Vertical simple harmonic motion concept

[caljuice]

Homework Statement

A 0.12-kg block is suspended from a spring. When a small stone of mass 30 g is placed on the block, the spring stretches an additional 5 cm. With the stone on the block, the spring oscillates with an amplitude of 12 cm. What is the net force of the stone when it is at a point of maximum upward displacement

The Attempt at a Solution

The answer is Fnet= mass of pebble x gravity. The solution says this is the case because the spring isn't moving.

But shouldn't Fnet = force of gravity + force of spring? Since at maximum compression, the spring will exert a down acceleration. Just because it's not moving doesn't have to mean it isn't causing acceleration right? And when I look at the position graph and the acceleration graph of horizontal simple harmonics, the greatest magnitude of acceleration of a spring is when the spring is at maximum compression or stretch- the amplitude. If there's acceleration then there must be force? Or is this different because this is vertical? Thanks.

 

[ehild]

You are right, zero velocity do not mean zero acceleration. Assuming the pebble attached to the block during the oscillation, its acceleration has the highest magnitude at maximum displacement.
The solution might be correct if the box did not push the pebble at the top. The pebble is not fixed, so the block can only push it. But for that, an acceleration higher than g would be needed. You can calculate the angular frequency of oscillation, assuming that the block and pebble move together, and from that you get the maximum downward acceleration as amplitude times w². It is less than g!

ehild

 

[kerimek]

I can provide a response to your question. In this scenario, the vertical simple harmonic motion concept is being applied to the suspended block and the small stone placed on it. This concept states that when an object is attached to a spring and is displaced from its equilibrium position, it will experience a restoring force that is directly proportional to the displacement and acts in the opposite direction.

In this case, when the small stone is placed on the block, it causes an additional 5 cm of displacement, resulting in a greater amplitude of 12 cm for the spring's oscillations. The net force acting on the stone is the sum of the forces acting on it, which includes the force of gravity and the force of the spring.

As you correctly pointed out, the force of the spring is not zero even when the spring is not moving, as it is still exerting a restoring force on the stone to bring it back to its equilibrium position. However, at the point of maximum upward displacement, the force of the spring is equal and opposite to the force of gravity, resulting in a net force of zero. This is because at this point, the stone is at its highest point and has no further potential energy to be converted into kinetic energy.

In terms of acceleration, you are correct in saying that the greatest magnitude of acceleration occurs at the maximum compression or stretch of the spring. However, at these points, the net force on the stone is not zero, as it is being accelerated in the opposite direction of the force of the spring.

Overall, the net force on the stone at the point of maximum upward displacement is Fnet= mg, where m is the mass of the stone and g is the acceleration due to gravity. This is because the force of the spring and the force of gravity are equal and opposite, resulting in a net force of zero.