Inelastic collision - pendulum

  • Thread starter ss85
  • Start date
  • #1
3
0
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?



Homework Equations


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
 

Answers and Replies

  • #2
BruceW
Homework Helper
3,611
120
I've gone through them, and they all look correct to me. Although part c should be equal to 3, your answer is slightly different due to rounding error. Part e is kind of vague, since the two masses end up being one mass, so its not like there is an impulse... But I think your answer is probably what they are looking for.
 

Related Threads on Inelastic collision - pendulum

  • Last Post
Replies
19
Views
4K
  • Last Post
Replies
2
Views
4K
Replies
2
Views
3K
Replies
6
Views
3K
Replies
0
Views
2K
Replies
2
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
5
Views
808
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
684
Top