Download 06 Momentum WS 08 [v6.0]

Honors Physics
Momentum
Worksheet
1. What is the MKS unit for each of the following?
force, momentum, impulse, change in momentum
kg • m
kg • m
(Answer: force- newton, momentum, impulse: N•s, change in momentums
s
kg • m
Note:
is equivalent to N•s. These units may look different, but they are really the
s
same.)
€
€
2. Classify each as a scalar or vector.
€ force, momentum, impulse, velocity, acceleration, mass, power, energy, time
(Answer: force- vector, momentum- vector, impulse- vector, velocity- vector,
acceleration- vector, mass- scalar, power- scalar, energy- scalar, time- scalar)
3. A pitcher supplies a constant force on a baseball whose mass is .14 kg. The pitcher’s hand is
in contact with the ball over a distance of 1.5 m. The ball’s speed as it is released is 40 m/s.
(a) What force acted on the ball? (Answer: 75 N)
kg • m
(b) What was the change in momentum of the ball? (Answer: 5.6
)
s
€
(c) How long did the force act on the ball? (Answer: .075 s)
€
4. Two skaters, initially at rest, push on each other for 1.5 s with a force of 60 N. The skaters
move in opposite directions as a result. Ignore the effects
€ of friction The mass of one skater is
50 kg and the mass of the other is 60 kg. .
(a) What is the final speed of the 50 kg skater? (Answer: 1.8 m/s)
(b) What is the final speed of the 60 kg skater? (Answer: 1.5€m/s)
(c) Over what distance did the 60 N force act on the 50 kg skater? (Answer: 1.4 m)
€
€ the momentum of a system be conserved?
5. Under what condition will
€ a system is conserved if the net external force on the system is zero.)
(Answer: Momentum of
€
€
6. A truck of mass 900 kg traveling 20 m/s, east makes a head on collision with a car of
mass 500 kg traveling 50 m/s, west. The vehicles lock together and move at speed V
after the collision.
(a) Determine the value of V. (Answer: 5.0 m/s)
€
(b) In which
direction do€the locked together vehicles move? (Answer: west)
€
€
7. (a) Distinguish between an elastic collision and an inelastic collision.
(Answer: Kinetic energy is conserved in an elastic collision. Kinetic energy is not
conserved in an inelastic collision.)
(b) Mass m is traveling with velocity v and mass M is traveling with velocity V. The masses
collide elastically. Mass m travels with velocity u and mass M travels with velocity U after
the collision.
i. Write an equation relating m, v, M, V, u and U using the definition of elastic collision.
1
1
1
1
(Answer: mv 2 + MV 2 =
mu2 + MU 2 )
2
2
2
2
ii. Write an equation relating m, v, M, V, u and U using conservation of momentum.
(Answer: mv + MV = mu + MU)
€
8. A 60 kg man throws a 20 kg package at 6.0 m/s from an 80 kg boat. The boat is originally at
rest. What is the final speed of the boat? (Answer: .86 m/s)
€
9. (a) Show that the units of impulse are really the same as the units of momentum.
Answer: €
€
Units of impulse= Units of FΔt = N•s

m
m
kg • m
From F= ma, unit of force= N= kg • 2 , so units of impulse=  kg • 2  • s =

