Springs, Kinetic Friction, and Distance help me please

[PhysicsOPhun]

Springs, Kinetic Friction, and Distance...help me please

1. In the figure below a 1.4 {\rm kg} block is held at rest against a spring with a force constant k = 740 {\rm N/m}. Initially, the spring is compressed a distance d. When the block is released, it slides across a surface that is frictionless except for a rough patch of width 5.0 {\rm cm} that has a coefficient of kinetic friction mu = 0.44.

2. Questions: Find d such that the block's speed after crossing the rough patch is 2.3 {\rm m/s}. /b]



[PLAIN][PLAIN]http://img84.imageshack.us/img84/1249/111it7.jpg






3. Relevant equations: Ok, I know how to apply the kinetic friction to the mass but how do I start this equation? What effect does the force of the spring have on the velocity and how does the defined distance work out? I really want to understand this but am afraid that conceptually it's hard for me to work out. Any pointers or all applicable equations would greatly be appreciated so I could get on with this. I have been doing Chemistry since 6am and my brain is just not tickin right now...



I apologize if I messed up the template, this is my first post so I will hope to not make any mistakes again if i did this time.

Also, my work as of right now for this problem consists of 2 pages front to back with writing all over, I really wouldn't know where to start and am so confused at this point that I could really use a push.

 

[Astronuc]

Starting with 2.3 m/s speed of the block after it passes, compute the kinetic energy of the block.

When the block passed over the rough surface, friction did work against the block, so some energy was lost. Determine the work done on the block. The kinetic energy of the block before it enountered the rough surface must be the sum of the KE after and the work done by friction.

The kinetic energy of the block comes from the energy stored in the spring, which is related to the deflection of the spring and spring constant.

 

[Moetasim]

Thank you for your question. It seems like you are working on a problem involving springs, kinetic friction, and distance. These concepts may seem daunting at first, but with some practice and understanding, you will be able to solve this problem and any others that come your way.

To start, let's break down the problem into smaller parts and identify the relevant equations. We have a block with a mass of 1.4 kg and a spring with a force constant of 740 N/m. The block is initially held at rest against the spring, which is compressed a distance d. When the block is released, it slides across a frictionless surface except for a rough patch with a coefficient of kinetic friction of 0.44 and a width of 5.0 cm. We are asked to find the distance d such that the block's speed after crossing the rough patch is 2.3 m/s.

First, let's consider the effect of the force of the spring on the block's velocity. The force of the spring is given by Hooke's Law, F = -kx, where k is the force constant and x is the displacement from the equilibrium position. Since the block is initially at rest, the spring force is the only force acting on it before it is released. This means that the spring force will accelerate the block, causing it to move in the direction of the spring's force.

Next, let's consider the effect of kinetic friction on the block's motion. Kinetic friction is a force that opposes the motion of an object and is given by the equation Fk = μkN, where μk is the coefficient of kinetic friction and N is the normal force. In this case, the rough patch has a coefficient of kinetic friction of 0.44 and the block's weight is the normal force acting on it. As the block slides across the rough patch, the kinetic friction force will act in the opposite direction of the block's motion, slowing it down.

Now, let's put these concepts together to solve the problem. We know that the spring force will accelerate the block and the kinetic friction force will decelerate it. Using the equation F = ma, where F is the net force, m is the mass, and a is the acceleration, we can set up the following equation:

-kx - μkN = ma

Since we are given the mass of the block and the force constant of the spring, we can