What is the maximum compression of the spring xmax during the collisio

In summary, to solve this problem, you need to consider the conservation of both energy and linear momentum. During the instant when the spring is at its maximum compression, the carts can be modeled as a system with no external forces, meaning that linear momentum must be conserved. The hint given suggests modeling the carts as connected by a rigid rod, and considering their relative velocities.
  • #1
Elleboys
4
0

Homework Statement


A 4.80kg cart has a spring with spring constant 3200N/m attached to its front, parallel to the ground. This cart rolls at 4.40m/s toward a stationary cart with mass 1.60kg .


Homework Equations


PEspiring = 1/2*kx^2
KE = 1/2*mv^2


The Attempt at a Solution


I was setting up the equations to be 1/2*kx^2 = 1/2*mv^2
So I got x = sqrt(mv^2/k)
But as I put it into mastering physics, it said 'If all the kinetic energy is converted to spring potential energy, then the speed of both carts is zero and the momentum is zero. This means the momentum is not conserved. Think about the motion. When the spring is compressed the most, the carts are the closest together. How are their motions related at this point?'
I don't quite understand what it is talking about so please help
 
Physics news on Phys.org
  • #2
Hello Elleboys.

The hint they are giving you is that momentum must be conserved as well as energy.

Can you use conservation of momentum to deduce the speed of the each cart at the instant the spring is compressed the most? (The second cart does not remain stationary - it is free to move.)
 
  • #3
Elleboys said:

Homework Statement


A 4.80kg cart has a spring with spring constant 3200N/m attached to its front, parallel to the ground. This cart rolls at 4.40m/s toward a stationary cart with mass 1.60kg .


Homework Equations


PEspiring = 1/2*kx^2
KE = 1/2*mv^2


The Attempt at a Solution


I was setting up the equations to be 1/2*kx^2 = 1/2*mv^2
So I got x = sqrt(mv^2/k)
But as I put it into mastering physics, it said 'If all the kinetic energy is converted to spring potential energy, then the speed of both carts is zero and the momentum is zero. This means the momentum is not conserved. Think about the motion. When the spring is compressed the most, the carts are the closest together. How are their motions related at this point?'
I don't quite understand what it is talking about so please help

In any system with no external forces acting upon it, linear momentum is always conserved. So you need a conservation of momentum equation here.

What the hint is telling you is to consider what happens when the spring is at its maximum compression. This only happens for an instant (before this the spring is compressing, and after it, it's expanding). But during that instant, the spring can be modeled as a rigid link connecting the two carts. What happens when you set two carts connected by a rigid rod in motion? What's their velocity relative to each other?
 

1. What is the maximum compression of the spring (xmax) during the collision?

The maximum compression of a spring during a collision is the point at which the spring is at its most compressed state. This value is denoted as "xmax" and can be calculated using the formula xmax = (m*v)/(k), where m is the mass of the object colliding with the spring, v is the velocity of the object, and k is the spring constant. This value represents the maximum displacement of the spring from its equilibrium position.

2. How is the maximum compression of a spring during a collision determined?

The maximum compression of a spring during a collision is determined by several factors including the mass of the object colliding with the spring, the velocity of the object, and the spring constant. These values are used in the formula xmax = (m*v)/(k) to calculate the maximum compression of the spring.

3. What happens to the maximum compression of a spring as the velocity of the object increases?

As the velocity of the object increases, the maximum compression of the spring also increases. This is because the kinetic energy of the object is transferred to the spring upon collision, causing it to compress further. Therefore, the higher the velocity of the object, the greater the maximum compression of the spring will be.

4. How does the spring constant affect the maximum compression of a spring during a collision?

The spring constant (k) is a measure of how stiff the spring is. As the spring constant increases, the maximum compression of the spring also increases. This is because a higher spring constant means that the spring is more resistant to compression, and therefore requires more energy to compress it to its maximum point.

5. Can the maximum compression of a spring be negative?

No, the maximum compression of a spring cannot be negative. This is because the maximum compression represents the greatest displacement of the spring from its equilibrium position. Since displacement is a vector quantity, it cannot have a negative value. Therefore, the maximum compression of a spring can only be a positive value or zero.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
22
Views
444
  • Introductory Physics Homework Help
Replies
15
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
408
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
993
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
4K
  • Introductory Physics Homework Help
Replies
2
Views
1K
Back
Top