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## Homework Statement

Part 1.

A(n) 2300 g block is pushed by an external

force against a spring (with a 22 N/cm spring

constant) until the spring is compressed by

15 cm from its uncompressed length. The

compressed spring and block rests at the bottom of an incline of 32

◦

.

The acceleration of gravity is 9.8 m/s

2

.

Note: The spring lies along the surface of

the ramp (see ﬁgure).

Assume: The ramp is frictionless.

Now, the external force is rapidly removed

so that the compressed spring can push up

the mass.

How far up the ramp (i.e., ℓ the length

along the ramp) will the block move (measured from the end of the spring when the

spring is uncompressed) before reversing direction and sliding back?

Remember, the block is not attached to the

spring.

Answer in units of cm.

Part 2.

Repeat the ﬁrst part of this question, but

now assume that the ramp has a coeﬃcient of

friction of = 0.423 .

Keep all other assumptions the same.

Answer in units of cm

## Homework Equations

Without friction = Ui + Ki = Uf + Kf, where in this problem Ui = 1/2kx^2, Ki = 0, Uf = mgh and Kf = 0. So 1/2 kx^2 = mgh

With friction = Ui + Ki + (-Fk*l) = Uf + Kf

So 1/2kx^2 - mu*(mgcosθ)*l = mgh

## The Attempt at a Solution

I figured out Part 1.

From the equation above

h = kx^2/2mg

l = h/sin32

Then I subtracted .15 m and converted to cm. I got the correct answer. When I tried to solve for the length with the added friction in, I first forgot to account for the length in (mu*(mgcosθ*l).

I remembered to add in l, but I think I'm using the wrong l. The first l I used was .45 because that is the length of the ramp. I then tried .30 ( because .45-.15)

Here is my current equation and answer but I am not sure if I chose the correct l and therefore I don't know if it is correct. Please advise.

2200 N/m *.15^2m - .423(2.3 kg * 9.8m/s^2*cos32°*.30/2*2.3kg*9.8 m/2^2

h = 1.044239263 m

l = h/sinθ

so: 1.044239263 m/sin32 = 1.97056294 m

1.97056294 m - .15 m = 1.821 m

1.821 m * 100 = 182.1 cm

Sorry for not having a picture.