Solving AP Physics: Spring Compression Problem

[devolg632104]

Homework Statement

A 20 kg mass released from rest slides down a frictionless plane inclined at an angle of 30 deg with the horizontal and strikes a spring of spring constant K=200 Newtons/meter. Assume that the spring is ideal, that the mass of the spring is negligible, and that mechanical energy is conserved. Use g = 10 m/s^2.

a. Determine the speed of the block just before it hits the spring.
b. Determine the distance the spring has been compressed when the block comes to rest.
c. Determine the distance the spring is compressed when the block reaches maximum speed.

Homework Equations

a. V^2=Vo^2 +2ad
b. PE spring = 1/2kx^2
PE = mgh
KE = 1/2mv^2
PE +KE = PE spring
c. Totally clueless

The Attempt at a Solution

For part a, I found what the force of gravity was in the x direction, divided by the mass, and then found the acceleration. Then I plugged that and the given variables into the kinematic equation

V^2=Vo^2 +2ad

And the answer I got was 7.75 m/s

For part b, I tried Ug+K=Us, but I cannot determine the height so I do not know how to do this.

Thanks for the help!

 

[Doc Al]

For part b, I tried Ug+K=Us, but I cannot determine the height so I do not know how to do this.

The amount of spring compression and the change in height are related by a little trig.

 

[thomate1]

I would like to commend you for attempting to solve this problem and using the relevant equations to find the speed of the block. However, I would like to point out that for part a, you have only calculated the final speed of the block just before it hits the spring. To find the initial speed, you would need to consider the block's motion before it reaches the spring.

For part b, you correctly identified that the potential energy of the block at the top of the incline would be converted into the potential energy of the compressed spring and the kinetic energy of the block at the bottom of the incline. However, to find the height, you can use the given information about the angle of the incline and the gravitational acceleration to find the vertical height of the incline. Then, you can use this height and the given angle to find the horizontal distance traveled by the block, which will be the same as the distance the spring has been compressed.

For part c, you can use the principle of conservation of energy to find the distance the spring is compressed when the block reaches its maximum speed. This means that the total energy of the system (kinetic energy of the block and potential energy of the spring) will remain constant throughout the motion. You can equate the initial and final energies and solve for the distance the spring is compressed.

I hope this helps and good luck with your problem-solving!