Newton’s First Law of MotionPage 40
Inertia
As a result of his experiments, Galileo claimed that a stationary object tends to stay at rest and a moving object tends to keep moving. Inertia is defined as that property of an object that resists changes in its state of rest or motion. All objects possess inertia. For example, a stationary curling stone on ice requires a force to start it moving. But once moving, the curling stone is difficult to stop.
You experience inertia when riding in a car .When the car accelerates forward, you feel as if your body is being pushed back. Your body resists the increase in speed. The headrest protects you against whiplash during rapid forward accelerations. If the car stops suddenly your body moves forward. Seat belts are designed to resist the tendency of your body to keep moving. When a car turns a corner, the car seat and door exert an inward force to counteract the tendency of your body to keep moving in a straight line.
The inertia of an object depends on its mass: the greater the mass of the object, the more inertia it has. A heavy child on a swing is more difficult to start moving, and to stop, than a light child. Thus, mass is a measure of the inertia of an object. Out in space, the gravitational field intensity and hence the force of gravity on an object are very small. The inertia of the object, however, is the same. This means that mass, rather than force of gravity, affects inertia. It is always more difficult to change the motion of a large mass than a small mass, even out in space!
Demonstrations of Inertia
Try this activity to experience inertia. Hold a nail vertically with the head facing up. Place a small stiff card on the nail. Position a quarter directly above the head of the nail. Try to remove the cardboard and leave the coin on the head of the nail.
Here is an activity to see how mass affects inertia. Use thread to hang a light mass and a heavy mass side by side from a rigid support. Attach another piece of thread to the bottom of each mass. Pull on each bottom thread and try to break it without breaking the top thread. Should you pull fast or slow? Why?
Newton's First Law (Galileo's Principle of Inertia)
Newton was born in the year that Galileo died. Fifty years after Galileo challenged Aristotle's theory.Newton summarized Galileo's ideas describing the motion of both stationary and moving objects. Newton's First Law of Motion states:
According to this law, every object at rest tends to stay at rest. Every object in motion tends to keep moving in a straight line at a constant speed. To change the speed or direction of motion (that is, to change the velocity) requires an external unbalanced force. Because Newton's First Law was based on Galileo's findings, it is sometimes called Galileo's Principle of Inertia.
Applications of Newton's First Law
Anyone who has thrown something out a window has experienced Newton’s first law.
Truck drivers carrying a load of logs are very aware of Newton's First Law. Imagine what would happen to the truck and load if the driver attempted to turn a corner too fast. Envisage the result if a truck was forced to stop too quickly. Trucks like this are equipped with barriers to prevent the logs from coming through the cab.
Newton's Second Law of Motion
Acceleration and Net Force for a Constant Mass
- When a net force, not equal to zero, acts on an object the object will accelerate in the direction of the force.
- The more mass an object has, the less likely it is to accelerate.
These 2 statements make up the basis for Newton’s second Law.
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Acceleration is directly proportional to the Net Force. Therefore:
Acceleration is inversely proportional to the mass. Therefore:
From these two statements we can derive a formula for acceleration:
The constant k has been made equal to one by defining the Newton as being a specific size. Therefore:
Example Problem
Danielle is ten-pin bowling with her friends. She gives a 7.0 kg bowling ball an acceleration of 5.0 m/s2[forward]. Calculate the net force she exerts on the ball.
The equation for net force, mass, and acceleration can be adapted to solve problems involving initial velocity, final velocity, and elapsed time.
Example Problem
Jim and his motorcycle have a combined mass of 280 kg. They accelerate from 7.0 m/s [E] to 34 m/s [E] in 4.2 s. What is the net force on Jim and his motorcycle?
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Example Problem
A peach that weighs 2.0 N is accelerated by a net force of 8.0 N [E]. The force of friction on the peach is 3.0 N [W]. Find the force the squirrel applies to the peach to overcome friction and accelerate the peach.
Newton's Third Law
Newton's Second Law describes quantitatively the relationship between a net force and the acceleration of a mass. But where does the force come from that is exerted on an object? Newton stated that a force applied to one object always comes from another object. The force of gravity on an apple comes from the Earth; the force on a ball that is struck comes from a bat; the magnetic force on a steel nail comes from a magnet; in atoms, the electric force of attraction on orbiting electrons comes from protons.
Forces always occur in pairs. One is called the action force and the other the reaction force. If an action force is exerted by object X on object Y, then a reaction force is exerted by object Y back on object X. The falling apple exerts a reaction force upward on the Earth; the ball pushes backward on the bat; the nail attracts the magnet; and electrons attract protons.
These Observations are summarized in Newton's Third Law of Motion. It states:
Newton's Third Law is often stated as "for every action force there is an equal and opposite reaction force". However, this is confusing because it does not emphasize that the action and reaction forces are on different objects. The action force that the Earth exerts on an apple is equal in size, but opposite in direction, to the reaction force that the apple exerts on the Earth. The reason we see the acceleration of the apple, but not the Earth, is because the apple has less mass than the Earth. Also, we look at the situation from the point of view of the Earth, not the apple.
