Section 3.2 Newton s Laws of Motion Objectives Analyze relationships between forces and motion Calculate the effects of forces on objects Identify force pairs between objects New Vocabulary Newton s first law of motion Inertia Mass Newton s second law of motion Newton s third law of motion Force pairs What do you think of when you think of a law? Whether they concern traffic, the environment, or the economy, laws set a limit on what can and cannot be done. There are laws in physics as well. The laws of physics govern the concepts of energy, matter, heat, and more. There are three major laws that govern linear motion. These laws, based on force and acceleration, describe the behavior and detail the limits of standard motion. Figure 3.1
Law of Inertia Newton s first law of motion states that an object will maintain its current state of motion unless it is acted upon by an unbalanced force. This law is often called the law of inertia. Inertia is a property of matter that describes its tendency to resist a change in motion. Jump to Net Force Mass is a measurement of the quantity of matter and is also related to inertia. A more massive object has more inertia. For example, a rock has mass and also inertia. If a rock is at rest on the ground, it does not experience an unbalanced force and will remain at rest. The downward pull of gravity is balanced by the upward normal force. If an additional unbalanced force, like the force from being kicked, were applied to the rock, the rock would no longer remain at rest. If the rock were more massive, it would have more inertia, so a more powerful kick is needed to make the larger rock begin moving with the same velocity as the less massive rock. The law of inertia also applies to objects in motion. An object in motion will continue moving at a constant velocity until it is acted upon by an unbalanced force. For example, if a bowling ball rolled across a completely frictionless surface with no other obstacles in the way, it would continue to roll at the same velocity forever. More force would be necessary to Figure 3.2-1 The cooler that was attached to the roof of a vehicle continues in motion after the vehicle is stopped by the force from a wall. abruptly stop the bowling ball than the force required to stop a marble traveling with the same velocity. Another example of the law of inertia is shown in Figure 3.2-1. The vehicle and the cooler on the roof were traveling at a certain velocity, until the vehicle experienced the unbalanced force from the wall. The force from the wall is great enough to drastically change the velocity of the vehicle, causing it to stop. At the moment of impact, the cooler, which does not experience the force of the wall, continues moving forward with the same velocity that it had when it was attached to the roof. Jump to Velocity Chapter 3 - Forces 96 Section continues
In everyday life, it often seems as if objects slow down on their own without a force being applied. If a book is initially pushed across a table and then released, it will slow down and stop. However, the book still obeys Newton s first law of motion, because the unbalanced force acting on the book is the frictional force. The book can move at a constant velocity while the applied force is equal to the frictional force opposing its motion, as shown in the free-body diagram in Figure 3.2-2. Objects traveling on near frictionless surfaces, such as a hockey puck on the ice, will slow down at a much slower rate than objects traveling on higher friction surfaces. Jump to Free-Body Diagrams Figure 3.2-2 A book is pushed across a table by an applied force. The net force on the book is zero so the book moves with a constant velocity. Chapter 3 - Forces 97 Section continues
Force & Acceleration When a non-zero net force acts on an object it causes the object to accelerate in the direction of the net force. Newton s second law of motion states that the acceleration of an object is directly related to the net force acting on the object and inversely related to the mass of the object. This means that when the net force on the object is increased, the acceleration of an object will also increase and if the net force on an object is decreased, the acceleration of the object will also decrease. Also, a net force applied to an object with a smaller mass will cause it to accelerate more than if the same net force was applied to an object with a larger mass. Jump to Acceleration Jump to Mass Newton s second law also takes the form of an equation where the net force acting on an object (F net ) is equal to the mass of an object (m) multiplied by its acceleration (a). net force = (mass)(acceleration)"" " " " F net = ma" Recall that force is measured in newtons, N. Now newtons can be broken down using Newton s second law. Since mass is measured in kilograms and acceleration is measured in meters per second squared, a newton is a kilogram meter per second squared. N = kg m s 2 " Chapter 3 - Forces 98 Section continues
Example problem A 91 N force causes an object to accelerate at 0.76 m/s 2. What is the mass of the object? I. Strategy The problem provides net force and acceleration and asks for the mass of the object. The mass can be found from the net force and acceleration using the equation for Newton s second law. II. Given and unknown F net = 91 N " " " " " a = 0.76 m /s 2 " " " " " m =? III. Formula F net = ma so m = F net a IV. Conversions needed? No. All variables are in standard SI units. V. Intermediates needed? No. Since values are given for all of the variables in the equation except for the one being solved for, no intermediate calculations are needed. " " " 91 N VI. Solve m = = 120 kg 0.76 m /s2 VII. Does the result make sense? This answer is reasonable because the force is quite large and the acceleration is relatively small. Also the units involved in the calculation cancel each other out to yield the correct units for mass. N = ( m s 2 ) ( kg m s 2 ) = kg" ( m s 2 ) Chapter 3 - Forces 99 Section continues
Example problem A 250 N net force is applied to a 72 kg object. What is the acceleration of the object? I. Strategy The problem provides net force and mass and asks for the acceleration of the object. The acceleration can be found from net force and mass by using the equation for Newton s second law. II. Given and unknown F net = 250 N" " " " " " " " m = 72 kg " " " " a =? III. Formula F net = ma so a = F net m IV. Conversions needed? No. All variables are in standard SI units. V. Intermediates needed? No. Since values are given for all of the variables in the equation except for the one being solved for, no intermediate calculations are needed. VI. Solve a = 250 N 72 kg = 3.5 m /s2 VII. Does the result make sense? This answer is reasonable because the units involved in the calculation cancel each other out to yield the correct units for acceleration. N kg = (kg kg m s 2 ) = m s 2 " Chapter 3 - Forces 100 Section continues
