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## Homework Statement

Two small spheres made of Play Doh hang from massless strings of length 2 meters. Sphere m

_{1}= 1kg is pulled to the left to an angle of θ

_{0}= 60° and has zero initial speed. It collides inelastically with sphere m

_{2}= 2kg, which is initially at rest. After the collision the two masses stick together and they act as a single pendulum.

(a) What is the speed of m

_{1}just before the collision?

(b) What is the speed of the two masses right after the collision?

(c) What is the ratio of mechanical energy before and after the collision?

(d) What is the amplitude θ

_{max}of the swinging pendulum?

(e) Assume that the collision lasted 10

^{-3}seconds. What was the average force that the mass m

_{1}was acting on mass m

_{2}during the collision?

## Homework Equations

KPE = 1/2 m v

^{2}

GPE = mgh

P = mv

F

_{avg}= I/(Δt)

## The Attempt at a Solution

**(a) v = 4.43 m/s**

mgh = 1/2 mv

^{2}

9.8 * 1 = 1/2 v

^{2}

v

^{2}= 19.6

v = 4.43 m/s

**(b) v**

_{2}= 1.48 m/sm

_{1}v

_{1}= (m

_{1}+ m

_{2}) v

_{2}

1 * 4.43 = (1 + 2) v

_{2}

v

_{2}= 4.43/3

v

_{2}= 1.48 m/s

**(c) 2.98**

E

_{i}/ E

_{f}

(1/2 m

_{1}v

_{1}

^{2}) / (1/2 (m

_{1}+ m

_{2}) v

_{2}

^{2})

= 9.81 / 3.29 = 2.98

**(d) θ = 19.3°**

1/2 (m

_{1}+ m

_{2}) v

^{2}+ 0 = 0 + (m

_{1}+ m

_{2}) gh

h = v

^{2}/(2g) = 1.48

^{2}/19.6 = 0.112m

h = L - L cos(θ)

cos(θ) = (L - h)/2

θ = cos

^{-1}((2-0.112)/2)

θ = 19.3°

**(e) F**

_{avg}= -4440NF

_{avg}= I / t

= (P

_{f}- P

_{i}) / t

= (0 - (1+2)1.48) / 0.001

= -4440N