Inelastic Collisions: Solving for Spring Displacement

In summary, two blocks with masses 1.4 kg and 2.0 kg collide on a frictionless surface, with one block initially at rest and the other traveling at 4.0 m/s. They stick together and come to a stop, causing the spring between them to compress. By using the equation for inelastic collisions, the velocity of the combined blocks after collision can be found, and then the kinetic energy of the combined blocks can be determined. The spring constant of 170 N/m is used to calculate the energy stored in the compressed spring, which is equal to 1/2kx^2. The resulting displacement of the spring is 0.33 m.
  • #1
patelkey
16
0

Homework Statement



In the figure below, block 2 (mass 1.4 kg) is at rest on a frictionless surface and touching the end of an unstretched spring of spring constant 170 N/m. The other end of the spring is fixed to a wall. Block 1 (mass 2.0 kg), traveling at speed v1 = 4.0 m/s, collides with block 2, and the two blocks stick together. When the blocks momentarily stop, by what distance is the spring

Homework Equations



m1v1=m2v2

The Attempt at a Solution


I attempted the solution but I am confused about the 170N/m
How would I use that information and relate it to the equations of inelastic collision?
 
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  • #2
Find the velocity of the combined blocks after collision. Then find the KE of the the combined blocks.
What is the expression for the energy stored in a compressed spring?
 
  • #3
ohhh okk i got it
I had to use W=1/2kx^2
they gave k and i figured out W through the KE equation.
it was 0.33 m if you were curious.
 

What is an inelastic collision?

An inelastic collision is a type of collision in which the kinetic energy of the objects involved is not conserved. This means that some of the initial kinetic energy is converted into other forms, such as heat or sound, during the collision.

What is the difference between an inelastic collision and an elastic collision?

In an elastic collision, the kinetic energy of the objects involved is conserved, meaning that no energy is lost during the collision. In an inelastic collision, some of the initial kinetic energy is converted into other forms.

How do you solve for spring displacement in an inelastic collision?

To solve for spring displacement in an inelastic collision, you need to use the equation for conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision. You also need to consider the energy lost in the collision, which can be calculated using the coefficient of restitution.

What factors affect the spring displacement in an inelastic collision?

The factors that affect the spring displacement in an inelastic collision include the masses and velocities of the objects involved, the coefficient of restitution, and the stiffness of the spring.

Can spring displacement be negative in an inelastic collision?

Yes, spring displacement can be negative in an inelastic collision. This indicates that the spring has been compressed or stretched in the opposite direction of the initial displacement. In some cases, the spring may return to its original position after the collision, resulting in a negative displacement.

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