Question

How much tension must a cable withstand if it is used to accelerate a 1000-kg car vertically upward at 0.60 m/s2 ?

Answer 1

Approximately
`10410\; {\rm N}` (assuming that
`g = 9.81\; {\rm m \cdot s^(-2)}`.)

Step-by-step explanation:

There are two forces on this car:

• Upward tension force from the cable, and
• Downward weight of the car (gravitational pull.)

The net force on this car would be:

`(\text{net force}) = (\text{tension}) - (\text{weight})`.

Rearrange to obtain:

`(\text{tension}) &= (\text{net force}) + (\text{weight})`.

Let the mass of this car be
`m`. The weight of the car would be
`m\, g`.

If the acceleration of the car is
`a`, the net force on this car would be
`m\, a`.

Thus:

`\begin{aligned}(\text{tension}) &= (\text{net force}) + (\text{weight}) \\ &= m\, a + m\, g \\ &= (m)\, (a + g) \\ &= (1000\; {\rm kg}) \, (0.60\; {\rm m \cdot s^(-2)} + 9.81\; {\rm m\cdot s^(-2)}) \\ &\approx 10410\; {\rm N}\end{aligned}`.