Download The force caused by the fan is internal and therefore will not cause

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Information: Newton’s Second Law and External Forces
We usually talk about an object, but now we are going to use the word “system”. A system is sometimes one object
and sometimes a group of objects. For example, a car is a group of several objects including wheels, an engine, and
passengers.
Remember that Newton’s Second Law says that to change the motion of a system (including momentum), a force must
act on the system. This force must be external and not internal. For example, a passenger of a car pushing really hard
on the dashboard will NOT cause a change in the car’s motion because the force is internal. A truck striking the car will
cause a change in the car’s motion because the force is external.
Critical Thinking Questions
A certain man was having a hard time sailing on a day with very little wind.
He suddenly thought of bringing out his fan and setting it up on the boat.
Using what you know about internal and external forces, is this a good
way to propel a sailboat? Explain.
The force caused by the fan is internal and therefore will
not cause the boat to move.
Information: Conservation of Momentum
If no external force acts on a system, then the system’s motion cannot change. Its momentum cannot change. We say
that the momentum of the system is conserved because the momentum remains the same unless an external force
acts on it.
Critical Thinking Questions
1. A cannon (with a cannonball inside) is ready to be fired. The mass of the cannon is 300 kg and the mass of the
cannonball is 3 kg. What is the momentum of the system? (This should be easy since the system is at rest.)
The system is at rest and therefore the velocity is zero. Momentum
must also be zero.
2. Once the cannon fires, the ball is shot out at a speed of 120 m/s. The cannon moves too, but in the opposite
direction. The speed of the cannon is 1.2 m/s. Using the masses given in the previous question, calculate the
momentum of both the cannonball and the cannon.
360 kg×m/s for both
3. Is the force that moves the cannonball external or internal to the system?
The force is internal
a) Using the concept of internal and external forces, explain why the total momentum of the system equals
zero in question 3.
Since the force is internal, the total momentum of the system must
equal zero.
b) Using the concept of the direction of momentum, explain why the total momentum of the system equals
zero in question 3.
The velocities of the cannon and ball are in opposite directions, thus, one of the
momentums should have a negative sign assigned to it
Our friend is having a hard time getting started on a skateboard. If he throws a ball while he is standing on the
skateboard, he will move in the opposite direction of the ball. Keep this in mind: Just like with the
cannon in the previous questions, the man and the cannonball will have the same momentum,
except in opposite directions.
a) The ball has a mass of 7.5 kg and the man throws it at a speed of 5.2 m/s. What is the
momentum of the ball?
39 kg×m/s
b) Using your answer to part a, calculate the speed of the man if he has a mass of 100 kg.
0.39 kg×m/s
c) Would a heavier ball cause the man to go faster or slower, assuming the ball was thrown at the same
speed?
The man would go faster if he used a heavier ball and was still able to
throw it at the same speed
4. The same man from question 4 decides to use a 9 kg ball and does his best to heave it at a speed of 12 m/s.
Calculate his speed. (His mass is still 100 kg.)
1.08 m/s
Information: Elastic Collisions
When two objects collide in the absence of any external forces, then the total momentum after the collision must
equal the total momentum before the collision. An example of an elastic collision is two rubber balls bouncing off each
other:
Remember that opposite directions of velocity get opposite signs. An object traveling to the right will have a positive
velocity and an object traveling to the left will be negative.
Critical Thinking Questions
1. Consider the two balls above. The white ball is travelling at 4 m/s and the black ball is traveling at 3 m/s. The
white ball has a mass of 6 kg and the black ball has a mass of 5 kg.
a) One of the balls has a “negative” velocity. Which one and why is it negative?
The black ball is negative because it is traveling to the left.
b) What is the momentum of the white ball?
24 kg×m/s
c) What is the momentum of the black ball? (Because of the negative velocity of the black ball, your answer
should be negative.)
-15 kg×m/s
d) What is the total momentum of the balls? (Add parts b and c)
9 kg×m/s
e) After the balls collide, what will be the total momentum? (Same as d!)
9 kg×m/s
f)
After the balls collide, the velocity of the black ball will be positive. Why?
The black ball has less mass and less initial velocity than the white ball and will therefore bounce
off of the white one, thereby changing direction.
g) Using your answer to part e, calculate the velocity of the white ball after the collision. The velocity of the black
ball after the collision is 3.5 m/s. (Use the masses of each ball given in the question.)
-1.4 m/s
2. Consider two balls colliding again. This time both balls are going in the same direction. A white ball (mass = 4 kg)
with a speed of 7.5 m/s is approaching a black ball (mass = 3.5 kg) that has a speed of 4.5 m/s.
a) Calculate the total momentum of the balls before and after collision.
45.75 kg×m/s
b) After collision the white ball is moving at a speed of 3.2 m/s. Calculate the speed of the black ball.
9.4 m/s
3. A red ball that has a mass of 12 kg and a blue ball with a mass of 20 kg collide in an elastic collision. The red ball is
initially moving to the left with a velocity of 14 m/s. The blue ball is moving to the right with a velocity of 18 m/s.
If the final velocity of the blue ball is 12.8 m/s, what is the final velocity of the red ball?
-5.3 m/s
4. A 10 kg red ball travels with a velocity of 8 m/s toward a 6 kg blue ball that is at rest. What is the velocity of the
blue ball after collision if the velocity of the red ball after collision is 3 m/s?
8.3 m/s
Information: Inelastic Collisions
Not all collisions are elastic. Some of them are “inelastic”, which means that the two objects colliding stick together
after the collision. For example, two railroad cars might stick together after collision.
Before Collision:
After Collision:
Critical Thinking Questions
1. Two railroad cars collide in an inelastic collision. The coal car has a mass of 12,300 kg. The steel car has a mass of
15,000 kg. The coal car’s initial velocity is westward at 21 m/s. The steel car is at rest.
a) Calculate the momentum of the coal car and the steel car. Then add them together to get the total
momentum of the system. (The system includes both cars.)
258300 kg×m/s
b) Again, the total momentum before collision equals the total momentum after collision. After collision, the two
cars stick together to become one. Find the total mass.
27300 kg
c) How fast are the two cars moving after collision? (Hint: Use the momentum from part a and the mass from
part b; solve for the velocity.)
9.46 m/s
2. Consider two cars that crash in an inelastic collision. The collision is so bad that the cars stick together on impact.
A brown car with a mass of 2100 kg is moving east at 45 km/hr. A white car with a mass of 2300 kg is moving west
at 65 km/hr. Calculate the speed and direction of the combined cars just after impact. We’ll break it into a few
steps:
a) Find the momentum of the brown car and the momentum of the white car. Then add them together to get the
total momentum. (The sign needs to indicate direction. If east is positive and west is negative, then your total
momentum will be a negative number.)
-55000 kg × km/h
b) Find the total mass of the cars after they stick together.
4400 kg
c) Divide the momentum (part a) by the mass (part b). The negative sign gives you the direction.
12.5 km/h west
3. Once again, two cars collide in an inelastic collision. A red car (mass = 2800 kg) traveling north at 50 km/hr strikes
a blue car (mass = 1900 kg) traveling south at 70 km/hr. Find the speed and direction of the cars as they stick
together just after impact.
1.5 km/h North