Large boxes of pumpkins are set on a ramp to be unloaded out of a truck. The 300.0 lb boxes are set on the ramp which has an incline of 35 degrees. They must then be pushed to get started down the plane towards the bottom. If the coefficient of the static friction between the boxes and the ramp is .8, how much push applied parallel to the ramp is required to get one of the boxes of pumpkins moving?
To determine the amount of push required to get the box of pumpkins moving, we'll need to calculate the force of static friction. Once we know the force of static friction, we can use that information to find the amount of push required parallel to the ramp.
First, let's calculate the force of static friction:
Force of static friction (Fs) = coefficient of static friction (μs) * weight (W)
Given:
- Coefficient of static friction (μs) = 0.8
- Weight (W) = 300.0 lb
Plug in the values into the formula:
Fs = 0.8 * 300.0 lb
Fs = 240 lb
Now we know that the force of static friction between the boxes and the ramp is 240 lb.
To find the amount of push required parallel to the ramp, we can use the concept of forces and Newton's second law. The parallel force applied to the box is equal to the force of static friction. Since the angle of the incline is 35 degrees, we can decompose this force into its horizontal and vertical components.
Here's how you can calculate the push required parallel to the ramp:
Push force parallel to the ramp = Force of static friction * sin(angle of incline)
Given:
- Force of static friction = 240 lb
- Angle of incline = 35 degrees
Plug in the values into the formula:
Push force parallel to the ramp = 240 lb * sin(35 degrees)
Push force parallel to the ramp ≈ 137.9 lb
Therefore, to get one of the boxes of pumpkins moving, you would need to apply approximately 137.9 lb of push force parallel to the ramp.