Elastic Potential Energy

In summary, Physics students are testing an old bed spring which is compressed 4cm when a force of 4 N is applied. This spring is secured to a wall and a bowling ball of 4kg is roled into it so that it hits at a speed of 2m/s. The compression force is 3.5 cm when the ball is hitting at a speed of 1 m/s. When the ball is hitting at a speed of 1.9 m/s, the compression force is 5.2 cm.
  • #1
Cummings
53
0
Physics students are testing an old bed spring which is compressed 4cm when a force of 4 N is applied. This spring is secured to a wall and a bowling ball of 4kg is roled into it so that it hits at a speed of 2m/s

1. Calculate the compression of the spring when the speed of the ball has been reduced to 1m/s by the spring

2. What is the value of the compression force when the speed of the ball is 1.9 ms to the right?

3. Calculate the compression of the spring what the ball has momentarily come to rest.

For the first question:
the kinetic energy of the ball at 2ms = .5 * 4 * (2 squared) = 8 N
the kinetic energy of the ball at 1ms = .5 * 4 * (1 squared) = 2 N

thus the kinetic energy transferred to the spring is 6 N

Now, .5k(x squared) gives us the potential energy in the spring.
so 6 = .5k(x squared)
k is the spring ocnstand which can be taken from 4N/.04 Meters = 100
6 = 50(x squared)
X = Square root of (6/50)
= .346 meters = 34.6 cm?

thats all i can get at the mo..i need help :)
 
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  • #2
Actually, you've done the hard part! Yes, subtracting the two kinetic energies gives the increase in potential energy and you have calculated the amount of compression correctly.

For Problem 2 repeat your solution to problem 1, using 1.9 m/s instead of 1 m/s for the final velocity. Once you have found the amount of compression, multiply that by k (force= k*compression) to find the force asked for.

For Problem 3, do the same as for problem 2 except that, now, the final velocity is 0 m/s. Find the compression as you did in problem 1 and then multiply by k to find the force.
 
  • #3
Uh... note though that the units of energy are Joules, or J, not Newtons (N).
 
  • #4
FZ+ yes true that..Jouls not Newtons just another simple error.

From the textbook i was working out of, it said it was 3.5cm compression, not 35cm so i think that would just be another typo.
 

1. What is Elastic Potential Energy?

Elastic potential energy is the energy stored in an object when it is stretched or compressed. It is a type of potential energy that is related to the amount of elastic potential an object has.

2. How is Elastic Potential Energy calculated?

Elastic potential energy can be calculated by multiplying the force applied to an object by the distance the object is stretched or compressed. The equation for elastic potential energy is PE = 1/2 * k * x^2, where PE is the potential energy, k is the spring constant, and x is the distance the object is stretched or compressed.

3. What is the difference between Elastic Potential Energy and Gravitational Potential Energy?

Elastic potential energy is the energy stored in an object due to its deformation, while gravitational potential energy is the energy an object has due to its position in a gravitational field. Elastic potential energy is dependent on the object's elasticity, while gravitational potential energy is dependent on the object's mass and height.

4. What are some everyday examples of Elastic Potential Energy?

Some everyday examples of elastic potential energy include a stretched rubber band, a compressed spring, a trampoline, and a bow and arrow. When these objects are released, the elastic potential energy is converted into kinetic energy, resulting in movement.

5. How is Elastic Potential Energy used in real-life applications?

Elastic potential energy has a variety of real-life applications. For example, it is used in bungee jumping to provide a thrilling experience as the elastic potential energy is converted into kinetic energy during the jump. It is also used in various mechanical devices such as shock absorbers, catapults, and pogo sticks. Additionally, elastic potential energy is important in the design of bridges and buildings, as it allows them to flex and absorb energy during earthquakes or strong winds.

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