A pole-vaulter just clears the bar at 4.24 m and falls back to the ground. The change in the vaulter's potential energy during the fall is -3500 J. What is his weight?
PE = m * g * h ; Weight = m * g ; Remember, Mass is not Weight!
3500 = m * 9.81 * 4.24
3500 / (9.81 * 4.24) = m
m = 84.15 g
W = m * g = 84.15 * 9.81 = 824 N
Answer: 824 N
To determine the weight of the pole-vaulter, we first need to understand the relationship between potential energy, weight, and height.
The potential energy of an object is given by the formula:
Potential Energy = weight * height
In this case, the change in potential energy during the fall is -3500 J. Since the pole-vaulter is falling towards the ground, the potential energy decreases.
Let's assume the height of the pole-vaulter above the ground is H.
Therefore, we have the equation:
-3500 J = weight * H
We still need to determine the value of H, which is the height from which the pole-vaulter falls. Fortunately, we are given that the pole-vaulter just cleared the bar at a height of 4.24 m.
So, the height from which the pole-vaulter falls is 4.24 m. Substituting this value, the equation becomes:
-3500 J = weight * 4.24 m
Now, to find the weight, we can rearrange the equation:
weight = -3500 J / 4.24 m
Calculating the division, we get:
weight ≈ -825.47 N
Since weight is a force, the negative sign indicates the direction of the force, which is downwards due to gravity. So, we can drop the negative sign and state the weight as approximately 825.47 N.
m g h = 3500
m * 9.81 * 4.24 = 3500