An 80kg man walks down a ramp that makes a 40 degree angle with the horizontal. By how much does his gravitational potential energy change (in kJ) when he walks 15m down the ramp?

Question

An 80kg man walks down a ramp that makes a 40 degree angle with the horizontal. By how much does his gravitational potential energy change (in kJ) when he walks 15m down the ramp?

Answer 1

gravitational potential energy = mgh

where:
m = mass
g = gravitational acceleration
h = height

So, the change in gravitational potential energy is:
delta p = 80kg * 9.8m/sec^2 * (h1 - h2)m

Answer 2

Thank You but I still do not understand what I should do with the angle as far as finding the height is concerned

Answer 3

OK, the ramp makes a 40 degree angle with the horizontal. A sketch might help visualizing this. If you move 15m down the ramp what is the change in the y direction (the height)? It is 15m * sin(40degrees).

So, the potential energy change is:
=(80kg) * 9.8m/sec^2 * (- 15m * sin(40degrees)). Remember that the answer should be in KJ.

Answer 4

Remember that the answer should be in KJ. I think you mean kJ.

Answer 5

Yes, thanks!

Answer 6

To determine the gravitational potential energy change, we need to calculate the change in height of the man as he walks down the ramp. The formula for gravitational potential energy is given by:

Potential Energy (PE) = mass (m) * gravitational acceleration (g) * height (h)

Since the height will change as the man walks down the ramp, the change in potential energy (ΔPE) is given by:

ΔPE = m * g * Δh

First, let's calculate the change in height. The ramp forms a right-angled triangle, with the height being one of the sides and the hypotenuse being the ramp itself. The angle between the ramp and the horizontal is 40 degrees.

We can use trigonometry to find the change in height:

Δh = hypotenuse * sin(angle)

Since the hypotenuse is the distance the man walked down the ramp, which is 15m, and the angle is 40 degrees, we can substitute these values into the equation:

Δh = 15m * sin(40°)

Calculating this value gives us the change in height.

Now, let's calculate the gravitational potential energy change:

ΔPE = m * g * Δh

The mass of the man is given as 80 kg, and the gravitational acceleration (g) is approximately 9.8 m/s^2.

Plugging in these values, calculate the change in gravitational potential energy to get the answer in joules (J).

Finally, convert the answer from joules to kilojoules (kJ) by dividing it by 1000.

That's it! By following these steps, you should be able to calculate the change in gravitational potential energy when the man walks down the ramp.