Maximum oscillation amplitude for block

In summary, the problem involves a 1.0 kg mass riding on top of a 5.0 kg mass on a frictionless surface, with a spring constant of 50 N/m and a coefficient of static friction of 0.50. The question is asking for the maximum oscillation amplitude at which the upper block does not slip. To solve this, we can use the maximum friction force on the top block, which is \mu_s n (where n is the normal force, in this case equal to mg). Using Newton's second law, the maximum acceleration occurs at the extremities of the motion, and in simple harmonic motion, the maximum acceleration is a_{max} = A \omega^2. We can
  • #1
CoasterGT
6
0
Problem:

A 1.0 kg mass is riding on top of a 5.0 kg mass as it oscillates on a frictionless surface. The spring constant is 50 N/m and the coefficient of static friction between the two blocks is 0.50.

What is the maximum oscillation amplitude for which the upper block does not slip?


I don't know where to start. I have looked at trying to do it by looking at the total mechanical energy, but there are too many unknown variables. Any hints to help me get started would be appreciated.
 
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  • #2
CoasterGT said:
Problem:

A 1.0 kg mass is riding on top of a 5.0 kg mass as it oscillates on a frictionless surface. The spring constant is 50 N/m and the coefficient of static friction between the two blocks is 0.50.

What is the maximum oscillation amplitude for which the upper block does not slip?


I don't know where to start. I have looked at trying to do it by looking at the total mechanical energy, but there are too many unknown variables. Any hints to help me get started would be appreciated.
The max friction force on the top block is [itex] \mu_s n [/itex] where "n" is the normal force on that block, right? (in this case n is simply mg). Using Newton's second law, the force is maximu when th acceleration is maximum. The acceleration is maximum at the extremities of the motion. In shm, the maximum acceleration is [itex] a_{max} = A \omega^2 [/itex], right? So find the maximum friction force on the top block, use that to find its maximum acceleration so that it does not slip and then use that to find the maximum amplitude A.

Hope this helps

Patrick
 
  • #3
It did. Thank you very much!
 
  • #4
I don't quite understand this problem. I know the formulas to use, but I'm confused as to which mass I should use in the w=root (k/m) equation. Also, the force of friction is around 4.9N, would that also be the block's acceleration? what would that do?
 

Related to Maximum oscillation amplitude for block

What is the maximum oscillation amplitude for a block?

The maximum oscillation amplitude for a block is the farthest distance that the block can move from its equilibrium position while oscillating back and forth.

How is the maximum oscillation amplitude determined?

The maximum oscillation amplitude is determined by the initial conditions of the block, including the initial displacement, velocity, and any external forces or constraints acting on the block.

What factors affect the maximum oscillation amplitude for a block?

The maximum oscillation amplitude for a block can be affected by the block's mass, the strength of the spring or other restoring force, and any external forces or constraints acting on the block.

What happens if the maximum oscillation amplitude is exceeded?

If the maximum oscillation amplitude is exceeded, the block may experience a larger displacement than expected and may even lose contact with the surface it is resting on.

How does the maximum oscillation amplitude relate to the frequency of oscillation?

The maximum oscillation amplitude is inversely proportional to the frequency of oscillation. This means that as the frequency increases, the maximum oscillation amplitude decreases, and vice versa.

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