Question

# This assignment is about energy. But one of the new things we’ve just learned about is...

This assignment is about energy. But one of the new things we’ve just learned about is spring forces, so

there should be a question about them. So some parts of this question are not about energy. One of the

hard things is deciding whether you should use energy methods or not in each part. I’ll give you some help

with making this decision by getting you to think about whether the system is energetically isolated.

Consider a setup similar to one you will encounter in the lab. A cart has a spring attached to one end of

it. We push the cart so that the spring compresses against a barrier. When we let go the spring pushes the

cart away from the barrier. The spring has an uncompressed length of 12.0 cm. We push the cart until the

spring’s length is 7.0 cm. The cart and spring have a combined mass of 420 g. After we release it and the

spring uncompresses the cart is moving at 15.0 cm/s.

(a) Consider the process of pushing the cart against the barrier and compressing the spring. Let the

system be the cart, the spring, and the barrier (specifically, your hand is

not

in the system). Is this

system energetically isolated?

(b) Now consider the process which occurs after we let go. The spring uncompresses, pushing the cart

away from the barrier so that at then end of the process the cart and spring are moving and the spring

is completely uncompressed. Again, the system is the cart, spring, and barrier. During this process is

the system energetically isolated?

(c) Use your conclusions from above to find what the spring constant of the spring must be. [

Hint: you

should have just concluded that energy was conserved in one process but not in the other. The process

in which energy is conserved can be used to solve for the spring constant since we can easily write

down the conservation equation for it.

(d) Just before we let go of the cart what force must we have been exerting on the cart?

Hint: since you

are not in the system, and we are thinking about a force exerted by you, is energy conservation of any

help here

A)

As the energy created by the force is completely stored in the spring, the system is energetically isolated.

B)

The energy stored in the spring converts into kinetic energy of the cart, if we can ignore friction then the system is energetically isolated. But if we mind friction in our calculation which is highly unlikely for a small cart at low speed, tiny amount of energy gets lost as thermal energy, but we can ignore it for the most part.

C)

The energy stored in the cart due to compression of the spring = , where k is the spring constant and x is the change of length of the spring during compression.

Kinetic energy of the cart system = , m =mass, v = velocity.

So, according to the conservation of energy:

d)

According to hook's law, force to hold in a compressed spring = k*x = 3.78*(0.12-0.07) = 0.189N.

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