How much tension must a rope withstand if it is used to accelerate a 1200-kg car vertically upwards at 0.8m/s2?

T = 12732 [N]

Explanation:

To solve this problem we must use newton's second law which tells us that the sum of forces on a body is equal to the product of mass by acceleration.

By means of the attached free body diagram, we can better understand the solution to this problem.

As we see in the diagram the tension Force T lifts the car upwards so the movement is upwards. Therefore we have two forces one upward (positive) of the force T and the other negative downward due to the weight of the vehicle.

As the movement is up the acceleration is also up (with a positive sign).

ΣF = m*a

where:

F = forces [N] (units of Newtons)

m = mass = 1200 [kg]

a = acceleration = 0.8 [m/s²]

T - 1200*9.81 = 1200*(0.8)

T = 12732 [N]

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