A 1.5 kg snowball is fired from a cliff 12.5m high with an inital velocity of 14 m/s directed 41 degrees above the horizontal.
a) how much work is done on the snowball by the gravitaitonal force during its flight to the flat ground below the cliff?
b) what is the change in the gracitational potential energy of the snowball-Earth system during the flight?
c) If that gravitational potential energy is taken to be zero at the height of the cliff, what is its value when the snowball reaches the ground?
a) Is this the equation I would use: mgh= 1/2mv^2?
For b) and c) can you please explain to me how I would solve these problems?
Yes for a.
There is no change in total gpe. What work is done on the snowball by gravity to change its KE is equal.
c: if the top is zero, then the bottom is -h, and gpe is -mgh
To solve parts b) and c) of this problem, we need to consider the concept of gravitational potential energy (GPE). Gravitational potential energy is the energy possessed by an object due to its position relative to a gravitational field.
b) The change in gravitational potential energy (ΔGPE) of the snowball-Earth system during its flight can be calculated using the formula:
ΔGPE = m * g * Δh
m represents the mass of the snowball (1.5 kg), g represents the acceleration due to gravity (9.8 m/s^2), and Δh represents the change in height from the cliff to the ground (which is the same as the height of the cliff, 12.5 m).
So, plugging in the values, we get:
ΔGPE = 1.5 kg * 9.8 m/s^2 * 12.5 m
= 183.75 Joules
Therefore, the change in gravitational potential energy during the flight is 183.75 Joules.
c) If we take the gravitational potential energy to be zero at the height of the cliff, then at the ground level, the gravitational potential energy can be determined by using the formula:
GPE = m * g * h
In this case, m represents the mass of the snowball (1.5 kg), g represents the acceleration due to gravity (9.8 m/s^2), and h represents the height of the cliff (12.5 m).
Plugging in the values, we get:
GPE = 1.5 kg * 9.8 m/s^2 * 12.5 m
= 183.75 Joules
Therefore, when the snowball reaches the ground, its gravitational potential energy is 183.75 Joules.