Question

Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that accelerated upward? Accelerated downward? Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that accelerated upward? Accelerated downward? upward, more compressed; downward, more compressed upward, less compressed; downward, less compressed upward, more compressed; downward, less compressed upward, less compressed; downward, more compressed

Answer 1

Accelerate up more compressed spring

Accelerate down spring less compressed

Step-by-step explanation:

For this problem we must analyze the forces that act on the scale on the one hand the weight of the man directed downwards and I have the other the elastic force of the spring directed upwards. Now let's write Newton's second law for these forces in various configurations,

When the elevator is quiet or moving at constant speed

Fe - W = 0 ⇒ Fe = W -k x = mg x = mg /k

Fe = mg

We use this value to compare

Now let's analyze when the elevator accelerates upwards

Fe -W = m a

Fe = ma + W

Fe = m (a + g)

So we can see that Fe increases, so the compression of springs is higher

Now let's analyze when the elevator acceleration is down

Fe -W = m (-a)

Fe = w - m a

Fe = m (g -a)

In this case Fe is smaller, so the compression of the spring is less