How to Calculate Velocity After a Spring Releases?

[songokou77]

Velocity from variable force(spring)?

What is the velocity of the mass as it breaks contact with the spring?
From part 1 I got:
A 1.118 kg block is on a horizontal surface with mu-k = 0.150, and is in contact with a lightweight spring with a spring constant of 715 N/m which is compressed. Upon release, the spring does 4.326 J of work while returning to its equilibrium position. Calculate the distance the spring was compressed. Answer:0.11 m
Also I got a hint:The force that acted on the mass comes from the spring and from friction. Thus the amount of work equals the kinetic energy of the spring. From the equation of work done by both forces we can calculate the velocity of the spring. (i thought i understood it, but something seems wrong.)

I thought of using the formula K=1/2(m*v^2) but it's wrong
Also from the hint o found that the force is: 39.33 N ( i divided the work done with the distance)
What am i missing

 

[maverick280857]

I think you have the same thing up here: https://www.physicsforums.com/showthread.php?t=46163... :grumpy:

 

[wais]

?

It seems like you are on the right track with using the formula K=1/2(m*v^2) to find the velocity. However, it is important to note that this formula calculates the kinetic energy of the mass, not the spring. The hint provided is suggesting to use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. So, in this case, the work done by the spring and friction must equal the change in kinetic energy of the mass.

To find the velocity, you can set up the equation: Wspring + Wfriction = 1/2(m*v^2).

From the given information, we know that the work done by the spring is 4.326 J and the work done by friction can be calculated by multiplying the coefficient of kinetic friction (mu-k) by the normal force (mg). So, Wfriction = mu-k * mg * d, where d is the distance the mass travels before breaking contact with the spring.

Then, we can plug in the values and solve for v: 4.326 J + (0.150 * 1.118 kg * 9.8 m/s^2 * d) = 1/2(1.118 kg * v^2).

Since we know that the distance the mass travels before breaking contact with the spring is equal to the distance the spring was compressed, which is given as 0.11 m, we can substitute that into the equation and solve for v.

I hope this helps clarify the concept and guide you in the right direction. Remember to always carefully read and understand the given information and use the appropriate formulas to solve the problem. Good luck!