Question

How much tension must a cable withstand if it is used to accelerate a 1200 kg car vertically upward at 0.70 m/s²?

Short answer

The tension in the cable is 12600 N.

Step-by-step solution

Step 1. Given data and assumption

The tension in the cable is equal to the weight and the force due to the acceleration.

Given data:

The mass of the car is $m=1200\mathrm{kg}$.

The upward acceleration of the car is $\mathit{a}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{70}\mathbf{}\frac{\mathbf{m}}{{\mathbf{s}}^{\mathbf{2}}}$.

The weight of the car is acting downward on the car.

Assumption:

Let T be the tension on the cable.

Step 2. Calculation of the tension

Now, applying Newton’s second law on the car,

$\begin{array}{c}ma=T-mg\\ T=m\left(g+a\right)\\ =\left(1200\mathrm{kg}\right)\times \left(9.80\frac{\mathrm{m}}{{\mathrm{s}}^2}+0.70\frac{\mathrm{m}}{{\mathrm{s}}^2}\right)\\ =12600\mathrm{N}\end{array}$

Hence, the tension on the cable is 12600 N.