How to Determine Velocity and Maximum Compression of a Pendulum-Spring System

[silentcoder]

Homework Statement

Hi, I have a question about pendelum which I don't know how to solve

A 1.0 kg ball swings from a pendulum and bounces into a spring with a spring constant of 750 N/m.

Here is the diagram:

1. How do i determine velocity of the ball at the bottom of the swing?
2. How do i determine the maximum compression of the spring?

Homework Equations

The Attempt at a Solution

Attempt for number 1

h = 1.5 m - (1.5 m cos 15)
h = 0.05111126 m

Eg = Ek
mgh = 1/2 mv^2
gh = 1/2 mv^2
2gh = v^2
sqrt(2gh) = v

v = 1.00 m/s
Is that right?

2. I don't know how to do 2.

Thanks

 

[haruspex]

sqrt(2gh) = v

v = 1.00 m/s

That's a remarkable leap. What do you think h equals?
For part 2, use energy again. How fast will the ball be moving when the spring is at maximum compression?

 

[silentcoder]

That's a remarkable leap. What do you think h equals?
For part 2, use energy again. How fast will the ball be moving when the spring is at maximum
compression?

For number 1:
sqrt(2gh) = v
sqrt(2(9.81)(1.5 - 1.5 cos 15))
v = 1.0 m/s

For number 2:
1/2 mv^2 = 1/2 ke^2
mv^2 = ke^2
e^2 = mv^2 / k
e^2 = (1.0 kg)(1 m/s)^2 / 750 N/m
e^2 = 1/750
e = sqrt(1/750)
e = 0.036 m

is this right?

 

[haruspex]

Looks good.

 

[silentcoder]

Looks good.

For both of them?

If yes, Thank You for verification!

 

[haruspex]

Yes, both.

 

[silentcoder]

Yes, both.

Appreciate your help!