Answer :
Final answer:
The work done on the elevator car by the cable is 427,540 J, the work done on the elevator car by the gravitational force is 480,200 J, and the total work done on the elevator car is 907,740 J.
Explanation:
To calculate the work done on the elevator car by the cable, we need to subtract the work done against friction from the total work done on the car.
Given:
- Mass of the elevator car (m) = 1400 kg
- Lifting height (d) = 35 m
- Friction (f) = 122 N
First, let's calculate the total work done on the elevator car:
Work done by the cable (Wcable) = force * displacement * cos(theta)
Since the elevator car is lifted at a constant speed, the net force on the car is zero. Therefore, the work done by the cable is equal to the work done against friction:
Wcable = f * d * cos(theta)
Substituting the given values:
Wcable = 122 N * 35 m * cos(theta)
Next, let's calculate the work done by the gravitational force:
Wgravity = force * displacement * cos(0)
Since the angle between the force of gravity and the displacement is 0 degrees, the cosine of 0 is 1:
Wgravity = m * g * d * cos(0)
Substituting the given values:
Wgravity = 1400 kg * 9.8 m/s2 * 35 m * cos(0)
Finally, the total work done on the elevator car is the sum of the work done by the cable and the work done by the gravitational force:
Total work done (Wtotal) = Wcable + Wgravity
Learn more about calculating work done on an elevator car here:
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