s
s 
s
€ Units of m•v= kg • m , but these are the same units of impulse found
Units of momentum=
s
above
€
€
(b) State whether each of the following could be used to find impulse, change in momentum,
neither impulse nor change€
in momentum or both impulse and change in momentum.
A) mΔv (Answer: both impulse and change in momentum)
B) mv (Answer: neither impulse nor change in momentum)
C) FΔt (Answer: both impulse and change in momentum)
D) FΔd (Answer: neither impulse nor change in momentum)
€
E) m(aΔt) (Answer: both impulse and change in momentum)
€ Sand pours onto a moving conveyor belt at the rate of 4.5 kg/s. The belt is moving at 2.0 m/s.
10.
€ How much force is required to keep the belt moving?
Δp
Δ(mv)
Δm
€
=
= v•
Hint: Use Newton’s Second Law of Motion in the form F =
Δt
Δt
Δt
instead of the usual F= ma.
(Answer: 9.0 N)
11. A rocket engine provides 7400 N of thrust for €
6.2 s.
(a) What impulse is imparted to the rocket? (Answer: 46000 N•s)
(b) What is the change in momentum of the rocket? (Answer: 46000
€
kg • m
)
s
12. Which of the following occur in equal and opposite pairs during a collision? Assume no net
external force acts.
(a) changes in kinetic energy
(b) changes in momentum
(c) impulses imparted
(d) forces
(e) accelerations
(f) changes in velocity
(Answer: These occur in equal and opposite pairs: (b), (c), (d) )
13. Which two of Newton’s Laws of Motion together imply that momentum is conserved if no net
external force acts?
(Answer: Newton’s Second Law and Newton’s Third Law)
14. Which of the following is always conserved in an elastic collision? Assume no net external
force acts.
(a) total energy
(b) kinetic energy
(c) momentum
(d) mass
(Answer: All are conserved in an elastic collision.)
€
€
15. Two masses m A = 15.0 kg and m B= 5.00 kg collide head on (motion before and after the
collision occurs on a line). Suppose the velocity of mass A before the collision is
vA = 6.00 m/s and the velocity of mass B before the collision is vB = −2.00 m/s. (Right is the
positive direction and left is the negative direction.) In each case, the velocity of mass A after
the€collision ( vA′ ) and€the velocity of mass B after the collision ( v′B) are given. Complete the
table by calculating the total momentum p before the collision, the total momentum p′ after the
collision, the total kinetic energy K before the collision€and€the total kinetic energy K′ after the
collision. Based on your calculations, decide if the collision is an elastic collision, inelastic
collision
€
or not permitted (because there is more energy
€ after the collision than before or
because momentum is not conserved).
€
€
Initial
Initial
Final
Final
Type of
vA′
v′B
Momentum Momentum Kinetic Energy Kinetic Energy Collision
2.00
10.0
€
3.00
7.00
−1.00
19.0
4.00
8.00
€
Note: velocity is in m/s, momentum is in
kg • m
and kinetic energy is in J.
s
Answer:
€
€
Initial
Final
Final
€
Momentum Kinetic Energy Kinetic Energy
vA′
v′B
Initial
Momentum
2.00
10.0
80.0
80.0
280
280
Elastic
€
3.00
7.00
80.0
80.0
280
190
Inelastic
−1.00
19.0
80.0
80.0 €
280 €
910
Not permitted
4.00
8.00
80.0
100 €
280 €
280
Not permitted
€
€
kg • m
Note: velocity is in m/s, momentum is in
and kinetic energy is in J.
€
€
s
€
€
Type of
Collision
16. A 1200 kg car traveling north on an icy road at 40 m/s collides with a 3200 kg truck traveling
east at 30 m/s. The two vehicles lock together and slide in the icy intersection.
(a) Find the speed with which the wreck moves immediately after the collision.
(Answer: 24 m/s)
€ travels immediately after the collision.
(b) Find the direction in which the wreck
(Answer: 27° N of E or 63° E of N)
€
17. A 4.00 kg ball traveling 10.0 m/s, east collides with a 6.00 kg ball traveling west at 2.00 m/s.
The 4.00 kg ball moves at 4.00 m/s, east after the collision.
(a) Find the velocity of the 6.00 kg ball after the collision. (Answer: 2.00 m/s, east)
(b) How much kinetic energy was lost in the collision? (Answer: 168 J)
18. A .085 kg bullet strikes a 5.000 kg block of wood. The bullet becomes embedded in the block,
which slides horizontally for 6.0 m before coming to rest. If the coefficient of sliding friction
is .30 then what was the original speed of the bullet? (Answer: 360 m/s)
19. State Newton’s Second Law in terms of force and momentum. (Newton never stated the
Second Law in terms of force and acceleration.)
Answer:
Force equals the time rate of change of momentum.
20. Which of the following is always conserved in an inelastic collision? Assume no net external
force acts.
(a) total energy
(b) kinetic energy
(c) momentum
(d) mass
(Answer: (a), (c), (d))
21. What braking force must be applied to stop a 1900 kg car traveling at 25 m/s in 11 s?
(Answer: 4300 N)
HOMEWORK
GUIDE
Section in the
Notes
Worksheet Problems
6.12
1, 2, 3, 9, 10, 11, 13, 19, 21
6.13
4, 5, 6, 8, 16
6.14
7, 12, 14, 15, 17, 18, 20