You are unloading a refrigerator from a delivery van. The ramp on the van is 5.0m long and its top end is 1.4m above the ground. As the refrigerator moves down the ramp, you are on the downside of the ramp trying to slow the motion by pushing horizontally against the refrigerator with a force of 300N.
How much work do you do on the refrigerator during its trip down the ramp?
a^2 + b^2 = c^2
a = sqrt(c^2 - b^2)
a=4.8
work is done in the direction of the 4.8 distance but opposes movement, so it will be negative.
4.8*-300 = -1440
To find out how much work you do on the refrigerator during its trip down the ramp, we can use the formula for work:
Work = Force × Distance × cos(θ)
where:
- force is the amount of force you are applying horizontally (300N),
- distance is the length of the ramp (5.0m),
- and θ is the angle between the direction of the force and the direction of motion of the refrigerator (which is the angle of the ramp).
In this case, since you are pushing horizontally against the refrigerator and the refrigerator is moving down the ramp (which is inclined), the angle θ is the angle of the ramp.
To determine the angle of the ramp, we can use trigonometry. The ramp forms a right-angle triangle, where the height of the ramp (1.4m) is the opposite side and the length of the ramp (5.0m) is the adjacent side.
The angle θ can be found using the inverse tangent (tan⁻¹) function:
θ = tan⁻¹(opposite/adjacent) = tan⁻¹(1.4/5.0)
Calculating this on a calculator, we find:
θ ≈ 15.94 degrees
Now we can plug in the values into the work formula:
Work = 300N × 5.0m × cos(15.94 degrees)
Using the cosine of the angle in degrees, we can calculate:
Work ≈ 300N × 5.0m × cos(15.94) ≈ 1309.7 Joules
Therefore, you do approximately 1309.7 Joules of work on the refrigerator during its trip down the ramp.
work = f x
w = 300(-5) = -1500 J