Distance a spring has been compressed

[Joe_I_Am]

Homework Statement

.

A 20 kg mass, released from rest, slides 12 meters down a frictionless plane inclined at an angle of 30º with the horizontal and strikes a spring of spring constant K = 200 Newtons/meter as shown in the diagram above. Assume that the spring is ideal, that the mass of the spring is negligible, and that mechanical energy is conserved. Use g = 10 m/s², (sin30º = ½, cos 30º = 0.866)
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. Is the speed of the block a maximum at the instant the block strikes the spring? Justify your answer.

Homework Equations

(1/2)kx^2, (i/2)mv^2

The Attempt at a Solution

For part b, wouldn't I just have to solve

original energy 20*10*12sin(30)= (1/2)(200)x^2

for x?

I do this and I get ~3.46 meters for x, but I'm being told that this is not the right answer.

What am I doing wrong? If energy is conserved, then (1/2)kx^2 would have to equal the original mgh

 

[Doc Al]

What am I doing wrong? If energy is conserved, then (1/2)kx^2 would have to equal the original mgh

Don't neglect the additional change in height as the spring is compressed. (Measure h from the lowest point, not the point where the mass first touches the uncompressed spring.)

 

[nlightner]

.


Your approach for part b is correct. However, there may be a mistake in your calculation. The correct answer for the distance the spring has been compressed is 3.46 meters, which you have already calculated. Make sure you are using the correct values for mass, gravity, and the angle in your calculation. It is also possible that the answer given to you is incorrect. Double check your work and if you are still unsure, ask your teacher or a classmate for help.

As for part c, the block's speed is not a maximum at the instant it strikes the spring. This is because the block has been accelerating down the inclined plane due to the force of gravity. When it reaches the spring, it is still accelerating and its speed is still increasing. Therefore, the block's speed will be a maximum at some point after it strikes the spring. This is evident from the fact that the kinetic energy of the block will continue to increase as it compresses the spring, until it reaches its maximum compression.