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 need to first understand the concept of potential energy and its relation to gravitational potential energy.
Potential energy is the energy possessed by an object due to its position or state. Gravitational potential energy is a specific type of potential energy related to an object's position in a gravitational field.
The formula for gravitational potential energy is:
Potential Energy = mass x gravitational acceleration x height
In this case, the change in potential energy during the fall is given as -3.8E3 J (negative because the potential energy decreases during the fall). The height of the fall is represented by the difference between the initial position (clearing the bar) and the final position (falling to the ground). Therefore, the change in potential energy can be expressed as:
Potential Energy = weight x gravitational acceleration x height
Rearranging the equation to solve for weight:
Weight = Potential Energy / (gravitational acceleration x height)
The given values are:
Change in potential energy, ΔPE = -3.8E3 J
Gravitational acceleration, g = 9.8 m/s^2 (approximately, on Earth)
Height, h = 5.34 m
Plugging these values into the formula:
Weight = (-3.8E3 J) / (9.8 m/s^2 x 5.34 m)
Weight ≈ -75 kg
Therefore, the weight of the pole-vaulter is approximately -75 kg. The negative sign indicates that the weight acts downward, which is the conventional direction for gravitational forces.