# Inelastic collision - pendulum

Alright, I did all the work for this problem, but do not know the correct answers and therefore cannot check my work with 100% confidence. So if somebody could look it over and let me know if I did everything correctly or not, I'd appreciate it. The answer I calculated for part e seemed kind of high to me.

## Homework Statement

Two small spheres made of Play Doh hang from massless strings of length 2 meters. Sphere m1 = 1kg is pulled to the left to an angle of θ0 = 60° and has zero initial speed. It collides inelastically with sphere m2 = 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 m1 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 θmax of the swinging pendulum?
(e) Assume that the collision lasted 10-3 seconds. What was the average force that the mass m1 was acting on mass m2 during the collision?

KPE = 1/2 m v2
GPE = mgh
P = mv
Favg = I/(Δt)

## The Attempt at a Solution

(a) v = 4.43 m/s
mgh = 1/2 mv2
9.8 * 1 = 1/2 v2
v2 = 19.6
v = 4.43 m/s

(b) v2 = 1.48 m/s
m1v1 = (m1 + m2) v2
1 * 4.43 = (1 + 2) v2
v2 = 4.43/3
v2 = 1.48 m/s

(c) 2.98
Ei / Ef
(1/2 m1 v12) / (1/2 (m1 + m2) v22)
= 9.81 / 3.29 = 2.98

(d) θ = 19.3°
1/2 (m1 + m2) v2 + 0 = 0 + (m1 + m2) gh
h = v2/(2g) = 1.482/19.6 = 0.112m
h = L - L cos(θ)
cos(θ) = (L - h)/2
θ = cos-1((2-0.112)/2)
θ = 19.3°

(e) Favg = -4440N
Favg = I / t
= (Pf - Pi) / t
= (0 - (1+2)1.48) / 0.001
= -4440N