A shot-putter puts a shot (weight = 70.1 N) that leaves his hand at distance of 1.53 m above the ground.
(a) Find the work done by the gravitation force when the shot has risen to a height of 2.18 m above the ground. Include the correct sign for work.
(b) Determine the change (PE = PEf - PE0) in the gravitational potential energy of the shot.
a. mg(delta h)= 70.1N x 9.81 x -0.65
= -446.99 J
b. mg(delta h) = 70.1N x 9.81 x 0.65
= 446.99 J
According to the system these answers are incorrect. Can you please tell me where I went wrong?
One item that is incorrect is the number of significant digits in the answer.
On the second (b), it is not clear to me where the gravitation PE change of the shot is measured. You put it at the top, I was thinking at ground level, but the problem does not state.
Well, it seems like you're in a bit of a gravitational pickle! Don't worry though, I'm here to help you sort things out, or at least provide you with a laugh along the way! Let's go through your calculations and see where the mistake might be hiding.
(a) You correctly used the formula mgΔh to calculate the work done by the gravitational force. Since the shot rises to a height of 2.18 m, the change in height (Δh) is -0.65 m (assuming ground level as the reference point). Multiplying this by the weight (70.1 N) and acceleration due to gravity (9.81 m/s^2) gives you -446.99 J. However, in terms of significant digits, the weight of the shot has three significant digits, so the final answer should be rounded to three significant digits as well. So, the correct answer would be -447 J.
(b) Here's where things get a bit tricky. The problem doesn't specify where the gravitational potential energy change is measured. You assumed it to be at the top of the shot's trajectory, which is a valid assumption. Using the same formula, mgΔh, with Δh = 0.65 m (the positive change in height from the starting point), the math gives you 446.99 J. However, once again, we need to consider significant digits. Since the height change has only two significant digits, the answer should also be rounded to two significant digits. So, the correct answer for the change in gravitational potential energy would be 450 J.
Remember, it's important to keep an eye on significant digits and make sure you're clear about the reference point for any potential energy calculations. Oh, and most importantly, keep smiling and have a good laugh along the way! 🤡
To find the work done by the gravitational force, you can use the formula:
Work = Force x Displacement x cos(theta)
In this case, the force is the weight of the shot (70.1 N) and the displacement is the change in height (2.18 m - 1.53 m = 0.65 m). The angle theta is the angle between the force and the displacement, which is 0 degrees since the force and displacement are in the same direction (upwards).
So the work done by the gravitational force is:
Work = 70.1 N x 0.65 m x cos(0 degrees)
= 70.1 N x 0.65 m x 1
= 45.57 J
Therefore, the correct answer is 45.57 J. Note that the work done by the gravitational force is positive because it is in the same direction as the displacement.
For part (b), to find the change in gravitational potential energy, you can use the formula:
Change in PE = m x g x delta h
Here, m is the mass of the shot and g is the acceleration due to gravity (approximately 9.81 m/s^2). The delta h is the change in height, which in this case is 0.65 m.
To find the mass, you can divide the weight of the shot (70.1 N) by the acceleration due to gravity (9.81 m/s^2):
m = 70.1 N / 9.81 m/s^2
= 7.14 kg (rounded to two decimal places)
Now, calculate the change in gravitational potential energy:
Change in PE = 7.14 kg x 9.81 m/s^2 x 0.65 m
= 45.43 J
Therefore, the correct answer for the change in gravitational potential energy is 45.43 J. Note that the change in gravitational potential energy is positive because the shot is moving upwards against gravity.
To determine the work done by the gravitational force, you need to use the formula:
Work = force x distance x cos(theta)
In this case, the force is the weight of the shot, which is 70.1 N. The distance is the difference in height, which is 2.18 m - 1.53 m = 0.65 m. The angle theta is the angle between the force and the displacement, which is 0 degrees because the force is acting vertically upward and the displacement is also vertical. Therefore, cos(0) = 1.
Using the formula:
Work = 70.1 N x 0.65 m x 1 = 45.565 J.
Since the work done by gravity is negative when the shot rises, the correct answer is:
Work = -45.6 J (rounded to one decimal place).
For the change in gravitational potential energy, you can use the formula:
Change in PE = mgh
Here, m is the mass of the shot (which was not given, but you can assume it's the weight divided by the acceleration due to gravity: m = 70.1 N / 9.81 m/s^2), g is the acceleration due to gravity (9.81 m/s^2), and h is the difference in height, which is 2.18 m - 1.53 m = 0.65 m.
Plugging in the values, you get:
Change in PE = (70.1 N / 9.81 m/s^2) x 9.81 m/s^2 x 0.65 m = 70.1 x 0.65 J.
Rounding this to two significant digits, the change in gravitational potential energy is:
Change in PE = 46 J.
So, the correct answer for part (a) is -45.6 J and for part (b) is 46 J.