) A crate is hauled 8m up a ramp under a force of 200N applied at an angle if 250
to
the ramp. Find the work done
25 degrees to ramp?
ramp length = 8 m or 8 m up? assume length = 8 m
then work = distance moved * force in direction of motion
= 8 * 200 cos 25 = 1600 cos 25 Joules
To find the work done in hauling the crate up the ramp, we need to calculate the displacement of the crate and the angle between the force applied and the displacement.
Step 1: Calculate the vertical displacement:
The ramp makes an angle of 250° with the ground. The vertical displacement can be found using the equation:
vertical displacement = distance * sin(angle)
Given that the crate is hauled 8m up the ramp, the vertical displacement can be calculated as:
vertical displacement = 8m * sin(250°)
Step 2: Calculate the work done:
The work done can be found using the equation:
work = force * displacement * cos(angle)
Given that the force applied is 200N, the displacement is the vertical displacement from step 1, and the angle between the force and displacement is 0° (since the force is acting vertically), the work done can be calculated as:
work = 200N * (vertical displacement) * cos(0°)
The work done will be in joules (J).
To find the work done, we need to multiply the force applied by the distance over which the force was applied.
In this case, the force applied is 200N and the distance is 8m. However, we need to take into account the angle between the force and the ramp.
The force can be split into two components: one along the ramp and one perpendicular to the ramp. The component along the ramp is given by the formula:
Force along ramp = Force * cos(angle)
The work done can then be calculated using the formula:
Work = Force along ramp * Distance
Substituting the given values:
Force along ramp = 200N * cos(250°)
Distance = 8m
Calculating:
Force along ramp = 200N * cos(250°) ≈ 200N * (-0.9397) ≈ -187.94N
Work = -187.94N * 8m ≈ -1503.52 J
Therefore, the work done to haul the crate up the ramp is approximately -1503.52 Joules.