A 185kg refrigerator is loaded into a van by moving it up a 10.0m long frictionless ramp that is at an angle of 11.0 degrees. How much work is done?
To find the work done in moving the refrigerator up the ramp, we need to calculate the gravitational potential energy change.
The formula to calculate work is given by:
Work = Force x Distance
The force involved here is the weight of the refrigerator, which is the product of its mass (m) and the acceleration due to gravity (g).
Weight (Force) = mass x gravity
Let's calculate the weight of the refrigerator:
Weight = mass x gravity
Weight = 185 kg x 9.8 m/s^2
Weight = 1813 N (rounding to three significant figures)
Now, we need to calculate the vertical distance the refrigerator is lifted.
Vertical distance = Length of ramp x sin(angle)
Vertical distance = 10.0 m x sin(11.0 degrees)
Vertical distance ≈ 1.91 m
Work = Force x Distance
Work = Weight x Vertical distance
Substituting the values we have:
Work = 1813 N x 1.91 m
Work ≈ 3466.83 J
Therefore, the work done to load the refrigerator into the van is approximately 3466.83 Joules.
To calculate the work done in moving the refrigerator up the ramp, we can use the formula:
Work = Force × Distance × cos(θ)
In this case, the force is the component of the weight of the refrigerator that acts parallel to the ramp. We can calculate this force using the formula:
Force = Weight × sin(θ)
Given that the weight of the refrigerator is 185 kg, and the angle of the ramp is 11.0 degrees, we can substitute these values into the formulas.
First, we calculate the force:
Force = 185 kg × 9.8 m/s^2 × sin(11.0 degrees)
≈ 329.92 N (rounded to two decimal places)
Now, we can calculate the work:
Work = Force × Distance × cos(θ)
= 329.92 N × 10.0 m × cos(11.0 degrees)
≈ 3,535.82 J (rounded to two decimal places)
Therefore, approximately 3,535.82 joules of work are done in moving the 185 kg refrigerator up the 10.0 m long ramp.
Since the ramp is frictionless
W = m•g•h = m•g•s•sin α