# Inelastic collision - pendulum

• ss85
In summary, the problem involves two spheres of different masses colliding inelastically and forming a single pendulum. The speed of the first sphere before the collision is 4.43 m/s and the speed of the combined masses after the collision is 1.48 m/s. The ratio of mechanical energy before and after the collision is 2.98 and the amplitude of the swinging pendulum is 19.3°. The average force during the collision is calculated to be -4440N.

#### ss85

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

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.

## 1. What is an inelastic collision?

An inelastic collision is a type of collision where the colliding objects stick together after impact and lose some of their kinetic energy. This is in contrast to an elastic collision where the objects bounce off each other without losing any kinetic energy.

## 2. How does a pendulum demonstrate an inelastic collision?

A pendulum demonstrates an inelastic collision because when it swings, the potential energy is converted into kinetic energy. However, due to friction and air resistance, some of the kinetic energy is lost, causing the pendulum to eventually come to a stop. This loss of kinetic energy is an example of an inelastic collision.

## 3. What factors affect the inelastic collision of a pendulum?

The factors that affect the inelastic collision of a pendulum include the mass of the pendulum, the length of the string or rod it is attached to, and the angle at which it is released. These factors can affect the amount of potential energy and the amount of friction and air resistance involved in the collision.

## 4. How is the conservation of momentum related to inelastic collisions?

Inelastic collisions still follow the law of conservation of momentum, which states that the total momentum of a closed system remains constant. In an inelastic collision, the total momentum of the colliding objects before and after the collision will be the same, but some of this momentum will be converted into other forms of energy.

## 5. Can a pendulum exhibit both elastic and inelastic collisions?

Yes, a pendulum can exhibit both elastic and inelastic collisions depending on the conditions. If the pendulum is released from a small angle and there is minimal friction and air resistance, it will behave more like an elastic collision. However, if the angle is large and there is more friction and air resistance, it will exhibit more of an inelastic collision.