You are loading a refrigerator weighing 2250 N onto a
truck, using a wheeled cart. The refrigerator is raised
1.00 m to the truck bed when it is rolled up a ramp.
Calculate the minimum work that must be done by the
force you apply and the magnitude of the force if the
ramp is at an angle with the horizontal of
To calculate the minimum work that must be done and the magnitude of the force required, we can use the concept of work-energy theorem.
The work done (W) by a force (F) is given by the formula:
W = F * d * cosθ,
where:
- F is the force applied,
- d is the displacement in the direction of the force,
- θ is the angle between the force and the displacement.
In this case, the displacement (d) is equal to the height that the refrigerator is raised, which is 1.00 m.
The angle (θ) is the angle between the ramp and the horizontal. Given that the ramp is at an angle with the horizontal, we need to know the specific angle to calculate θ.
Once we have the angle (θ), we can calculate the force (F) required by rearranging the formula:
F = W / (d * cosθ).
Please provide the angle of the ramp with the horizontal so that we can continue with the calculation.
To calculate the minimum work done by the force you apply and the magnitude of the force, we can use the concept of work and energy.
The work done to lift the refrigerator is equal to the change in potential energy. Potential energy is given by the formula:
Potential energy = mass * gravity * height
where mass is the mass of the refrigerator, gravity is the acceleration due to gravity (approximately 9.8 m/s^2), and height is the height the refrigerator is lifted (1.00 m in this case).
Given that the weight of the refrigerator is 2250 N, we can convert it to mass using the formula:
Weight = mass * gravity
Rearranging the equation, we get:
mass = weight / gravity
Substituting the given values, we have:
mass = 2250 N / 9.8 m/s^2
Now, we can calculate the potential energy:
Potential energy = mass * gravity * height
Potential energy = (2250 N / 9.8 m/s^2) * 9.8 m/s^2 * 1.00 m
Simplifying, we find:
Potential energy = 2250 N * 1.00 m
Therefore, the work done by the force is equal to the potential energy, which is 2250 N * 1.00 m = 2250 N·m.
Now, let's calculate the magnitude of the force.
The force you apply is equal to the weight of the refrigerator, as you need to counteract its weight to lift it. So the magnitude of the force is 2250 N.
Therefore, the minimum work that must be done by the force you apply is 2250 N·m, and the magnitude of the force is 2250 N.