Physics 253 In-Class Worksheet Solutions
Impulse-Momentum (Canadian version)
A puck (m1 = 0.5 kg) and a curling rock (m2 = 18 kg) sit motionless on a centre-ice,
eh. A hoser pushes each of them separately with a constant force of F = 1 N over a
distance ∆x = 2 m. The Zamboni just drove by, eh, so like, the ice is frictionless.
1. Which mass has a greater acceleration?
According to Newton’s law, the smaller mass will have the greater acceleration:
a1 =
F
1
2
=
= 2 m/s
m1 0.5
;
a2 =
F
1
2
=
= 0.05 m/s
m2 18
2. How long (time-wise) does it take each mass to travel down the 2 m stretch of
ice? (Recall: ∆x = 21 at2 ).
√
It will take them ∆t = 2∆x
a to go that distance, so
√
∆t1 =
√
2∆x
=
a1
2(2)
= 1.4 s ;
2
√
∆t2 =
√
2∆x
=
a2
2(2)
= 8.9 s
0.05
3. Use the impulse-momentum theorem to determine the momentum of each mass
at the end of the push (eh?).
The impulse momentum theorem states that the applied impulse changes the
momentum by I = F ∆t = ∆p, so for the two masses
I1 = F ∆t1 = (1)(1.4) = 1.4 kg m/s ;
I2 = F ∆t2 = (1)(8.9) = 8.9 kg m/s
The larger mass has a greater momentum because the force was applied for a
longer period of time (impulse is greater).
4. Now suppose the same force (F = 1 N) is applied to each mass for the same
duration of time, ∆t = 2 s. If the masses were initially motionless, determine
their respective momenta at the end of the push.
In this case, the impulses on each mass will be the same, and thus so will be
their final momenta:
I = F ∆t = (1)(2) = 2 kg m/s
5. How fast is each mass moving?
Each mass will move with a velocity vi =
start from rest). So:
v1 =
2
p
=
= 4 m/s ;
m1 0.5
p
mi ,
where p = I (we assume the masses
v2 =
p
2
=
= 0.11 m/s
m2 18
This makes sense. We would expect the larger mass to be moving slower if
the force is applied for an equal amount of time to the smaller mass (their
accelerations reflect this).
6. Bonus questions (Canadians only): What is your favourite colour? Do you prefer
poutine or KD at supper, and do you drink pop with it? What flavours of Timbits do
you get with your double-double?
This is nonsense! Surely no one actually talks like this, eh? ,