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.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

KPE = 1/2 m v^{2}

GPE = mgh

P = mv

F_{avg}= I/(Δt)

3. 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/s

m_{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}= -4440N

F_{avg}= I / t

= (P_{f}- P_{i}) / t

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

= -4440N

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# Homework Help: Inelastic collision - pendulum

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