A ball of mass 0.1 kg is thrown vertically upwards with an initial velocity of 80 m/s. Calculate the potential energy (i) halfway up (ii) at its maximum height. What is the kinetic energy as it leaves the ground?
ground K.E. ... 1/2 * 0.1 kg * 80 m/s = ? Joules
(i) P.E. halfway equals half of ground K.E.
(ii) max P.E. equals ground K.E.
To calculate the potential energy at different points during the motion of the ball, we need to consider the gravitational potential energy formula:
Potential Energy (PE) = mass (m) * gravity (g) * height (h)
(i) Halfway up:
To find the potential energy halfway up, we need to determine the height when the ball is at that position. Assuming the positive direction is upwards, halfway up the ball will have reached its maximum height, and its velocity will be zero.
At the highest point, the kinetic energy will be zero (KE = 0), as the ball momentarily comes to a stop. Therefore, all the initial kinetic energy would be converted to potential energy.
Since the ball is thrown vertically upwards with an initial velocity of 80 m/s, its kinetic energy at this point is given by the formula:
Kinetic Energy (KE) = (1/2) * mass (m) * velocity (v)^2
Kinetic Energy (KE) = (1/2) * 0.1 kg * (80 m/s)^2
= 320 J
(ii) Maximum height:
At maximum height, the velocity of the ball is zero, so the kinetic energy is also zero. All the initial kinetic energy will be converted to potential energy.
Therefore, the potential energy at the maximum height would be the same as the kinetic energy as it leaves the ground, which is 320 J.
To summarize:
(i) Potential energy halfway up = 320 J
(ii) Potential energy at the maximum height = 320 J
The kinetic energy as the ball leaves the ground is also 320 J.