Elastic Potential Energy Problem

In summary, when a 1.2 kg spring laboratory cart with a spring constant of 65.0 N/m is compressed 8.0 cm against a wall, the compression of the spring when the cart's velocity is 42.0 cm/s is 5.6 cm. This takes into account the initial displacement of 8 cm when the cart is held against the wall.
  • #1
phizics09
38
1

Homework Statement


A 1.2 kg spring laboratory cart is held against a wall. The spring constant is 65.0 N/m. The spring is compressed 8.0 cm when held against the wall. What is the compression of the spring when the cart's velocity is 42.0 cm/s?


Homework Equations


(1/2)mv^2=(1/2)kx^2


The Attempt at a Solution



(1.2)(0.42)^2=65(x)^2
x=5.71 cm

But the answer says 5.6 cm, so I think I did something wrong.
 
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  • #2
Since the cart is starting out already compressed to 8cm, you would have to consider that initial displacement in your equation. Subtract the final elastic potential energy from the original (x=8cm) elastic potential energy on the right side. Do that and you should get 5.6cm.
 

Related to Elastic Potential Energy Problem

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 stored in elastic materials, such as springs or rubber bands, and is released when the object returns to its original shape.

What is an elastic potential energy problem?

An elastic potential energy problem is a physics problem that involves calculating the amount of potential energy stored in an object due to its elastic properties. This type of problem often involves determining the displacement, stiffness, and spring constant of an elastic material.

How is elastic potential energy calculated?

Elastic potential energy can be calculated using the equation PE = 1/2 kx^2, where PE is the potential energy, k is the spring constant, and x is the displacement of the object. This equation represents the relationship between the amount of potential energy stored and the characteristics of the elastic material.

What are some real-life examples of elastic potential energy?

Some common examples of elastic potential energy include a stretched rubber band, a compressed spring in a toy car, or a bungee cord before it is released. These objects store potential energy when they are stretched or compressed and release it when they return to their original shape.

How is elastic potential energy used in daily life?

Elastic potential energy is used in many everyday items, such as trampolines, mattresses, and shock absorbers in cars. It is also used in more complex systems, such as in the design of bridges and buildings, to help absorb and distribute energy from external forces.

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