Isaac Newton, whom you have learned about in other lessons, studied the motion of objects. He developed three laws of motion, which are now called Newton's laws of motion. (You will learn more about these laws in lessons 8-10 of this module.)

In Newton's second law of motion, he described the relationship of force, mass, and acceleration mathematically. Force can be calculated by multiplying the mass of an object by the acceleration of the object.

The formula is

Net Force= (mass)(acceleration) or F = ma

In honor of Newton's contribution to the understanding of force and motion, the standard unit of force is called the newton (N). A newton is defined as the amount of force that it takes to accelerate one kilogram (1 kg) of mass one meter per second squared (1 m/s2). So 1 N is the same as 1 kg • m/s2.

When solving net force problems, make sure that the mass in in kilograms and the unit for acceleration is m/s2.

If you are given the mass in grams, make sure and convert to kilograms (move the decimal three places to the left.) For example,

5g = .005kg

Let's do some practice problems.

### Practice Problem 1 What force is needed to accelerate a 10 kg shopping cart 3 m/s2?

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F = ma
F = 10kg • 3 m/s2
F = 30 kg • m/s2 or 30 N ### Practice Problem 2 The Space Shuttle has a lift off mass of 2,041,000 kg and accelerates at a rate of 16 m/s2. Calculate the force (thrust) that is accelerating the Space Shuttle.

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F = ma
F = 2,041,000 kg • 16 m/s2
F = 32,656,000 kg • m/s2 or 32,656,000 N ### Practice Problem 3 A person on a scooter is accelerating 2 m/s2. If the person has a mass of 50,000 g, how much force is acting on that person?

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In this problem the mass is in grams so you must convert to kg first.
50,000 g = 50 kg
F = ma
F = 50 kg • 2 m/s2
F = 100 kg • m/s2 or 100 N ### Challenge Problem

Which of the following requires more force?

Moving a 500 kg box at an acceleration of 1 m/s2 Or

Moving a 50 kg box at an acceleration of 1 m/s2

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Calculate the force needed to move each box.
 F = ma F = 500kg • 1 m/s2 F = 500 kg • m/s2 or 500 N F = ma F = 50kg • 1 m/s2 F = 50 kg • m/s2 or 50 N

So we can say the greater the objects mass, the greater the force needed to move the object. 