Question

The ACE towing company tows a disabled 1050-kg automobile off the road ata constant speed. If the tow line makes an angle of 10.0° with the vertical asshown, what is the tension in the line supporting the car?

Answer 1

Answer:

10,448.74 N

Explanation:

First, we know that the mass of the car is 1050 kg and the tow line makes an angle of 10.0° with the vertical and we want to know the tension in the line, so

The given

m = 1050 kg

θ = 10.0°

g = 9.8 m/s²

The unknown

T = ?

To write the formula, we need to draw a free body diagram as follows

They are moving at a constant speed, so there is no acceleration and the sum of the forces is equal to 0.

In the vertical direction, we have the following equation

$\begin{gathered} T\cos\theta-mg=0 \\ T\cos\theta=mg \\ T=\frac{mg}{cos\theta} \end{gathered}$

Therefore, the formula is

$T=\frac{mg}{cos\theta}$

Replacing the values, we get

$T=\frac{(1050kg)(9.8\text{ m/s}^2)}{cos(10)}=10448.74\text{ N}$

So, the answer is 10448.74 N