a ball of mass 200 g is thrown vertically upwards with a velocity of 20ms-1 ignoring air resistance.
a) calculate the kinetic energy of the ball as it is released
b)calculate the maximum height reached by the ball
c) state the velocity of the ball when it returns to its starting position
d)state which conservation principle you used to obtain your answers to questions (b) and (C)
e) if the ball hit the ground 2 metres below the point from which it was thrown, calculate the impulse and impulse force of the 1 millisecond impact.
a) To calculate the kinetic energy of the ball as it is released, we can use the equation for kinetic energy:
Kinetic energy = (1/2) * mass * velocity^2
Given:
Mass of the ball (m) = 200 g = 0.2 kg
Initial velocity (u) = 20 m/s (as it is thrown upwards)
Plugging in these values into the equation, we get:
Kinetic energy = (1/2) * 0.2 kg * (20 m/s)^2
= 40 J
Therefore, the kinetic energy of the ball as it is released is 40 J (joules).
b) To calculate the maximum height reached by the ball, we can use the concept of conservation of mechanical energy. At the maximum height, the ball has no kinetic energy (all energy converted to potential energy). Thus, the initial kinetic energy is equal to the final potential energy at the highest point.
Initial kinetic energy = Final potential energy
Kinetic energy = (1/2) * mass * velocity^2
Potential energy = mass * gravitational acceleration * height
At the highest point, the ball comes to rest, so final velocity (v) is 0.
(1/2) * mass * velocity^2 = mass * gravitational acceleration * height
Plugging in the given values:
(1/2) * 0.2 kg * (20 m/s)^2 = 0.2 kg * 9.8 m/s^2 * height
Solving for the height (h):
height = (1/2) * (20 m/s)^2 / (9.8 m/s^2)
= 20.41 m
Therefore, the maximum height reached by the ball is 20.41 meters.
c) Since we know the ball is thrown vertically upwards and returns to its starting position, we can infer that the velocity when it returns is equal in magnitude but opposite in direction to its initial velocity. Thus, the velocity when it returns is -20 m/s.
d) The conservation principle used to obtain the answers for questions (b) and (c) is the principle of conservation of mechanical energy. It states that the total mechanical energy (sum of kinetic energy and potential energy) of a system remains constant if there are no external forces acting on it. In this case, neglecting air resistance, the only force acting on the ball is its weight due to gravity.
e) To calculate the impulse and impulse force during the impact, we need additional information such as the time taken for impact and the change in momentum of the ball.