1. Conservation of Mechanical Energy
A 2.5 kg ball hangs from a 30 m massless string. I smack it, so
it initially flies horizontally at 15 m/s. What is its speed after the
ball has ascended 45°?
MEi = MEf
PEi + KEi = PEf + KEf
45°
1/2mvi2 = mghf + 1/2mvf2
30cos45°
30 m h
h = 30m – 30cos45°
= 8.79 m
vf = 7.25 m/s
SMACK!!

2. Work-Kinetic Energy Theorem
A 2000 kg car travelling 50 km/h slams on the brakes. If the tires provide a frictional force of 5000 N, at what distance does the car stop?
W = DKE
50 km/h = 13.9 m/s
Fd = 1/2mvf2 – 1/2mvi2
d = 38.6 m

3. Find the velocity at point c.
A wagon with passengers has a mass of 40 kg as it travels at 4 m/s over a hill as shown. Find the velocity at point b. Assume there is no friction.
4 m/s
MEi = MEf
0 J
mghi + 1/2mv2i = mghf + 1/2mv2f
v2f = 2ghi + v2i
vf = 24.6 m/s
30 m c
14 m b
Find the velocity at point c.
mghi + 1/2mv2i = mghf + 1/2mv2f
vf = 18.2 m/s