QuestionI

A physics textbook is suspended on a spring scale in an elevator. Of the following, the scale shows the highest reading when the elevator:

A moves downward with decreasing speed

B remains stationary

Cmoves upward at constant speed

D moves upward with decreasing speed

E moves downward with increasing speed

The scale is reading a value for the apparent weight of the object, aka the downward force acting on the spring. So the question is esentially asking about the force on the spring.

For the following I am defining upward to be the positive direction.

Let's take each of the answers and look at the value of the spring force.

A moves downward with decreasing speed

This means the acceleration is upward. So Newton's 2nd Law says:

SumF = F - w = + ma

(Where F is the spring force, w is the weight, etc.)

Solving for F gives us:

F = w + ma > w

So the spring force is greater than the weight.

B remains stationary

If the elevator is stationary, then there is no acceleration, thus:

SumF = F - w = m*0 = 0

F = w

So the spring force is equal to the weight.

Cmoves upward at constant speed

Again, there is no acceleration, so F = w as in case B.

D moves upward with decreasing speed

If the elevator is moving upward with decreasing speed the acceleration is downward, so:

SumF = F - w = -ma

F = w - ma < w

So the spring force is less than the weight.

E moves downward with increasing speed

Again the acceleration is downward, so F < w as in case D.

Putting it all together we see that answer A gives the largest spring force.

-Dan