# Caculating the decline angle of a swing

1. Oct 28, 2009

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

The seat of a child’s swing with a mass of 6 kg hangs on lightweight strings that are
2.5 m long. A dog with mass of 3 kg sleeps on the swing’s seat. The dog jumps from the swing with velocity of 2 m/s in a horizontal direction.
- How much is the maximum angle of decline when the dog jumps from the seat?

2. Relevant equations

G= mv
W(kinetic)= ½ mv²
W(gravitational)= mgh

3. The attempt at a solution

According to arithmetic:
cosθ= (l-h) / l → 1- (h/l)

W(kinetic)= W(gravitational)
½ mv²= mgh → h= v² / 2g

Substitution:
cosθ= 1- (h/l) = 1- (v² / 2gl)

Because we have one system, the gravitational force of the dog should equal gravitational force of the swing, I hope this is correct:
m(dog)*v(dog)= m(seat)*v(seat) → v(seat)= m(dog)*v(dog) / m(seat)

Another substitution:
cosθ= 1- (m(dog)²*v(dog)² / 2m(swing)²*gl)
θ= 11.6º

2. Oct 28, 2009

### Delphi51

I got the same answer, similar method.

3. Oct 28, 2009