Solving Exploding Spring: Find Car Speeds

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In summary, the masses of the carts initially have the same KE and the spring pushes them apart with a speed of .5m1v1^2+.5m2v2^2.
  • #1
Juntao
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A massless spring of spring constant 20 N/m is placed between two carts. Cart 1 has a mass M1 = 5 kg and Cart 2 has a mass M2 = 2 kg. The carts are pushed toward one another until the spring is compressed a distance 1.7 m. The carts are then released and the spring pushes them apart. After the carts are free of the spring, what are their speeds?

a) velocity of car 1 =?
b) velocity of car 2 =?

I know that for this problem, I got to use conservation of momentum and conservation of energy, but I don't even know how to even start off this problem. Major help needed!
 
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  • #2
You need to apply two equations:
1. Conservation of energy.
2. Conservation of momentum.
 
  • #3
Just give it a try. Here are some hints.

What's the initial momentum of the system? (Hint: the masses start from rest.) What's the final momentum (m1v1 + m2v2)?

What's the initial KE of the masses? (see previous hint).

How much energy is stored in the compressed spring?

What's the final KE of the masses?
 
  • #4
Baby steps, right?

Ok. Initial momentum equals final momentum.
and I realized objects start from rest, so initial velocity is zero
thus,
initial momentum =0
so 0=(m1v1+m2v2)
or -m1v1=m2v2

Ok, that part wasnt so bad.

Initial KE=0
Final KE= .5m1v1^2+.5m2v2^2

Spring potential energy=.5kx^2

ah, so yea, I guess then .5m1v1^2+.5m2v2^2=.5kx^2
 
Last edited:
  • #5
Originally posted by Juntao
So for the energy part, is it going to be like the KE of both carts equal the potential energy of the spring?

so like this:
.5*m1v1^2+.5m2v2^2=.5kx^2
Yep. You're half-way home.
 
  • #6
Awesome, I figured it out...Lol, it took me like 1 hr of frustration, then like 5 mins of guidance here, and I got it in like 10 mins. :-)
 
  • #7
Sweet. :smile:
 

1. How do I determine the velocity of a car using an exploding spring?

The velocity of a car can be determined by measuring the distance traveled by the car during the explosion of the spring. This distance can then be used in the formula v = √(2kd), where v is the velocity, k is the spring constant, and d is the distance traveled. By plugging in the known values of k and d, the velocity of the car can be calculated.

2. How accurate is the method of using an exploding spring to find car speeds?

The accuracy of this method depends on the precision of the instruments used to measure the distance traveled by the car and the spring constant. The more precise the measurements, the more accurate the results will be. However, other factors such as air resistance and friction may affect the accuracy of the calculated velocity.

3. Can this method be used for all types of cars?

Yes, this method can be used for all types of cars as long as the necessary measurements are taken accurately. However, the spring constant may vary for different types of springs, so it is important to use the correct value for the specific spring being used.

4. Is this method safe to use?

The use of an exploding spring to find car speeds should only be performed by trained professionals in a controlled environment. It involves potential risks such as flying debris and loud noises. Safety precautions should always be taken to ensure the well-being of the individuals involved.

5. Are there any other methods for determining the velocity of a car?

Yes, there are other methods for determining the velocity of a car, such as using a radar gun, a speedometer, or a GPS device. These methods may be more practical and safer for everyday use. The exploding spring method is typically used for scientific research purposes or in special circumstances where other methods may not be feasible.

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