A box is dragged with a force of 115 N up a ramp a distance of 3 m. If the force makes an angle of 35 degrees with the ramp and the ramp makes an angle of 20 degrees with the ground, how much work is done?
To find the work done, we need to calculate the component of the force that is acting in the direction of the displacement and then multiply it by the displacement.
The component of the force that acts in the direction of the displacement can be found using trigonometry. Let's break down the problem step by step:
Step 1: Find the component of the force parallel to the ramp.
To find this, we need to determine the horizontal component of the force. We can use the formula:
Horizontal component of force = Force * cos(angle)
Given: Force = 115 N, angle = 35 degrees
Plugging in the values into the formula, we get:
Horizontal component of force = 115 N * cos(35°)
Step 2: Find the displacement along the ramp.
The displacement along the ramp is the distance traveled along the ramp. In this case, it is given as 3 m.
Step 3: Calculate the work done.
The work done is given by the formula:
Work done = Component of force parallel to the ramp * displacement
Plugging in the values we found in step 1 and step 2, we have:
Work done = (115 N * cos(35°)) * 3 m
Calculating this expression will give us the work done.
Please note that the angle of the ramp with the ground (20 degrees) is not required to find the work done in this scenario. It is provided for additional context.