Block dropped onto a spring down an incline

In summary, a block of mass 12 kg is released from rest on a frictionless incline of angle 30 degrees. It compresses a spring by 5.5 cm and momentarily stops. To find its distance from the rest position, k = 135 N/cm and h = 0.15 m are used in the law of conservation of energy. The speed of the block just as it touches the spring is found to be 1.7 m/s using the same equation. The approach and calculations used are correct.
  • #1
esoteric deviance
17
0
A block of mass m = 12 kg is released from rest on a frictionless incline of angle theta = 30 degrees. Below the block is a spring that can be compressed 2.0 cm by a force of 270 N. The block momentarily stops when it compresses the spring by 5.5 cm.

a) How far does the block move down the incline from its rest position to this stopping point?
b) What is the speed of the block just as it touches the spring?


Okay, so I got the answer to part a like this:
k = F/x = 270/2.0 = 135 N/m​
h = ((1/2)kx^2)/(mg) = 17.4 cm (used law of conservation of energy for this one)​
(L + x) = h/sin(30) = 35 cm​

But I'm having some trouble with part b :frown:.

Anyone think they can help me out a bit with part b?
 
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  • #2
The units for your k are not N/m, so be careful what you do next. You have everything you need to find L and L is proportional to the change in height of the mass from the initial point to where it touches the spring. Use conservation of energy again to find the KE and the velocity.
 
  • #3
Oh..yeeeah, meant to type N/cm sorry lol.

K, so I found L
L = (h/sin(30)) - x = 0.29 m​
(switched to meters b/c the answer in the book switched to meters, though I don't know why)​


and then used that to find the new h
h = Lsin(30) = 0.29sin(30) = 0.15 m​


which I then plugged into mgh = (1/2)mv^2 to find the velocity
v^2 = 2gh = 2(9.8)(0.15) = 2.94​
v = 1.7 m/s​


and I found the mgh = 1/2mv^2 by using the following
KE initial + PE initial = KE final + PE final​
0 + mgh = ((1/2)mv^2) + 0​


I know the answer is right, but did I find it the right way?
B/c someone was telling me that the h should = -Lsin(30) rather than +Lsin(30)...
 
  • #4
The way you defined things, the + sign is correct. Someone else might have defined the zero of potental energy at the top and used negatives from there. Your approach and calculation are fine.
 
  • #5
Ah, okay :smile:.


Thanks for the help ^_^.
 

Related to Block dropped onto a spring down an incline

1. What is the purpose of dropping a block onto a spring down an incline?

The purpose of this experiment is to observe and measure the relationship between the height at which a block is dropped and the resulting compression of a spring. This can help us understand the principles of potential energy, kinetic energy, and the elastic properties of a spring.

2. How does the angle of the incline affect the results of this experiment?

The angle of the incline can affect the results in a few ways. A steeper incline will result in a greater acceleration of the block, leading to a larger compression of the spring. Additionally, a steeper incline may also result in a greater loss of energy due to friction, which can affect the final compression of the spring.

3. What factors can affect the accuracy of the results in this experiment?

The accuracy of the results can be affected by various factors such as the accuracy of the measurements taken, the smoothness of the incline and surface, the air resistance, and the precision of the spring used. It is important to control these factors and take multiple trials to ensure accurate results.

4. Can this experiment be used to determine the spring constant of the spring?

Yes, this experiment can be used to determine the spring constant of the spring by measuring the compression of the spring at different heights and using the formula F = kx, where F is the force applied to the spring, k is the spring constant, and x is the distance the spring is compressed.

5. What are some real-world applications of this experiment?

This experiment can help us understand and analyze the behavior of springs in various systems, such as in shock absorbers, car suspensions, and pogo sticks. It can also be used in engineering and design to determine the required spring constant for a specific application.

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