A pole-vaulter just clears the bar at 4.42 m and falls back to the ground. The change in the vaulter's potential energy during the fall is -3800 J. What is his weight?
To find the weight of the pole-vaulter, we can use the formula for potential energy:
Potential Energy = mgh
Where:
m = mass of the vaulter
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height
Given that the change in potential energy during the fall is -3800 J, we know that the potential energy at the top of the jump was higher than at the bottom. Therefore, the initial potential energy can be calculated as:
Initial Potential Energy = Final Potential Energy + Change in Potential Energy
Let's assume the final potential energy at the bottom is zero. So:
0 = Final Potential Energy + (-3800 J)
Solving for the final potential energy:
Final Potential Energy = - (-3800 J) = 3800 J
Now, we can use the formula for potential energy to calculate the weight of the pole-vaulter:
Potential Energy = mgh
Rearranging the formula, we have:
m = Potential Energy / (g * h)
m = 3800 J / (9.8 m/s^2 * 4.42 m)
m ≈ 87.48 kg
Therefore, the weight of the pole-vaulter is approximately 87.48 kg.
To calculate the weight of the pole-vaulter, we need to use the formula for potential energy:
Potential Energy = Weight × Height × gravity
Given:
Change in potential energy (ΔPE) = -3800 J
Height (h) = 4.42 m
Gravity (g) = 9.8 m/s²
We can rearrange the formula to solve for weight:
ΔPE = Weight × Height × gravity
Weight = ΔPE / (Height × gravity)
Let's substitute the given values:
Weight = -3800 J / (4.42 m × 9.8 m/s²)
Weight ≈ -3800 J / 43.316 m²/s²
Weight ≈ -87.79 kg*m²/s² / 43.316 m²/s²
Weight ≈ -2.027 kg
The negative sign indicates that the weight acts in the opposite direction of gravity. Therefore, the weight of the pole-vaulter is approximately 2.027 kg.
PE = mgh
3800 = (mg)(4.42)
His weight is mg