## Homework

Ch 2, Intertia; Ex 1, 9, 10, 18, 22, 23, 24, 25, 26, 27, 34

Ex1. A ball is rolling across the top of a billiard table and slowly rolls to a stop. How wold Aristotle interpret this observation? How would Galileo interpret it?

Aristotle would say the "nature" of a ball is to come to rest.

Galileo would say there is a friction force that brings the ball to rest.

Ex9. Your friend says that inertia is a force that keeps things in their place, either at rest or in motion. Do you agree? Why or why not?

Inertia is an "idea" rather than a force. So I disagree with my friend.

Ex10. Your other friend says that bureaucratic organizations have a lot of inertia. Is this akin to Newton's first lasw of inertia?

Hmmmm, . . . sort of :-)

The "key" word in Newton's First Law of Motion, the Law of Inertia, is "continue". In the absence of outside forces, an object continues to do what it was doing. Bureaucrats are often/usually like that. It is easier to continue than to change or innovate. (Of course, that is also true for most/many of us as ordinary people; it is not just a "problem" of bureaucrats.)

Ex18. Consider a pair of forces, on having a magnitude of 20 N and the other, 12N. What maximum net force ispossible for these two forces? What is the minimum net force possible?

If the two forces act in the same direction, their net force is 20 N + 12 N = 32 N; this is the maximum net force.

If the two forces act in opposite directions, their net force is 20 N - 12 N = 8 N; this is the minium net force.

If the two forces act at some other angle relative to each other, the net force they produce will be between these two extremes.

Ex22. The sketch shows a painting staging in mechanical equilibrium. The person in the midles weighs 250 N, and the tensions in each rope are 200 N. What is the weight of the staging?

From the diagram, we see that there is a total of 200 N + 200 N = 400 N pulling UP and a total of 250 N + W pulling DOWN. The net force is zero because the system is in equilibrium. That means the force DOWN must equal the force UP or

250 N + W = 400 N

W = 150 N

Ex23. A different staging that weighs 300 N supports two painters, one 250 N and the other, 300 N. The reading in the left scale is 400 N (the tension in the left rope is 400 N). What is the reading in the right hand scale (what is the tension in the right rope)?

From the diagram, we see a total of 250 N + 300 N + 300 N = 850 N pulling DOWN and a total of 400 N + T pulling UP. The net force is zero because the system is in equilibrium. That means the force UP must equal the force DOWN or

400 N + T = 850 N

T = 450 N

Ex24. Nellie Newtons hangs at rest from the ends of the rope as shown. How does te reading on the scale compare to her weight? Nellie is supported TWICE by the tensionin the rope. The tension in the rope pulls up on her left hand AND it pulls up on her right hand. The total force lifting her UP is equal to her weight pulling her DOWN. So the tension in the rope -- the force the rope exerts -- must be equal to ONE-HALF her weight.

Ex25. Harry the painter swings year after year from his bo'sun's chair. His weight is 500 N and the rope, unknown to Harry, has a breaking point of 300 N. Why doesn't the rope break when he is supported as shown below?

One day Harry is painting near a flagpole, and, for a change, he ties the free end of he rope to the flagpole instead of to his chair as shown below. Why did Hary end up taking sick leave? When Harry has both ends of the rope attached to his swing or bo'sun's chair, each end of the rope needs to support only ONE-HALF his weight; this is just like little Nellie Newton in the previous question.

However, when only one end of the rope is attached to his swing or bo'sun's chair, then thatend of the rope needs to support ALL of his weight! If the rope needs to support 500 N but breaks when the tension gets to 300 N, the Harry is in for a bad fall!

Ex26. For the pully system shown, what is the upper limit of weight the strongman can lift?

He can lift only his own weight.

Ex27. The rope supports a lantern that weighs 50 N. Is the tension in the rope less than, equal to, or more than 50 N.

There are two pieces of the rop supporting to 50 N of the lantern so each piece needs to support less than the full 50 N. If both pieces of the rope were vertical, they would need to support only one-half of the 50 N weight. Since they are at some other angle, the tension will need to be more than that 25 N, but it will still be less than 50 N.

Ex34. Two forces act on a parachutist falling in air; weight and air drag. If the fall is steady, with no gain or loss of spedd, then the parachutist is in "dyamic equilibrium". How do the magnitude of weight and air drag compare?

"In the absence of a net force, and object in motion continues along a straight line with a constant speed."

The net force on the parachutist must be ZERO. That means the downward force of the weight must be just equal to or just balanced by the upward force of the air drag on the parachute.

When this occurs, we say the parachutist has reached "terminal velocity".

Multiple-guess question over these ideas.

1. Aristotle thought and talked about motion. Aristotle was

A. Galileo's mentor or teacher.

B. a Greek philosoper.

C. prominent in the Renaissance.

D. prominent in the Industrial Revolution.

2. Copernicus may, indeed, be called the world's first Revolutionary. He shocked the world with a theory that

A. the Earth was not flat, but round!

B. the Earth was the center of the Universe.

C. the Earth orbited the Sun.

D. the moon orbited the Sun.

3. Galileo Galilei may, indeed, be called the Father of Modern Science. This is because Galileo

A. had great insight, even in electricity, magnetism, and optics.

B. put great emphasis on experimental results.

C. used very accurate sundials.

D. invented the pendulum clock.

4. Galileo may or may not have actually used the Leaning Tower of Pisa. But Galileo did demonstrate that

A. heavier bodies fall slower that lighter ones.

B. heavier bodies fall faster than lighter ones.

C. all bodies fall at the same rate.

5. The NET FORCE on an object is

A. the largest force.

B. the horizontal force.

C. the sum of all the forces acting on an object.

D. the smallest force.

Multiple-guess question -- and their answers -- over these ideas.

1. Aristotle thought and talked about motion. Aristotle was

A. Galileo's mentor or teacher.

B. a Greek philosoper.

C. prominent in the Renaissance.

D. prominent in the Industrial Revolution.

2. Copernicus may, indeed, be called the world's first Revolutionary. He shocked the world with a theory that

A. the Earth was not flat, but round!

B. the Earth was the center of the Universe.

C. the Earth orbited the Sun.

D. the moon orbited the Sun.

3. Galileo Galilei may, indeed, be called the Father of Modern Science. This is because Galileo

A. had great insight, even in electricity, magnetism, and optics.

B. put great emphasis on experimental results.

C. used very accurate sundials.

D. invented the pendulum clock.

4. Galileo may or may not have actually used the Leaning Tower of Pisa. But Galileo did demonstrate that

A. heavier bodies fall slower that lighter ones.

B. heavier bodies fall faster than lighter ones.

C. all bodies fall at the same rate.

5. The NET FORCE on an object is

A. the largest force.

B. the horizontal force.

C. the sum of all the forces acting on an object.

D. the smallest force.  Summary Back to "Table of Contents" Ch 3, Linear Motion