Textbook with spring sliding, use work-energy thm to solve

In summary, a 2.20kg textbook is compressed against a spring with a force constant of 220 N/m and a distance of 0.270m. When released, the textbook slides on a horizontal tabletop with a coefficient of kinetic friction of 0.30. Using the work-energy theorem, the textbook will move 1.2m from its initial position before coming to rest.
  • #1
makeAwish
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0
A 2.20kg textbook is forced against a horizontal spring of negligible mass and force constant 220 N/m, compressing the spring a distance of 0.270 m. When released, the textbook slides on a horizontal tabletop with coefficient of kinetic friction 0.30. Use the work-energy theorem to find how far the textbook moves from its initial position before coming to rest.


The answer is 1.2m. Can someone help me solve?

Thanks.


My attempt was:


change in KE + change in Elastic potential energy = -friction x distance
0 + (-0.5k(x^2)) = - 0.30(mg)(L)
L = 2.48m
 
Last edited:
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  • #2
Oh. I had a careless mistake! Ahh. Okay i know le. Haha Thanks.
 
  • #3



Hello,

Your attempt at solving the problem is on the right track. However, there are a few things that need to be clarified and corrected.

Firstly, the work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. In this case, the net work done on the textbook is equal to the work done by the spring (elastic potential energy) minus the work done by friction.

Secondly, the value of the gravitational acceleration (g) should be included in the equation for the work done by friction. Also, the distance traveled by the textbook should be represented by x, not L.

With these corrections, the equation should look like this:

Change in KE = Work done by spring - Work done by friction
0.5mv^2 = 0.5kx^2 - μmgx

Substituting the given values, we get:

0.5(2.20)v^2 = 0.5(220)(0.270)^2 - (0.30)(2.20)(9.8)x
v^2 = 3.704 - 6.804x

Since the textbook comes to rest at the end, its final velocity (v) is 0. Therefore, we can solve for x:

0^2 = 3.704 - 6.804x
x = 0.544 m or 54.4 cm

Therefore, the textbook moves 54.4 cm from its initial position before coming to rest.

I hope this helps. Keep up the good work!
 

Related to Textbook with spring sliding, use work-energy thm to solve

1. How do I use the work-energy theorem to solve problems involving a textbook with a spring sliding?

The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. In the case of a textbook with a spring sliding, we can use this theorem to determine the work done by the spring on the textbook and the resulting change in the textbook's kinetic energy.

2. What is the equation for calculating work done by a spring?

The equation for calculating work done by a spring is W = (1/2)kx^2, where W is the work done, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

3. How do I determine the spring constant for a given spring?

The spring constant can be determined by dividing the force applied to the spring by the resulting displacement of the spring. This can be represented by the equation k = F/x, where k is the spring constant, F is the applied force, and x is the displacement.

4. Can the work-energy theorem be used for a textbook with a spring sliding on an incline?

Yes, the work-energy theorem can be used for a textbook with a spring sliding on an incline. The gravitational potential energy of the textbook can be taken into account in the equation W = ΔK + ΔU, where W is the work done by the spring, ΔK is the change in kinetic energy, and ΔU is the change in gravitational potential energy.

5. Are there any other methods for solving problems involving a textbook with a spring sliding?

Yes, there are other methods for solving these types of problems, such as using conservation of mechanical energy or Newton's laws of motion. However, the work-energy theorem is a commonly used and effective method for solving problems involving a textbook with a spring sliding.

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