30°

hf

d

2 SIRm m1 SCm m

Realizing that he could not drive up a 30° ice-covered hill because there was no friction, Sir Isaac Newton had

stopped his cart, of total mass 500kg, at the bottom. He was struck in the rear by a London stagecoach, of total

mass 1500kg, travelling at 20 m/s. The two vehicles stuck together, with nothing breaking loose, and slid up the hill in a straight line. How far up the slope did the

wreckage get before coming to rest? (SIN 70)

30°

hf

d

2 SIRm m1 SCm m

30°

hf

d

2 SIRm m1 SCm m

2

1

2

500

1500

20 /

0 /

30

9.81 /

?

?

SIR

SC

SCi

SINi

incl

f

m m kg

m m kg

v m s

v m s

g m s

h

d

List what is known and what is required.

30°

hf

d

2 SIRm m1 SCm m

Because there is a collision involved we must first deal with conservation of momentum in order to find the final velocity of the conjoined carriages.

30°

hf

d

2 SIRm m1 SCm m

Determine which energies are present and absent with the initial and final object locations.

m1 and m2 Questions to ask yourself initial final

Ek Is the object moving? √ x

Ep What’s with its height? x √

Es Is there a spring involved? x x

Wf Do they mention ice or any other frictionless surface?

x x

30°

hf

d

2 SIRm m1 SCm m

Now that we have the velocity of the two conjoined carriages as they begin to slide up the hill.

30°

hf

d

2 SIRm m1 SCm m

sin

sin

11.5

sin 3023

fincl

f

incl

h

dh

d

md

d m

Conservation of energy can find the height to which the carriages rise. We use trigonometry to find the distance up the hill.