Inelastic collision, spring compression

In summary: The block of mass m1 slid along the table with a speed of 10 m/s and the block of mass m2 slid along the table with a speed of 2.8 m/s. When they collided, the block of mass m1 compressed the spring by 1.8 kg, and the block of mass m2 compressed the spring by 4.4 kg.
  • #1
peachpie
6
0
A block of mass m1 = 1.8 kg slides along a frictionless table with a speed of 10 m/s. Directly in front of it, and moving in the same direction, is a block of mass m2 = 4.4 kg moving at 2.8 m/s. A massless spring with spring constant k = 1160 N/m is attached to the near side of m2, as shown in Fig. 10-35. When the blocks collide, what is the maximum compression of the spring? (Hint: At the moment of maximum compression of the spring, the two blocks move as one. Find the velocity by noting that the collision is completely inelastic to this point.)




velocity of center of mass = (m1v1 + m2v2)/ (m1 + m2), energy = 1/2mv^2 = 1/2kx^2



my velocity of center of mass = (1.8x10 + 4.4x2.8)/(1.8 + 4.4) = 4.89m/s, i plugged that into the energy equations [KE = 1/2(m1 + m2)(4.89)^2 = 1/2kx^2], and tried to solve for x. I also solved for x without finding the velocity of the center of mass using relative velocity; the faster object is traveling @ 7.2 m/s relative to the other object, so i plugged that into the energy equations. they were all wrong, and I'm not sure how to solve this.
 
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  • #2
peachpie said:
my velocity of center of mass = (1.8x10 + 4.4x2.8)/(1.8 + 4.4) = 4.89m/s,
OK.
i plugged that into the energy equations [KE = 1/2(m1 + m2)(4.89)^2 = 1/2kx^2], and tried to solve for x.
No, you have it backwards. That's the amount of energy that did not go into compressing the spring. (Compare this to the initial KE of the system.)

Mechanical energy is conserved. At the point of maximum compression both masses move as one, but the system has both KE and spring potential energy.
 
  • #3
got it, thanks!
Could you also help me with this one?

Two 2.0 kg masses, A and B, collide. The velocities before the collision are vA = 20i + 25j and vB = -15i + 10.0j. After the collision, v'A = -3.0i + 18j. All speeds are given in meters per second.
How much kinetic energy was gained or lost in the collision?

I tried finding the total velocity of each particle (v = square root of vx^2 + vy^2) before and after the collision and plugging them into the energy equation, 1/2mv^2, then finding the difference of the before and after KE.
 
  • #4
peachpie said:
I tried finding the total velocity of each particle (v = square root of vx^2 + vy^2) before and after the collision and plugging them into the energy equation, 1/2mv^2, then finding the difference of the before and after KE.
That's fine, but first you have to find v'B. Did you?
 
  • #5
Yes, i found v'B to be <8i, 17j> (which was correct)
 
  • #6
peachpie said:
Yes, i found v'B to be <8i, 17j> (which was correct)
Then just tabulate the total KE before and after. Hint: You can calculate the KE directly from the components. KE = 1/2m(Vi^2 + Vj^2). That might save you some arithmetic and reduce the chance for errors.
 
  • #7
ahh, a calculation error...
i got it now!
 

1. What is an inelastic collision?

An inelastic collision is a type of collision in which the total kinetic energy of the colliding objects is not conserved. This means that some of the kinetic energy is lost through the deformation or breaking of the objects involved.

2. What is spring compression?

Spring compression refers to the decrease in length or volume of a spring when a force is applied to it. This causes the spring to store potential energy, which can be released when the force is removed.

3. How does an inelastic collision affect the spring compression?

In an inelastic collision, the kinetic energy of the colliding objects is not conserved, so some of the energy is transferred to the spring, causing it to compress. The amount of compression depends on the mass and velocity of the objects involved in the collision.

4. What factors affect the amount of spring compression in an inelastic collision?

The amount of spring compression in an inelastic collision is affected by the mass and velocity of the objects involved, as well as the stiffness of the spring. A heavier object or a faster-moving object will cause more compression, while a stiffer spring will resist compression more.

5. How is the coefficient of restitution related to inelastic collisions and spring compression?

The coefficient of restitution is a measure of the elasticity of a collision. In an inelastic collision, the coefficient of restitution is less than 1, indicating that some kinetic energy is lost. This loss of energy is transferred to the spring, causing it to compress. The amount of compression can be calculated using the coefficient of restitution and other factors such as the mass and velocity of the objects involved.

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