Examples of Newton' s Third Law
There are countless examples of Newton's Third Law in nature. Try pushing downward on a ball of putty with the palm of your hand. The putty changes shape, indicating that a force is present. But your hand also changes shape. Where does the force come from that changes your hand? From the putty, of course!
Try standing on a skateboard facing a partner on another skateboard. Choose a partner with a mass about equal to your own. Give your partner a gentle push. What happens? The partner accelerates away from the initial position because of the action force you exert. But you also accelerate in the opposite direction because your partner exerts a reaction force on you. This reaction force has the same magnitude as, but is opposite in direction to, your action force.
The motion of a rocket illustrates Newton's Third Law. In order to move, the rocket expels gaseous molecules. The rocket exerts a large force backward on the molecules to expel them at a very high speed. At the same time, the gaseous molecules exert a forward force of equal magnitude on the rocket. Many people think that the expelled molecules must push against the ground or the atmosphere to propel the rocket. This is not true. If this was the case, the rocket would be unable to accelerate in the vacuum of outer space.
Example Problem
Two steel blocks rest on a frictionless, horizontal surface. Block X has a mass of 6.0 kg, and is attached by means of a light taut string to block Y, that has a mass of 12 kg. A force of 36 N [E] is applied to block X, as shown below.
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Applications of Newton's Third Law
Lawn Sprinklers The motion of some lawn sprinklers involves Newton's Third Law. Can you explain why the water goes in one direction, and the lawn sprinkler head of a rotary sprinkler goes in the opposite direction?
Propeller Driven Machines Have you ever wondered what exerts the force to move a propeller-driven machine, such as an airplane, through the air?
It is hard to believe that air, thrust backward by the propeller, pushes the propeller and machine forward. The blades of the propeller are slanted so that they grab new air during each revolution. This air is accelerated backward by the propeller. But according to Newton's Third Law, the accelerated air pushes forward on the propeller. The faster the propeller turns, the greater the mass of air directed backward, and the faster the machine moves forward.
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Review QuestionsName:
1. Use Newton's First Law to describe the following:
a) dint on a shovel when the shovel is suddenly stopped.
b) a car that attempts to go around an icy curve too quickly.
c) a child on a sled that is suddenly jerked forward.
2. a) How are mass and inertia related?
b) Give an example (that we haven’t already talked about)that illustrates the property of inertia for both a stationary and a moving object.
3. Use Newton's First Law and the property of inertia to explain the following.
a) If a sheet of newspaper under a beaker, is pulled slowly, the beaker is pulled off the table. If the newspaper is pulled rapidly, the beaker stays on the table.
b) While moving horizontally at a constant velocity on the snowmobile Shawn throws a ball vertically upward so that it reaches a height of 5 m. If the snowmobile continues moving at a constant velocity, the ball returns to Shawn. But if the snowmobile stops, the ball lands ahead of Shawn. (ignore wind resistance)
4. Compare the motion of a hockey puck shot along clean, hard ice, and
a sponge of the same size, hit with the same force along the same ice.
5. The net force on a 6.0 kg grocery cart is 12 N [S]. Calculate its acceleration.
6. In a road test, a 1988 Corvette is given an acceleration of 2.7 m/s2 [E] by a net force of 4.2 x 103 N [E]. Calculate the Corvette's mass.
7. What net force is needed to accelerate a 208 kg motorboat at 3.61 m/s2 [S]?
8. Shannon applies a force of 8.0 N [S] to give a 2.5 kg sled an acceleration of 3.0 m/s2 [S]. Calculate the force of kinetic friction.
9. What total force does Trevor have to apply to accelerate a 2.0 Kg steel bolt at 3.0 m/s2 [forward] along a rough surface against a force of friction of 9.0 N.
10. Use Newton's Third Law to explain why
a) a walker exerts a force backward on the ground to walk forward.
b) the larger the bullet fired by a gun, the more the gun recoils.
c) a swimmer at the edge of a pool pushes backward on the wall to move forward.
d) when a person throws a package onto the shore from a canoe, the canoe moves away from shore.
11.State the reaction force to each of the following action forces:
a) the Earth attracts the moon with a force of 9.7 x 1024 N
b) a book pushes down on a table with a force of 18 N
c) water pushes sideways on the centre board of a sailboat with a force of 600 N
d) the weight of a mass exerts a force of 30 N [down] on a string
12. A 5.0 kg block Y is attached to a 10 kg block X on a smooth level table bya light taut string, as shown below. Calculate the action and reaction forces on the blocks if a force of 36 N [5] acts on block X.
6. For Question 12, assume that the force of friction on the 5.0 kg block is 4.0 N and the force of friction on the 10 kg block is 8.0 N. Calculate the action and reaction forces.