1) A 70 kg woman dives from a 2.5 m high diving board.
The gravitational field strength is 10 N/kg. Describe whether she gains or loses gravitational potential energy, and calculate the change in gravitational potential energy
she loses potential energy as she falls and gains speed (kinetic energy)
m g h = -70 * 10 * 2.5 Joules
To determine whether the woman gains or loses gravitational potential energy, we need to consider the height she dives from and the direction of her motion.
1) The woman dives from a 2.5 m high diving board. This means that she starts with a certain amount of gravitational potential energy due to her position above the ground.
2) When she dives, she moves downward towards the ground. This indicates that she is losing height or distance from the ground.
Based on these observations, we can conclude that the woman loses gravitational potential energy.
To calculate the change in gravitational potential energy, we can use the formula:
Change in gravitational potential energy (ΔPE) = mass (m) * gravitational field strength (g) * change in height (h)
Given:
mass (m) = 70 kg
gravitational field strength (g) = 10 N/kg (assumed to be on Earth)
change in height (h) = -2.5 m (negative because the woman is moving downwards)
Using the formula:
ΔPE = 70 kg * 10 N/kg * (-2.5 m)
ΔPE = -1750 joules
Therefore, the change in gravitational potential energy is -1750 joules.
To determine whether the woman gains or loses gravitational potential energy, we need to compare her initial and final states.
Gravitational potential energy (GPE) is given by the formula:
GPE = m * g * h
where:
m = mass of the object (in this case, the woman) = 70 kg
g = gravitational field strength = 10 N/kg
h = height (or vertical distance) = 2.5 m
Initially, when the woman is at the top of the diving board, her gravitational potential energy is:
Initial GPE = 70 kg * 10 N/kg * 2.5 m = 1750 J
Finally, when the woman reaches the water, her height from the ground is zero, and her GPE is:
Final GPE = 70 kg * 10 N/kg * 0 m = 0 J
To calculate the change in gravitational potential energy, we can subtract the initial GPE from the final GPE:
Change in GPE = Final GPE - Initial GPE
= 0 J - 1750 J
= -1750 J
Therefore, the woman loses 1750 Joules of gravitational potential energy as she dives from the 2.5 m high diving board.