Work-energy principle for a block fired up a vertical track

[Andrew1234]

Homework Statement

The problem is attached.

Relevant Equations

Work energy principle

I know how to solve the problem but have a question related to it. When the block is initially released from the spring the spring, having been pulled back, should give an initial velocity to the block. In that case why is the block's initial velocity zero?

 

[Lnewqban]

What are you calling block?
It seems to me that there is a pre-compression of the spring before the plunge is pulled back and then released and then hits the ball that has been in repose.

 

[haruspex]

When the block is initially released from the spring the spring, having been pulled back, should give an initial velocity to the block. In that case why is the block's initial velocity zero?

The question is a little unclear, but I believe the idea is that when the plunger is pulled back, compressing the spring further, the ball stays in contact with it. Thus, when the plunger is released the ball has acceleration but not velocity.

I note that the question describes it as a ball, not a block, and refers to the existence of friction. It follows that the ball would make rolling contact with the track, though not immediately. Assuming the ball is uniform, 2/7 of the KE imparted by the spring will be lost to friction, and at the point where the ball leaves the track 2/7 of its remaining KE will be in the form of rotational KE.
The statement that the ball is "of negligible size" does nothing to change that.

Where does the question come from?

 

[Andrew1234]

The question is a little unclear, but I believe the idea is that when the plunger is pulled back, compressing the spring further, the ball stays in contact with it. Thus, when the plunger is released the ball has acceleration but not velocity.

I note that the question describes it as a ball, not a block, and refers to the existence of friction. It follows that the ball would make rolling contact with the track, though not immediately. Assuming the ball is uniform, 2/7 of the KE imparted by the spring will be lost to friction, and at the point where the ball leaves the track 2/7 of its remaining KE will be in the form of rotational KE.
The statement that the ball is "of negligible size" does nothing to change that.

Where does the question come from?

Thanks for the clarification. I asked the question because it was not clear to me that the ball when released from the track has no initial velocity but accelerates forward, but thought that when the plunger comes in contact with it gives it a velocity rather than an acceleration.

 

[haruspex]

Thanks for the clarification. I asked the question because it was not clear to me that the ball when released from the track has no initial velocity but accelerates forward, but thought that when the plunger comes in contact with it gives it a velocity rather than an acceleration.

Yes, that is a possible interpretation; but then you would need more information, like the mass of the plunger and the coefficient of restitution in the impact.

 

[Andrew1234]

Do you mean that it is possible for the plunger when released to give the ball, which is initially at rest, both an initial velocity and acceleration?

 

[jbriggs444]

Do you mean that it is possible for the plunger when released to give the ball, which is initially at rest, both an initial velocity and acceleration?

Any initial acceleration is irrelevant except to the extent that it results in an initial velocity. Accelerations do not persist after the force is removed.

The plunger could impart some energy (determined in part by considering a coefficient of restitution) which could then be used to determine the initial velocity of the ball/block.

 

[haruspex]

Do you mean that it is possible for the plunger when released to give the ball, which is initially at rest, both an initial velocity and acceleration?

Strictly, no. To go instantly from stationary to a nonzero velocity implies an infinite acceleration, so an infinite force. But in sudden impacts the forces can be very high, and unknowable, so we use conservation of momentum as the main principle and take the transition from rest to velocity after impact as effectively instantaneous.

If we take what I believe is the intended model, we ignore the mass of the plunger and it makes contact with the ball from the start and until the spring returns to its initial state. So, no sudden impact. Since the plunger has no mass, all the lost spring PE goes into the KE of the ball.

Alternatively, pulling back the plunger causes it to lose contact with the ball. The spring PE goes into accelerating the plunger, which strikes the ball just before the spring reaches its initial state. The difficulty with this is arranging that nearly all that energy goes into the KE of the ball. Seems to need that the plunger and ball have equal mass and the collision is perfectly elastic.

Either way, you get the same velocity of the ball as it starts up the ramp.

As I posted, the more serious issue with the question is the energy that goes into friction and rotation. That makes a marked difference to the answer.