Block held against a spring going up a frictionless plane

In summary, the problem involves a 3 kg block being held against a spring with a spring constant of 580 N/m at the bottom of a frictionless 25 degree incline. The spring is compressed 0.18m and the task is to find how far along the incline the block will go when released. By calculating the potential energy of the spring and equating it to the potential energy of the block at its maximum height, the distance along the incline can be found. This does not require finding the speed of the block at any point.
  • #1
TaxiDriver113
2
0

Homework Statement


A 3 kg block is held against a spring (k=580nt/m) at the bottom of a frictionless 25 degree incline. The spring is compressed 0.18m. How far along the incline does the block go when released.

Homework Equations


Usp=1/2kx^2

The Attempt at a Solution


So far the only thing I've been able to do was calculate the velocity which i got to be 1.65m/s if I did it correctly.

Usp= 1/2 * 580 * .18^2
= 9.396

then I did this equation but I didn't know exactly what h was that I was trying to calculate. I think i just ended up calculating how much the spring was compressed and I already knew that.

9.396 + (1/2)(3)(0) = (3)(9.8)(h) + (1/2)(3)(1.654^2)
9.396 = 29.4h + 4.103
h = .18
 
Last edited:
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  • #2
did I not supply enough information?
 
  • #3
Welcome to PF.

The PE at the bottom should really give you your height shouldn't it?
 
  • #4
TaxiDriver113 said:

Homework Statement


A 3 kg block is held against a spring (k=580nt/m) at the bottom of a frictionless 25 degree incline. The spring is compressed 0.18m. How far along the incline does the block go when released.


Homework Equations


Usp=1/2kx^2



The Attempt at a Solution


So far the only thing I've been able to do was calculate the velocity which i got to be 1.65m/s if I did it correctly.

The speed at what position?

Actually, you don't need to find any speed to solve the problem. At the beginning and at the end of the motion (at the max height) the speed is zero.
Usp= 1/2 * 580 * .18^2
= 9.396

then I did this equation but I didn't know exactly what h was that I was trying to calculate. I think i just ended up calculating how much the spring was compressed and I already knew that.

9.396 + (1/2)(3)(0) = (3)(9.8)(h) + (1/2)(3)(1.654^2)
9.396 = 29.4h + 4.103
h = .18

You could simply do

9.396 J = 3 * 9.8 * h

find h and then use the angle to find the distance along the incline.
 

Related to Block held against a spring going up a frictionless plane

1. What is the equation for the force of a block held against a spring going up a frictionless plane?

The equation for the force of a block held against a spring going up a frictionless plane is F = kx, where F is the force, k is the spring constant, and x is the displacement from the equilibrium position.

2. How does the angle of the plane affect the force of the block against the spring?

The angle of the plane does not affect the force of the block against the spring. As long as the plane is frictionless, the force will be determined solely by the spring constant and the displacement of the block.

3. Does the mass of the block have an impact on the force of the spring?

The mass of the block does not have an impact on the force of the spring. The force is determined by the spring constant and the displacement of the block, not its mass. However, the mass of the block will affect its acceleration up the plane.

4. What is the relationship between the displacement of the block and the force of the spring?

The relationship between the displacement of the block and the force of the spring is directly proportional. This means that as the displacement increases, the force also increases, and vice versa.

5. How does friction play a role in the movement of the block up the plane?

Friction does not play a role in the movement of the block up the plane in this scenario since the plane is assumed to be frictionless. However, in real-world situations, friction would oppose the movement of the block and affect its acceleration.

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