1/12 Linear Momemtum problems.pdf (1/12)2012-10-17 10:39:48
Linear Momentum Collisions Problems
Example Problem
Water leaves a hose at a rate of 1.5 kg/s with a speed of 20 m/s and is aimed at the side of a car, which
stops it. What is the force exerted by the water on the car
Variables
Drawing
Solution
Answer: -30 N
Physics for Scientist and Engineers third edition
RoessBoss 1
2/12 Linear Momemtum problems.pdf (2/12)2012-10-17 10:39:48
Linear Momentum Collisions Problems
Example Problem
A 10,000 kg railroad car traveling at a speed of 24.0 m/s strikes an identical car at rest. If the cars lock
together as a result of the collision, what is their common speed afterward?
Variables
Drawing
Solution
Answer: 12.0 m/s
Physics for Scientist and Engineers third edition
RoessBoss 2
3/12 Linear Momemtum problems.pdf (3/12)2012-10-17 10:39:48
Linear Momentum Collisions Problems
Example Problem
Calculate the recoil velocity of a 5.0 kg rifle that shoots a 0.050 kg bullet at a speed of 120 m/s
Variables
Drawing
Solution
Answer: -1.2 m/s
Physics for Scientist and Engineers third edition
RoessBoss 3
4/12 Linear Momemtum problems.pdf (4/12)2012-10-17 10:39:48
Linear Momentum Collisions Problems
Example Problem
A billiard ball moving with speed v1= 3.0 m/s in the +x direction strikes an equal mass ball initially at
rest. The two balls are observed to move off at 45˚, ball 1 above the x axis and ball below. That is ø1
= 45˚ and ø2 = -45˚. What are the speeds of the two balls after the collision.
Variables
Drawing
Solution
Answer: 2.1 m/s
Physics for Scientist and Engineers third edition
RoessBoss 4
5/12 Linear Momemtum problems.pdf (5/12)2012-10-17 10:39:49
Linear Momentum Collisions Problems
Example Problem
A) calculate the impulse experienced when a 70 kg person lands on firm ground after jumping from a
height of 3.0 m. Then estimate the average force exerted on the person’s feet by the ground, if the
landing is B) stiff legged and C) with bent legs. In the former case assume the body moves 1.0 cm
during impact, and in the second case, when the legs are bent about 50 cm
Variables
Drawing
Solution
Answer: -540 N•s; 2.1 E 5 N; 4.9 E 3 N
Physics for Scientist and Engineers third edition
RoessBoss 5
6/12 Linear Momemtum problems.pdf (6/12)2012-10-17 10:39:49
Linear Momentum Collisions Problems
Example Problem
A billiard ball of mass m moving with speed v collides head on with a second ball of equal mass.
What are the speeds of the two balls after the collision, assuming it is elastic. Assume A) both balls
are moving B) ball 2 is initially at rest (v2 = 0)
Variables
Drawing
Solution
Answer:
Physics for Scientist and Engineers third edition
RoessBoss 6
7/12 Linear Momemtum problems.pdf (7/12)2012-10-17 10:39:49
Linear Momentum Collisions Problems
Example Problem
A very common practical situation is for moving object (m1) to strike a second object (m2- the target)
at rest (v2= 0). Assume the objects have unequal masses and the collision occurs along a line (head-
on) A) derive equations for v2’ and v1’ in terms of the initial velocity v1 of mass m1 and the masses
m1 and m2. B) determine the final velocities if the moving object is much more massive than the
target (m1>> m2). C) determine the final velocities if the moving object is much less massive than the
target (m1 << m2)
Variables
Drawing
Solution
Answer:
Physics for Scientist and Engineers third edition
RoessBoss 7
8/12 Linear Momemtum problems.pdf (8/12)2012-10-17 10:39:49
Linear Momentum Collisions Problems
Example Problem
A proton of mass 1.01 u (unified atomic mass units) traveling with speed of 3.60 E 4 m/s has an elastic
head on collision with a helium (He) nucleus (mHe= 4.00 u) initially at rest. What are the velocities of
the proton and helium nucleus after the collision? (1u= 1.66 E -27 kg- but you dont need that fact)
Variables
Drawing
Solution
Answer: -2.15 E 4 m/s
Physics for Scientist and Engineers third edition
RoessBoss 8
9/12 Linear Momemtum problems.pdf (9/12)2012-10-17 10:39:49
Linear Momentum Collisions Problems
Example Problem
The ballistic pendulum is a device used to measure the speed of a projectile, such as a bullet. The
projectile of mass m is fired into a large block of mass M, which is suspended like a pendulum
(usually M is somewhat greater than m). As a result of the collision, the pendulum projectile system
swings up to a maximum height h. Determine the relationship between the initial horizontal speed of
the projectile v and the height h
Variables
Drawing
Solution
Answer:
Physics for Scientist and Engineers third edition
RoessBoss 9
10/12 Linear Momemtum problems.pdf (10/12)2012-10-17 10:39:50
Linear Momentum Collisions Problems
Example Problem
A proton traveling with speed 8.2 E 5 m/s collides elastically with a stationary proton in a hydrogen
target. One of the protons is observed to be scattered at a 60˚ angle. At what angle will the second
proton be observed, and what will be the velocities of the two protons after the collision?
Variables
Drawing
Solution
Answer: 7.1 E 5 m/s; -0.50 or ø= -30˚
Physics for Scientist and Engineers third edition
RoessBoss 10
11/12 Linear Momemtum problems.pdf (11/12)2012-10-17 10:39:50
Linear Momentum Collisions Problems
Example Problem
Three people of roughly equivalent mass m on a lightweight (air filled ) banana boat sit along the x
axis at positions x1= 1.0 m, x2= 5.0 m, and 6.0 m. Find the position of CM
Variables
Drawing
Solution
Answer:
Physics for Scientist and Engineers third edition
RoessBoss 11
12/12 Linear Momemtum problems.pdf (12/12)2012-10-17 10:39:50
Linear Momentum Collisions Problems
Example Problem
Three particles each of mass 2.50 kg are located at the corners of a right triangle whose sides are 2.00
m and 1.50 m long. Locate the center of the mass
Variables
Drawing
Solution
Answer:
Physics for Scientist and Engineers third edition
RoessBoss 12
