A pole-vaulter just clears the bar at 5.34 m and falls back to the ground. The change in the vaulter's potential energy during the fall is -3.8E3 J. What is his weight?
To find the weight of the pole-vaulter, we can use the equation for potential energy:
Potential Energy = m * g * h
where
m = mass of the pole-vaulter (in kilograms)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height (in meters)
Given:
Potential Energy change = -3.8E3 J
Height = 5.34 m
g = 9.8 m/s^2
We can rearrange the equation to solve for weight:
m * g = Potential Energy change / h
Substituting the given values into the equation, we have:
m * 9.8 = -3.8E3 / 5.34
Simplifying the right side of the equation:
m * 9.8 = -712.71
Dividing both sides by 9.8:
m = -712.71 / 9.8
m ≈ -72.69
Since mass cannot be negative, it seems there might be an error in the problem or the calculations. Please double-check the given values and try again.
To find the weight of the pole-vaulter, we need to use the principle of conservation of energy. The change in potential energy of an object is equal to the work done on it, which, in this case, is the gravitational potential energy.
The formula for gravitational potential energy is given by:
Potential Energy = m * g * h,
where m is the mass of the object, g is the acceleration due to gravity, and h is the height from which the object falls.
Here, the change in potential energy is given as -3.8E3 J, which means the potential energy decreases during the fall. Therefore, the formula becomes:
Change in Potential Energy = -m * g * h.
Rearranging the equation, we get:
m = -(Change in Potential Energy) / (g * h).
Given that the change in potential energy is -3.8E3 J and the height h is 5.34 m, we need the value of g, which is the acceleration due to gravity.
The average acceleration due to gravity on Earth's surface is approximately 9.8 m/s^2. However, it may vary slightly depending on the location.
Now we can calculate the weight:
m = -(-3.8E3 J) / (9.8 m/s^2 * 5.34 m).
m = -(-3.8E3) / (9.8 * 5.34).
m ≈ 71.26 kg.
Therefore, the weight of the pole-vaulter is approximately 71.26 kg.