Springs, Kinetic Friction, and Distance help me please

In summary, the problem involves finding the distance the spring is compressed and the work done by friction in order to determine the kinetic energy of the block before and after it passes over the rough surface.
  • #1
PhysicsOPhun
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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.

 
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  • #2
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.
 
  • #3




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
 

Related to Springs, Kinetic Friction, and Distance help me please

1. What is a spring and how does it work?

A spring is a mechanical device that is designed to store and release energy. When a spring is compressed or stretched, it stores potential energy, which is then released when the spring returns to its original shape. This is known as elastic potential energy.

2. How does kinetic friction affect the movement of objects?

Kinetic friction is the force that opposes the movement of two surfaces that are in contact with each other. When an object is moving, kinetic friction acts in the opposite direction of its motion, causing it to slow down. This force is dependent on the type of surfaces in contact and the amount of force pressing them together.

3. Can the distance a spring is compressed or stretched affect its potential energy?

Yes, the distance a spring is compressed or stretched directly affects its potential energy. As the distance increases, so does the potential energy stored in the spring. This is because the spring must use more force to stretch or compress over a longer distance, resulting in more potential energy being stored.

4. How is the amount of kinetic friction calculated?

The amount of kinetic friction can be calculated using the formula Fk = μkN, where Fk is the kinetic friction force, μk is the coefficient of kinetic friction, and N is the normal force between the two surfaces. The coefficient of kinetic friction is a number that represents the roughness of the surfaces in contact.

5. What factors can affect the distance an object travels when released from a spring?

The distance an object travels when released from a spring can be affected by several factors, including the initial force applied to the spring, the mass of the object, the spring constant (k), and the amount of potential energy stored in the spring. These factors can also affect the speed and direction of the object's motion.

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