a crate is hauled 8m up a ramp under a constant force of 200N applied at angle of 25 degree the ramp. Find work done?
the vertical height h is 8sin25°
work is thus 200N * h
I don't know how to work it out.
To find the work done in hauling the crate up the ramp, we can use the formula:
Work = Force × Distance × cos(θ)
where:
- Force is the applied force (200N),
- Distance is the distance moved (8m), and
- θ is the angle between the applied force and the direction of motion (25 degrees).
Plugging in the values:
Work = 200N × 8m × cos(25 degrees)
To calculate cos(25 degrees), we need to convert the angle to radians since the cosine function takes input in radians.
Converting 25 degrees to radians:
25 degrees × π/180 ≈ 0.4363 radians
Now, we can substitute the value into the formula:
Work ≈ 200N × 8m × cos(0.4363 radians)
Using a scientific calculator, we can find cos(0.4363 radians) ≈ 0.9093.
Finally, we can calculate the work:
Work ≈ 200N × 8m × 0.9093 ≈ 1458.88 Joules
Therefore, the work done in hauling the crate up the ramp is approximately 1458.88 Joules.