Module 3 Lesson 1

Module 3—Effects of Force on Velocity

Read

Read pages 146 to 148 in your textbook starting at “Relating Acceleration and Net Force.” Look for the way acceleration is related to force and to mass, and read about what inertial mass means.

Self-Check

SC 3. The same net force is applied to two objects, A and B. If object B has three times the mass of object A, what can you say about the acceleration of object B compared to object A?

Check your work.

SC 3. Object B will have one-third the acceleration of object A.

Newton's Second Law

Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.

The modern translation of the second law is as follows:

The rate of change of velocity of an object is proportional to and in the same direction as the unbalanced force acting on it.

Recall that kinematics describes the motion of an object in terms of its velocity, displacement, and acceleration. Now consider that dynamics explains the motion of an object in terms of the force causing it. The basic equation that allows motion to be explained is contained in the second law: If an unbalanced force is applied to an object, the object will accelerate in the direction of the unbalanced force.

The word unbalanced can be replaced by the word net, as you will notice in the following examples:

The magnitude and direction of acceleration is directly proportional to the magnitude and direction of the net (unbalanced) force causing it.
The magnitude of the acceleration is inversely proportional to the mass of the object. For example, if the same net (unbalanced) force acts on two objects, one being half as massive as the other, the acceleration of the less massive object will be larger.

Newton’s second law relates the change in velocity of an object with the unbalanced force causing it.

The equation is as follows:

Quantity	Symbol	SI Unit
net force		N
acceleration		m/s2
mass	m	kg
* 1 N is equivalent to 1 kg·m/s2. In other words, 1 N of force will cause a 1-kg object to accelerate at 1 m/s2. ** F = ma is a common convention that describes Newton’s second law, but it is actually a combination of the first and third laws, presented in a useful form. This form did not begin to be used until the eighteenth century, after Newton had died; however, it is clearly implied in his laws.

Problem Solving with Newton’s Second Law

net force: the sum of the forces acting on an object (see unbalanced force)

Newton’s second law can be used to predict the acceleration of an object. In the simplest case, a single force acts on an object, causing it to accelerate. In a more complex case, the vector sum of many forces (net force) acts on an object, causing it to accelerate. In all cases, however, the observed acceleration of the object will be in the same direction as the net force (the vector sum of all the forces acting on the object).

The following three example problems show how the calculations are to be done.

Example Problem 1

A car being driven on a road experiences several forces—the force of friction due to the road and the air, and the force of the engine that pushes the car forward. Describe the car’s acceleration in the following situations:

The engine force is greater than the frictional force.
The engine force is less than the frictional force.
The engine force equals the frictional force.

Solution

There is a net force that will cause the car to accelerate forward (speed up).

© Tomasz Pietryszek/shutterstock
There is a net force that will cause the car to accelerate backwards (slow down).

© Tomasz Pietryszek/shutterstock
The net force is zero. According to Newton’s first law, the car will maintain a constant velocity.

© Tomasz Pietryszek/shutterstock

Example Problem 2

What force is required to accelerate a 60.0-kg mass at –4.00 m/s2?

Given

m = 60.0 kg = –4.00 m/s2

Required

the net force ()

Analysis and Solution

Use Newton’s second law to find the net force.

Paraphrase

The required force is –240 N.

Example Problem 3

A 4.00-kg mass resting on a frictionless surface experiences a 16.0-N force acting west. What is the resulting acceleration?

Given

m = 4.00 kg = 16.0 N [W]

Required

the acceleration of the mass ()

Analysis and Solution

Use the scalar form of Newton’s second law to find the acceleration, because the acceleration will be in the same direction as the force.

Paraphrase

Correct to 3 significant digits, the resulting acceleration is 4.00 m/s2 [W].

Module 3: Lesson 1 Assignment

Remember to submit the answers to TR 3, TR 4, TR 5, and TR 6 to your teacher as part of your Module 3: Lesson 1 Assignment.

Try This

In solving the following problems, be sure to write the equation, rearrange the equation (if necessary), and substitute values for the variables in the equation. Then solve and answer the question.

TR 3. If a vehicle is involved in a collision that produces a −1500 N net force, what is the acceleration of a 75.5-kg passenger in the car?

TR 4. If an unbalanced force of +55.2 N causes a hockey puck to accelerate across some ice with an acceleration of +100 m/s2, what is the puck's mass?

TR 5. A plane with a mass of 4.50 × 103 kg accelerates on takeoff at 10.0 m/s2. What is the net force acting on the plane?

TR 6. A car can accelerate at 18.0 m/s2 and has a mass of 3500 kg. A motorcycle engine can produce 9000 N of force at maximum power output. If the motorcycle has a mass of 565 kg, can it accelerate faster than the car?