Block/Spring Problem (Kinetic Energy)

In summary, a 13 kg block on a horizontal surface is attached to a horizontal spring with a spring constant of 4.3 kN/m. When pulled to the right and released from rest, the spring is stretched 13 cm beyond its relaxed length. The frictional force between the block and the surface is 100 N. The kinetic energy of the block can be calculated using the equations for elastic potential energy and kinetic energy. Taking into account the energy lost due to friction, the block's kinetic energy at a distance of 4.8 cm from its point of release can be found. The maximum kinetic energy attained by the block as it slides from its point of release to the point at which the spring is relaxed can also be
  • #1
lshine09
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Homework Statement



A 13 kg block on a horizontal surface is attached to a horizontal spring of spring constant k = 4.3 kN/m. The block is pulled to the right so that the spring is stretched 13 cm beyond its relaxed length, and the block is then released from rest. The frictional force between the sliding block and the surface has a magnitude of 100 N.

(a) What is the kinetic energy of the block when it has moved 4.8 cm from its point of release?

(b) What is the kinetic energy of the block when it first slides back through the point at which the spring is relaxed?

(c) What is the maximum kinetic energy attained by the block as it slides from its point of release to the point at which the spring is relaxed?f

Homework Equations



ElasticPotentialEnergy= 1/2ky^2
K=1/2mv^2
F=ma

The Attempt at a Solution



I honestly don't know where to begin. I used the numbers I was given to find the elastic potential energy at the beginning and came up with 36.34 J... and now I am not sure what to do.

(Us=1/2Ky^2
Us= (1/2)(4300N/m)(.13)^2
Us= (36.34J)
 
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  • #2
Use the conservation of energy, remembering to account for the energy lost by friction.
 

1. What is the "Block/Spring Problem"?

The Block/Spring Problem is a commonly used physics problem that involves a block attached to a spring. The block is placed on a horizontal surface and the spring is compressed, causing the block to be pushed forward. The goal of the problem is to determine the kinetic energy of the block as it moves away from the spring.

2. What is the formula for calculating kinetic energy in the Block/Spring Problem?

The formula for calculating kinetic energy in the Block/Spring Problem is KE = 1/2 * m * v^2, where m is the mass of the block and v is the velocity of the block. This formula is derived from the basic equation for kinetic energy, KE = 1/2 * m * v^2, where m is mass and v is velocity.

3. How does the spring constant affect the kinetic energy in the Block/Spring Problem?

The spring constant, also known as the stiffness of the spring, directly affects the kinetic energy in the Block/Spring Problem. A higher spring constant will result in a higher amount of kinetic energy, as the spring will exert a greater force on the block as it is compressed and released.

4. What is the role of friction in the Block/Spring Problem?

Friction plays a significant role in the Block/Spring Problem, as it is responsible for dissipating some of the kinetic energy of the block. Friction is caused by the block rubbing against the surface it is moving on, and it acts in the opposite direction of the block's motion. This means that the kinetic energy of the block will decrease over time as a result of friction.

5. Can the Block/Spring Problem be solved using conservation of energy?

Yes, the Block/Spring Problem can be solved using conservation of energy. This principle states that energy cannot be created or destroyed, only transferred from one form to another. In the Block/Spring Problem, the initial potential energy stored in the compressed spring is converted into kinetic energy as the block moves, and this can be calculated using the conservation of energy equation, PE = KE.

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