Example problem A 5.0 kg object is traveling at a constant velocity of 3.2 m/s. What is the net force acting on the object? I. Strategy The problem provides mass and velocity and asks for the net force. Since the problem states that the object is traveling at a constant velocity, its acceleration is zero. The net force can be found from mass and acceleration using the equation for Newton s second law. II. Given and unknown m = 5.0 kg " " " " " v = 3.2 m /s " " " " " a = 0 m /s 2 " " " " " F net =? III. Formula F net = ma IV. Conversions needed? No. All variables are in standard SI units. V. Intermediates needed? No. Since values are given for all of the variables in the equation except for the one being solved for, no intermediate calculations are needed. VI. Solve F net = (5.0 kg)(0 m /s 2 ) = 0 N VII. Does the result make sense? The answer is reasonable because the object is not accelerating. Also, the units involved in the calculation combine to yield the correct units for force. ( kg m )( s 2 ) = kg m s = N" 2 Chapter 3 - Forces 101 Section continues
Lab - Force & Acceleration Newton s second law of motion describes the relationship between the net force applied to an object, the mass of the object, and its acceleration. The following virtual lab will provide you with the opportunity to vary the force on a ball and the mass of the ball to determine the effects on its acceleration. By increasing the force or decreasing the mass, you should have been able to increase the acceleration of the ball. Since force and acceleration are directly related and mass and acceleration are inversely related, this is consistent with Newton s second law of motion. Chapter 3 - Forces 102 Section continues
Friction & Acceleration Because friction is a force, the amount of friction acting on an object has an effect on its acceleration. Video 3.2-1 shows two blocks nearly identical in mass and shape sliding down an inclined plane. The bottom of one block is covered with a smooth surface, and the bottom of the other is covered with a rough surface. The smooth block slides down the ramp from rest in about 0.6 s, whereas the rough block slides the same distance down the ramp from rest in about 1.2 s, so the smooth block has more acceleration. The difference in acceleration between the two blocks can be accounted for by the difference in frictional force acting on them. The smooth block has more acceleration because there is less friction between it and the inclined plane than there is between the rough block and the inclined plane. Video 3.2-1 The amount of friction acting on each block affects its acceleration. The block with the greater acceleration has less friction acting on it, whereas the block with less acceleration has more friction acting on it. Chapter 3 - Forces 103 Section continues
Force Pairs Newton s third law of motion states that for every action there is an equal and opposite reaction. This means that whenever a force is applied by one object to another, the second object applies the same amount of force onto the first object in the opposite direction. Jump to Force The equal and opposite forces between two objects are often called force pairs. An example of a force pair occurs when a person pushes against a wall. The person applies a force to the wall (F person on wall ) and the wall applies a force equal in magnitude, but opposite in direction, to the person (F wall on person ). F person on wall = F wall on person " For example, if the person applies a force of 300 N on the wall, the wall will apply force of -300 N on the person, where the negative sign denotes the direction of the force. A subtle force pair can be observed when a ball is resting on the ground. The force of gravity by the Earth pulls down on the ball, while the ball exerts an equal but opposite force upward on the Earth. Although these forces do not seem apparent, the world would be very different without them. The book on the table in Figure 3.2-2 is not accelerating, which means that according to Newton s second law of motion, the net force on the book is zero. Since the net force on the book is zero, the normal force (F N ) is equal to the force of gravity (F g ) but in the opposite direction. It might be tempting to think that the normal force on the book and the force of gravity on the book make up a force pair described by Newton s third law, but this is not the case. There are two force pairs in this situation. One is the force of gravity by the Earth on the book and the force of gravity by the book on the Earth. The other force pair is the force by the table on the book and the force by the book on the table. Force pairs are always symmetrical and of the same type, such as gravitational, normal, or applied, to name a few. Notice that the force by the book on the Earth and the force by the book on the table are not shown on the free-body diagram. This is because a freebody diagram only shows forces acting on the object of interest and not forces by the object of interest. Jump to Figure 3.2-2 The applied force on the book (F A ) and the frictional force (F F ) on the book are not considered a force pair as described by Newton s third law, either. The force applied to the book creates a force pair with the force applied by the book. Similarly, the frictional force from the surface applied to the book creates a force pair with the force applied to the surface by the book. Chapter 3 - Forces 104 Section continues
There are three different force pairs in the example in Figure 3.2-3. One force pair is the downward force of the string on the ceiling and the upward force of the ceiling on the string. The second force pair is the upward tension force of the string on the mass and the downward tension force of the mass on the string. The third force pair is the downward pull of the gravity by the Earth on the mass and the upward pull of the gravity by the mass on the Earth. The force of gravity on the mass and the tension force on the mass do not make a force pair. Figure 3.2-3 There are three different force pairs present in this diagram of a mass suspended from the ceiling by a string. Chapter 3 - Forces 105 Section complete