What Determines the Direction of Motion in a Plank and Spring System?

In summary, the conversation discusses the possibility of a block stopping and reversing its direction of motion. It is noted that the initial velocity of the block, Vo, can be any value except 0. The question is raised whether there is a range of velocities for which the block does not reverse direction. It is also mentioned that the block and plank will eventually have the same speed, regardless of the initial velocity. The conversation then considers the event of the block subsequently moving in the other direction relative to the plank, and the ways in which the block can transfer its initial kinetic energy to the plank. Finally, it is concluded that the event of the block stopping and reversing its direction relative to the plank is possible, and the conversation ends with a thank
  • #1
Rikudo
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Homework Statement
A block of mass m is placed on a plank of mass M that rests on a frictionless floor. The block is connected to an obstruction on the plank with the help of a light spring of stiffness k as shown in the figure . Coefficient of friction between the plank and the block is μ. Initially when the spring is relaxed , the block is given a velocity Vo towards the obstruction . If the block stops on the plank before reversing its direction of motion relative to the plank , find the velocity Vo . Acceleration due to gravity is g.
Relevant Equations
Momentum conservation
Work - Energy theorem (?)
Screenshot_2022-08-21-08-03-19-02.png

I don't understand the question. If it want the mass to stop and reverse its direction, then does that not means ##vo## can be anything? (obviously not 0 since it will make the system not moving at all).
 
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  • #2
Rikudo said:
If it want the mass to stop and reverse its direction, then does that not means ##vo## can be anything?
Could there be some range of velocities for which it does not reverse direction?
 
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  • #3
Consider that initial velocity Vo is measured respect to both, the plank and the floor.
By the time the block stops respect to the plank ("the block stops on the plank before reversing its direction of motion"), the plank has acquired certain velocity respect to the floor; therefore, its velocity respect to the floor must match that certain plank's velocity.
 
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  • #4
When they are in motion, the mass's speed will decrease while the plank's will increase. Eventually, they will have the same speed (which means at this instant, the mass is not moving with respect to the plank). No matter what Vo is, they will undergo this event.
 
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  • #5
Rikudo said:
No matter what Vo is, they will undergo this event.
That is for the event that the block comes to rest relative to the plank. I asked about the event that the block subsequently moves in the other direction relative to the plank.
 
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  • #6
Consider as well that the sliding block has two simultaneous ways to transfer part of its initial KE to the plank: constant force of friction and variable elastic force of the spring, both reducing its velocity.
 
  • #7
Now I understand. Thank you, all of you!
 
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What is a block on plank with spring?

A block on plank with spring is a simple physics experiment that involves a block placed on top of a plank, with a spring attached to the block and the other end of the spring fixed to a support. The block is then displaced from its equilibrium position and released, causing it to oscillate back and forth on the plank.

What is the purpose of this experiment?

The purpose of this experiment is to demonstrate the principles of simple harmonic motion and the relationship between force, mass, and acceleration. It also allows for the calculation of the spring constant, which is an important factor in many other physics experiments.

What factors affect the oscillation of the block?

The oscillation of the block is affected by several factors, including the mass of the block, the spring constant, the amplitude of the displacement, and the presence of any external forces such as friction or air resistance.

How is the spring constant calculated in this experiment?

The spring constant can be calculated by measuring the displacement and period of the oscillation of the block. Using the equation T=2π√(m/k), where T is the period, m is the mass of the block, and k is the spring constant, the value of k can be determined.

What real-life applications does this experiment have?

The principles demonstrated in this experiment have many real-life applications, such as in the design of shock absorbers, musical instruments, and pendulum clocks. It also helps in understanding the behavior of systems in which there is a restoring force, such as springs and pendulums.

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