A 0.720 kg snowball is fired from a cliff 8.10 m high. The snowball's initial velocity is 14.2 m/s, directed 30.0° above the horizontal. (a) How much work is done on the snowball by the gravitational force during its flight to the flat ground below the cliff? (b) What is the change in the gravitational 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?
I think I understand each problem. But I'll post what I think I need to do then someone can confirm if its right or not.
a)mgyi - mgyf = Wg I get 57 J
b)Change in Gravitational Potential Energy is just the negative of that work so its -57 J
c)The answer should just be zero since it was zero at the top of the cliff.
I'm skeptical because I didn't use the angle or velocity given. That's why I'm not sure if these answers are right or not. Do I use W = change in kinetic energy for part a or no?
c. If inital GPE is zero, then at the base of the clift it has to be -57J
How can that be because the height at the ground is 0. So mgyf would be zero as well wouldn't it? How is my work for part a and b?
To solve this problem, you will need to understand the concepts of work, gravitational potential energy, and how to use them in relation to the given information. Let's go through each part of the question to determine the correct steps.
(a) To find the work done on the snowball by the gravitational force, you need to consider the gravitational potential energy at two different points: the initial height and the final height. The formula for work done by the gravitational force is given by:
Work (W) = Change in Gravitational Potential Energy
Here, m is the mass of the snowball, g is the acceleration due to gravity, and y is the height difference.
In this case, the snowball is initially at a height of 8.10 m and finally reaches the flat ground. So, we can calculate the work done by substituting the values into the formula:
W = m * g * (yf - yi)
= (0.720 kg) * (9.8 m/s^2) * (0 - 8.10 m)
= - 57 J
Your calculation of 57 J is correct. The negative sign indicates that work is done by the gravitational force as the snowball falls.
(b) To find the change in gravitational potential energy of the snowball-Earth system during the flight, you can use the formula:
Change in Gravitational Potential Energy = m * g * (yf - yi)
Where m is the mass of the snowball, g is the acceleration due to gravity, and yf and yi are the final and initial heights, respectively.
By substituting the given values:
Change in Gravitational Potential Energy = (0.720 kg) * (9.8 m/s^2) * (0 - 8.10 m)
= - 57 J
The change in gravitational potential energy is also -57 J, as you correctly calculated. This negative sign indicates a reduction in potential energy as the snowball falls.
(c) The question asks for the value of gravitational potential energy when the snowball reaches the ground, taking the height of the cliff as the reference point (where potential energy is zero). Since the snowball is on the ground, its height is zero. Therefore, the gravitational potential energy at this point is also zero.
So, your answer stating that the value of gravitational potential energy when the snowball reaches the ground is zero is correct.