Solving Friction & Spring Homework: .75kg Mass, 12000N/m Spring

[Seahawks]

Homework Statement

A mass of .75kg moves at 1.043m/s across a frictionless surface. Then it hits a .5m rough patch which has a coefficient of friction of .25. After moving through the rough patch, it continues on a frictionless surface. The mass then collides with a long spring. The spring coefficient is 12000N/m. Calculate how far the spring is compressed when the block just comes to rest.

Homework Equations

Spring Potential energy=.5*k*x^2
Kinetic Energy=.5*m*v^2
Friction force=μ(Fn)

The Attempt at a Solution

I tried finding the frictional force to be -1.837N and the the work due to friction to be -.9187J. Then I found the initial Kinetic Energy to be .408J. I am stuck here because the oeverall energy would be negative which means I can't find the answer involving the spring. How do I solve this correctly.

 

[Doc Al]

I tried finding the frictional force to be -1.837N and the the work due to friction to be -.9187J. Then I found the initial Kinetic Energy to be .408J. I am stuck here because the oeverall energy would be negative which means I can't find the answer involving the spring. How do I solve this correctly.

Your calculations look correct. Must be a typo or mistake in the problem statement. (If it's from a textbook, give a reference.)

Have you posted the question exactly as given, word for word?

 

[rude man]

You're right. The mass never makes it to the spring.

 

[Rellek]

Yeah, there must have been a typo or something. If you set your initial kinetic energy equal to the frictional force times the distance, you'll find that the object stops after .2218 meters on the rough patch, so there's no way for it to get past it.

In fact, the absolute minimum velocity to get past the rough patch would be about 1.567 m/s.

 

[HalfLostAndSearching]

As a scientist, it is important to approach problems like this with a systematic and organized approach. First, let's review the given information and understand the problem at hand. We have a .75kg mass moving at a velocity of 1.043m/s on a frictionless surface. It then encounters a rough patch with a coefficient of friction of .25, causing it to slow down. After the rough patch, it continues on a frictionless surface. Finally, it collides with a long spring with a coefficient of 12000N/m.

To solve this problem, we need to consider the conservation of energy principle. This principle states that energy cannot be created or destroyed, only transferred or transformed. In this case, we can use the initial kinetic energy of the mass to calculate the work done by friction, which will then be transferred to the spring as potential energy.

First, let's calculate the work done by friction. As you correctly stated, the frictional force can be calculated using the equation μ(Fn), where μ is the coefficient of friction and Fn is the normal force. In this case, the normal force will be equal to the weight of the mass, which can be calculated as mg, where g is the acceleration due to gravity. So, the frictional force can be calculated as μmg. Plugging in the values, we get a frictional force of -1.837N.

Next, we can calculate the work done by friction using the formula W=Fd, where W is work, F is force, and d is distance. In this case, the distance traveled on the rough patch is given as .5m. So, the work done by friction is -1.837N * .5m = -0.9187J.

Now, we can use the conservation of energy principle to calculate the final potential energy of the spring. We know that the initial kinetic energy of the mass is equal to the final potential energy of the spring. So, we can set up the equation as follows:

.5*m*v^2 = .5*k*x^2

Where m is the mass of the block, v is the final velocity after the rough patch (which we can calculate using the work done by friction and the initial kinetic energy), k is the spring coefficient, and x is the distance the spring is compressed.

Solving for x, we get x = √(m*v^2/k). Plugging in the values