Conservation of Energy of cart Problem

In summary, the 1.2 kg cart slides eastward down a frictionless ramp from a height of 1.8 m and then onto a horizontal surface where it has a head-on elastic collision with a stationary 2.0 kg cart cushioned by an ideal Hooke’s law spring. The maximum compression of the spring during the collision is 2.0 cm.
  • #1
physics411
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A 1.2 kg cart slides eastward down a frictionless ramp from a height of 1.8 m and then onto a horizontal surface where it has a head-on elastic collision with a stationary 2.0 kg cart cushioned by an ideal Hooke’s law spring. The maximum compression of the spring during the collision is 2.0 cm. (5.4)

  1. (a) Determine the spring constant.

    There were more parts to this question, however, I just need help with this portion of it.

    Law of Conservation of Energy:

    Et1 = Et2

    Force of Spring formula: F= kx

    Kinetic Energy, Gravitational Potential Energy, Elastic Potential Energy formulas will come in handy too.

    So in terms of solving this, I though I should find the final speed of the 1.2 kg cart which will end up being the initial velocity right before the collision takes place. I got 5.94 m/s for that (mgh = 1/2mv^2).

    Using this speed, how should i incorporate it to get the "k" value? I could use conservation of energy for the second block... (1/2mv^2 = 1/2kx^2)

    But I would need the speed for block 2, which is tricky because it was stationary initially..

    The answer for the k value is 6.6x10^4 N/m.

    Let me know what you guys suggest!
 
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  • #2
I just realized this should have been posted in the homework thread, if there is a moderator here, please feel free to move it to the appropriate homework thread for Physics.

Thanks!
 
  • #3
Here's an idea: Consider using the centre of mass reference frame to study the collision.
 
  • #4
Momentum is conserved and their velocities will be identical when the spring is fully compressed. That should give you another equation to work with. You could consider it as a totally inelastic collision up until the spring starts to return energy.
 
  • #5
sophiecentaur said:
Momentum is conserved and their velocities will be identical when the spring is fully compressed. That should give you another equation to work with. You could consider it as a totally inelastic collision up until the spring starts to return energy.
That's giving quite a lot away!
 
  • #6
Yes. I realize that but I didn't write any equations out for him / her.

PS I am not mean enough to be a H/H. :wink:
 

Related to Conservation of Energy of cart Problem

1. What is the conservation of energy in the cart problem?

The conservation of energy in the cart problem refers to the principle that energy cannot be created or destroyed, only transferred or converted from one form to another. In the cart problem, this means that the total energy of the system (cart and track) remains constant throughout the motion.

2. How is the conservation of energy applied in the cart problem?

In the cart problem, the conservation of energy is applied by considering the initial and final energy states of the system. This includes potential energy due to height, kinetic energy due to motion, and any other forms of energy present. The sum of the initial energy must equal the sum of the final energy, according to the law of conservation of energy.

3. What is an example of the conservation of energy in the cart problem?

One example of the conservation of energy in the cart problem is when a cart is released from the top of a hill and rolls down the incline, reaching a certain distance at the bottom. At the top, the cart has a certain amount of potential energy due to its height. As it rolls down, this potential energy is converted into kinetic energy, and at the bottom, the kinetic energy is equal to the initial potential energy.

4. What happens if the conservation of energy is violated in the cart problem?

If the conservation of energy is violated in the cart problem, it means that the total energy of the system is not constant. This could happen if external forces, such as friction or air resistance, are not taken into account. In this case, the final energy state of the system would not equal the initial energy state, and the calculations would be incorrect.

5. How does the conservation of energy relate to the concept of work in the cart problem?

In the cart problem, work is done when a force is applied to the cart, causing it to move a certain distance. The conservation of energy is related to work because the work done on the cart by an external force is equal to the change in the kinetic energy of the cart. This is another way of stating the law of conservation of energy - the work done on the cart is equal to the change in the total energy of the system.

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