A 1.4 kilogram sphere ball hangs at the end of a rope. A person kicks the ball, and it rises 3 meters above the ground.
1. What's the ball's maximum GPE?
41.16 J
2. What would be the velocity of the ball at the lowest point of the swing?
7.67 m/s
3. What would be the KE of the ball at the lowest point of the swing?
41.16 J, because all the GPE is converted into KE.
To answer these questions, we need to understand the concepts of gravitational potential energy (GPE), kinetic energy (KE), and conservation of energy.
1. The ball's maximum GPE can be calculated using the formula:
GPE = mass * gravity * height
In this case, the mass is 1.4 kg, gravity is approximately 9.8 m/s^2, and the height is 3 meters.
GPE = 1.4 kg * 9.8 m/s^2 * 3 m = 41.16 J
So, the ball's maximum GPE is 41.16 J.
2. To find the velocity of the ball at the lowest point of the swing, we can use the law of conservation of energy. According to this law, the total mechanical energy (which includes GPE and KE) remains constant throughout the motion.
At the highest point, when the ball is momentarily at rest, all of the GPE is converted into KE. So, the total mechanical energy (GPE + KE) is equal to the ball's maximum GPE.
GPE + KE = 41.16 J
At the lowest point of the swing, the ball's GPE is zero, as it is at its minimum height. Therefore, all of the mechanical energy is converted into KE.
KE = 41.16 J
To find the velocity at the lowest point, we can use the formula:
KE = 0.5 * mass * velocity^2
Since we know the KE and the mass (1.4 kg), we can solve for the velocity.
41.16 J = 0.5 * 1.4 kg * velocity^2
Simplifying the equation, we get:
velocity^2 = (41.16 J * 2) / 1.4 kg
velocity^2 = 58.8 m^2/s^2
velocity = √(58.8 m^2/s^2) ≈ 7.67 m/s
Therefore, the velocity of the ball at the lowest point of the swing is approximately 7.67 m/s.
3. As mentioned earlier, at the lowest point of the swing, all of the GPE is converted into KE.
KE = 41.16 J
Therefore, at the lowest point of the swing, the KE of the ball is 41.16 J, because all of the GPE has been converted into KE.