a 98 K crate is pushed to the top of a 2.5m ramp, which is inclined at 18 degrees with the horizontal. what is the potential energy of the crate?
mass m=98kg height h=2.5m
potential energy U=mgh
U= 98*2.5*9.8
U= 24010J
U= 24.01 kJ
h = 2.5*sin18.
PE = M*g*h.
To calculate the potential energy of the crate, you need to use the formula:
Potential Energy (PE) = Mass (m) * Gravity (g) * Height (h)
Given:
Mass (m) = 98 kg
Height (h) = vertical height of the ramp = 2.5 m
However, you first need to determine the height along the inclined plane because the height you provided is the vertical height. To find the height along the inclined plane, you can use trigonometry.
The height along the inclined plane can be calculated using the formula:
Height along inclined plane = Height (h) * sin(angle)
Angle (θ) = 18 degrees
Let's calculate the height along the inclined plane first:
Height along inclined plane = 2.5 m * sin(18 degrees)
Using a scientific calculator or online trigonometry tool:
Height along inclined plane ≈ 0.7309 m
Now, you have all the required values to calculate the potential energy of the crate.
Potential Energy (PE) = Mass (m) * Gravity (g) * Height (h)
Potential Energy (PE) = 98 kg * 9.8 m/s² * 0.7309 m
Calculating it:
Potential Energy (PE) ≈ 711.4476 Joules
Therefore, the potential energy of the crate is approximately 711.4476 Joules.