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# Newton's Second Law

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These boys are racing around the track at Newton’s Skate Park. The boy who can increase his speed the most will win the race. Tony, who is closest to the camera in this picture, is bigger and stronger than the other two boys, so he can apply greater force to his skates.

Q : Does this mean that Tony will win the race?

A : Not necessarily, because force isn’t the only factor that affects acceleration.

### Force, Mass, and Acceleration

Whenever an object speeds up, slows down, or changes direction, it accelerates. Acceleration occurs whenever an unbalanced force acts on an object. Two factors affect the acceleration of an object: the net force acting on the object and the object’s mass. Newton’s second law of motion describes how force and mass affect acceleration. The law states that the acceleration of an object equals the net force acting on the object divided by the object’s mass. This can be represented by the equation:

$\mathrm{Acceleration=\frac{Net\;force}{Mass}}$

or $\mathrm{a=\frac{F}{m}}$

Q : While Tony races along on his rollerblades, what net force is acting on the skates?

A : Tony exerts a backward force against the ground, as you can see in the Figure below , first with one skate and then with the other. This force pushes him forward. Although friction partly counters the forward motion of the skates, it is weaker than the force Tony exerts. Therefore, there is a net forward force on the skates.

### Direct and Inverse Relationships

Newton’s second law shows that there is a direct relationship between force and acceleration. The greater the force that is applied to an object of a given mass, the more the object will accelerate. For example, doubling the force on the object doubles its acceleration. At the following URL, you can simulate pushing a 2000-kilogram elephant on skates, using different amounts of force. Do the simulation to see how changing force while holding mass constant changes the acceleration of the skating elephant.

The relationship between mass and acceleration is different. It is an inverse relationship. In an inverse relationship, when one variable increases, the other variable decreases. The greater the mass of an object, the less it will accelerate when a given force is applied. For example, doubling the mass of an object results in only half as much acceleration for the same amount of force.

Q : Tony has greater mass than the other two boys he is racing above. How will this affect his acceleration around the track?

A : Tony’s greater mass will result in less acceleration for the same amount of force.

### Summary

• Newton’s second law of motion states that the acceleration of an object equals the net force acting on the object divided by the object’s mass.
• According to the second law, there is a direct relationship between force and acceleration and an inverse relationship between mass and acceleration.

### Vocabulary

• Newton’s second law of motion : Law stating that the acceleration of an object equals the net force acting on the object divided by the object’s mass.

### Practice

At the following URL, use the simulator to experiment with force, mass, and acceleration. First keep force constant at 1 N, and vary mass from 1–5 kg. Next keep mass constant at 1 kg, and vary force from 1–5 N. In each simulation, record the values you tested and the resulting acceleration. Finally, make two line graphs to plot your results. On one graph, show acceleration when force is constant and mass changes. On the other graph, show acceleration when mass is constant and force changes. Describe in words what the two graphs show.

### Review

1. State Newton’s second law of motion.
2. How can Newton’s second law of motion be represented with an equation?
3. If the net force acting on an object doubles, how will the object’s acceleration be affected?
4. Tony has a mass of 50 kg, and his friend Sam has a mass of 45 kg. Assume that both friends push off on their rollerblades with the same force. Explain which boy will have greater acceleration.