Calculating Potential Energy of Spring at Point A on Incline

[Xtasy]

A wooden block with mass 1.50 kg is placed against a compressed spring at the bottom of an incline of slope 30.0 degrees (point A). When the spring is realeased, it projects the block up the inline. At point B, a distance of 6.00 m up the incline from A, the block is moving up the incline at 7.00 m/s and is no longer in contact with the spring. The coefficient of kinetic friction between the block and incline is μk = 0.50. The mass of the spring is negligible. Calculate the amount of potential energy that was initially stored in the spring. Answer at the back of the book is 119 J.
This question is from University Physics 11th edition ques. 7.73 from Chapter 7.
I have been trying to do this question for like 3 hours and is sarting to piss me off . I am using the formula:

(PEb + PEs + KE)i + Wother = (PEb + PEs + KE)f
PEb= pot. enery. of block
PEs =pot. energy of spring
Woher= work other
i= initial
f= final
Since there is no kE initial i said its 0 and since there is PEb & PEs final i said its 0. So I hae
mgxsintheta + PEs + μmgcostheta = (1/2) mv^2
Plugged in values and tried to solve for PEs but can't get 119J. I have simiar problem due (with the values different) that is due in about a hour and half. So need help fast!

 

[Doc Al]

I am using the formula:

(PEb + PEs + KE)i + Wother = (PEb + PEs + KE)f

That's OK, as long as you realize that that Wother (the work done by friction) is negative--friction reduces the total mechanical energy.

PEb= pot. enery. of block
PEs =pot. energy of spring
Woher= work other
i= initial
f= final
Since there is no kE initial i said its 0 and since there is PEb & PEs final i said its 0.

If you call the initial PEb = 0, then the final PEb cannot be zero; if you call the final PEb = 0, then the initial PEb will be negative. The final spring PE will be zero.

So I hae
mgxsintheta + PEs + μmgcostheta = (1/2) mv^2

Redo this equation in the light of my comments above.

 

[m2003]

I understand your frustration and I am happy to help you with this problem. Let's break down the steps to solve it.

First, we need to understand that the potential energy stored in a spring is given by the formula PE = (1/2)kx^2, where k is the spring constant and x is the displacement from the equilibrium position. In this case, the wooden block is compressed against the spring, so the displacement is the initial length of the spring, which we can call x0.

Next, we can use the conservation of energy principle to solve this problem. This principle states that the total energy of a system remains constant, so the initial energy of the system (at point A) is equal to the final energy of the system (at point B). We can express this as:

PEi + KEi = PEf + KEf

Since kinetic energy is not mentioned in the problem, we can assume that it is zero at both points A and B.

Now, let's calculate the initial potential energy of the system at point A. We know that the block has a mass of 1.50 kg and is at a height of 0 (since it is at the bottom of the incline). Using the formula for potential energy, we get:

PEi = mgh = (1.50 kg)(9.8 m/s^2)(0 m) = 0 J

Next, we need to calculate the final potential energy of the system at point B. The block has now moved a distance of 6.00 m up the incline, so its height is now 6.00sin(30.0) = 3.00 m. The spring has also been compressed, so its displacement is now x = x0 - 6.00cos(30.0) = x0 - 5.20 m. We also know that the coefficient of kinetic friction is 0.50, so the work done by friction is:

Wfriction = μkmgd = (0.50)(1.50 kg)(9.8 m/s^2)(6.00 m) = 44.1 J

Using the formula for potential energy again, we get:

PEf = (1/2)k(x0 - 5.20 m)^2

Now, we can set up the equation for conservation of energy:

0 J + 0 J = (