Workbook Chapter 5a: Force, Mass, & Newton's Laws of Motion

Overview:

Force: A push or pull that causes an object to slow down, speed up, change direction, or heat up. To put it briefly, force causes a change in velocity of either an object or the molecules it contains. The concept of force permeates every facet of physics and everyday life. If you obtain a thorough understanding of this concept you will find yourself using it from time to time to make life a little easier. It may even save your life. Mention seatbelts, babies and Hodini Buried alive in a coffin trick.

Aristotle believed that all motion required a force, or "impetus" due to a force. That is, he believed when the force stopped, or the impetus given by a force was exhausted, used up in some way, that the object stopped. In fact, believers in Aristotle believed arrows shot into the air and cannon balls fired out of cannons did this

in spite of visual evidence to the contrary for 2000 years!

New concepts -

Inertia: First coined by Galileo observing objects' resistance to change in motion.

Mass : Newton's refinement, mass, is a measure of how much matter an object contains. Those that contain more matter require more force to cause the same change in velocity.

 

Weight: The gravitational force exerted on an object by the planet. Mass and weight are often confused because of the amazing "coincidence ?" that the force of gravity on an object at the surface of the Earth is proportional to its mass. In other words, gravitational mass turns out to be the same as inertial mass!

Just how force, mass, velocity and acceleration are related is the subject of these activities.

Newton's First Law. Mass- A measure of Inertia

Objects in motion tend to stay in motion.

.

(Left) The ball rolling down the incline rolls up the opposite incline and reaches its initial height. (Center) As the angle of the upward incline is reduced, the ball rolls a greater distance before reaching its initial height. (Right) How far will the ball roll along the horizontal?

Combinations of forces, vector components of force.

(Left) When a 10-N load hangs vertically from a single spring scale, the scale pulls upward with a force of 10 N. (Right) When the load hangs vertically from two spring scales, each scale pulls upward with a force equal to half of the load's weight, or 5 N.

As the angle between the spring scales increases, the scale readings increase to maintain the 10-N upward resultant. The 10-N resultant, shown as the dashed line vector, is needed to support the 10-N load.

You can safely hang from a vertically hanging clothesline, but you'll break the clothesline if it is strung horizontally.

Activity 1. A massive ball is suspended on a string and slowly pulled by another string attached to it from below, as shown in Figure A below.

a. Is the string tension greater in the upper or the lower string? Which string is more likely to break? Which property, mass or weight, is important here?   b. If the string is instead snapped downward, which string is more likely to break? Is mass or weight important this time?

Newton's Second Law

Activity 2. Motion: How is acceleration related to force, how is acceleration related to mass? Does constant force cause constant velocity? More batteries, more force, more acceleration, how related? More mass, same force, less acceleration, how related?

Number of batteries	acceleration	Mass ( in carts)	acceleration
1
2
3
4

Activity 3. The effect of mass on gravitational acceleration

Mass (in carts) 3 4

Acceleration

The trouble with gravity is that an object falls nearly 10 stories in only 2 seconds, which makes observing or measuring gravitational acceleration difficult. We have already measured the acceleration due to gravity for two objects and discussed the effects of air resistance. Now we will use Galileo's trick of using an inclined plane to slow down the effects of gravity so we can study it more carefully for several masses.

Set up the ramp as indicated in the figure above. Place several books or a box under the end of the ramp to make the angle at least 10o.

First release the empty cart from rest and allow it to roll down the incline. Obtain its acceleration.

Place a bar mass on it to double its mass (each bar has the same mass as the cart). Then place enough mass on it to triple its mass and repeat. Do the accelerations appear to be significantly different? (If you're still not convinced, try cramming 4 times as much mass on the cart.) Use GA to draw a graph of mass vs acceleration. Draw some kind of conclusion about the relationship between acceleration and mass.

A by-the-way question: Can you figure out how this acceleration is related to the angle of the inclined ramp?

Activity 4. What kind of force really does cause constant velocity?

What happens when one hanging mass is larger? Fnet > 0 What happens when they are the same ? Fnet = 0 (give it a shove.) Make a chart showing acceleration as Fnet goes to zero.

PC 0929-Q1

QUESTION 1: Consider a block of ice on a friction-free frozen lake. Suppose a constant force is acting on the block. After the force has acted for some time the speed of the block has increased a certain amount.

Now if we repeat this experiment and let this same force act for twice as long an amount of time, then the increase in speed will be

1. unchanged

2. doubled

3. tripled

4. four-fold

5. cut in half

PC 0929-Q2

QUESTION 2: Consider the same situation as before.

Now we repeat this experiment again and leave the force and action time unchanged, but we double the mass of the block. Now the increase in speed will be

1. unchanged

2. doubled

3. cut in half

4. four-fold

5. cut to one fourth PC 0929-Q3

QUESTION 3: Once again, same situation.

We repeat the experiment again, leaving the mass and action-time unchanged, but doubling the force of the block. Now the increase in speed will be

1. unchanged

2. doubled

3. tripled

4. four-fold

5. cut in half PC 0929-Q4

QUESTION 4: Still, the same situation.

Suppose mass, action time, and force are kept the same, but that by some magical trick, the force of gravity is doubled. Then, the increase in speed will be

1. unchanged

2. doubled

3. cut in half

4. four-fold

5. cut to one fourth PC 1001-Q1QUESTION 1:

The Levi Strauss trademark shows two horses trying to pull apart a pair of pants. Suppose Levi had only one horse and attached the other side of the pants to a fencepost.

Using only one horse would:

1. cut the tension on the pants by one-half

2. not change the tension at all

3. double the tension on the pants

Homework for Chapter 5a: (1 point each for 1-9, 5 pts bonus for #10)

Mass and Weight

Answer each of the following questions. If needed, use a value of 10 m/s2 for the gravitational acceleration on earth and 3 m/s2 on the moon.

1. What is the SI unit for mass?
2. What is the SI unit for weight?
3. What is the mass of a 3 kg object on the earth?
4. What is the mass of a 3 kg object on the moon?
5. What is the weight of a 3 kg object on the earth?
6. What is the weight of a 3 kg object on the moon?
7. An object weighs 60 N when on the earth. What is the mass of this object?
8. What is the weight of this object on the moon?
9. Another object weighs 60 N when on the moon. What is the mass of this object?
10. Research and reward. The gravitational force on a satellite when a distance r from the center of the earth is 4000N. Determine the gravitational force when a distance of 2r from the center of the earth. Hint: Look up gravitational force in your text.