Question

A body of mass 16 kg accelerates vertically down with a force of 8 N. What is the minimum force required to make it move upward with the same acceleration? [Take `"g = 10 m/s"^2`].

Answer 1

It would require an upward force of 328 N (-328 N).

Explanation:

I am not sure I am correctly visualizing the situation. I will assume that the body will remain fixed in place by static friction if the applied downward force is less than 8 N.

In the first case the applied force, `F_"applied-1"`, is 8 N. The total downward force, `F_1`, would be

`F_1 = "weight" + 8 N = 16 kg*10 m/s^2 + 8 N = 168 N`

So 168 N is able to break the static friction and start the mass moving. Now in case 2, we want it to accelerate it upward. Since we have already done an equation in which downward forces are positive, we will continue to use that convention. To have the same value of acceleration the total force, `F_2`, needs to be -168 N (the negative sign makes that force an upward force).

The question is what does the applied force, `F_"applied-2"` need to be? To begin, we can see that the applied force will need to be upward and we need to remember that the weight is still a downward force.

`F_2 = F_"applied-2" + 16 kg*10 m/s^2`

We said above that `F_2` needs to be -168 N. So we can say that

`F_"applied-2" + 16 kg*10 m/s^2 = - 168 N`

Then

`F_"applied-2" = -16 kg*10 m/s^2 - 168 N`

`F_"applied-2" = -160 N - 168 N = -328 N`

I hope this helps,
Steve