s. Assuming tht there is no air resistance, which statement is true? 1. the initial potential energy is greater than the final kinetic energy 2. the mechanical energy is conserved 3. the mechanical energy is not conserved 4. the initial potential energy is less than the final kinetic energy

Answer 1

“The mechanical energy is conserved" in the given system is true out of all given options.

Answer: Option 2

Explanation:

According to law of conservation of energy, the energy will neither be created nor be destroyed, irrespective of the type of energy. As in the present case, the ball is bowled and it is travelling to ground, so the mechanical energy is working in this case. Thus the mechanical energy will be conserved. Even it can be shown as follows.

As the 2 kg ball is travelling with a speed of 7 m/s, the kinetic energy exhibited by the ball while falling to ground will be

`\text {Kinetic energy}=(1)/(2) * \text { mass of the ball } *\left(\text { speed of the ball) }^(2)\right.`

Thus, applying given values, we get,

`\text {Kinetic energy exhibited by the ball}=(1)/(2) * 2 * 7 * 7=49 \mathrm{J}`

Similarly, as the ball is 2.5 m above ground, the potential energy will also be exhibited by the ball at that position. So the potential energy will be

`\text {Potential energy}=\text {Mass} * \text {acceleration} * \text {height}`

Thus,

`\text { Potential energy exhibited by the ball }=2 * 9.8 * 2.5=49 \mathrm{J}`

Thus as the magnitude of kinetic energy is equal to the magnitude of potential energy exhibited by the ball with varying direction, the net energy will be zero. This is because the kinetic energy will be acting in opposite direction to the potential energy exhibited by the ball. Hence as the net energy is zero, the mechanical energy is conserved.