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# Newton’s Laws of Motion Help

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## Introduction to Newton's Law

Three laws, credited to the physicist, astronomer, and mathematician Isaac Newton, apply to the motions of objects in classical physics. These laws do not take into account the relativistic effects that become significant when speeds approach the speed of light or when extreme gravitational fields exist.

### Newton’s First Law

This law is twofold: (1) Unless acted on by an outside force, an object at rest, stays at rest; and (2) unless acted on by an outside force, an object moving with uniform velocity continues to move at that velocity.

### Newton’s Second Law

If an object of mass m (in kilograms) is acted on by a force of magnitude F (in newtons), then the magnitude of the acceleration a (in meters per second squared) can be found according to the following formula:

a = F/m

The more familiar version of this formula is

F = ma

When force and acceleration are defined as vector quantities, the formula becomes

F = m a

### Newton’s Third Law

Every action is attended by an equal and opposite reaction. In other words, if an object A exerts a force vector F on an object B, then object B exerts a force vector – F (the negative of F ) on object A .

## Newton's Law Practice Problems

#### Problem 1

A spacecraft of mass m = 10,500 (1.0500 × 10 4 ) kg in interplanetary space is acted on by a force vector F = 100,000 (1.0000 × 10 5 ) N in the direction of Polaris, the North Star. Determine the magnitude and direction of the acceleration vector.

#### Solution 1

Use the first formula stated earlier in Newton’s second law. Plugging in the numbers for force magnitude Fand mass m yields the acceleration magnitude a:

a = F/m

= 1.0000 × 10 5 /1.0500 × 10 4

= 9.5238 m/s 2

The direction of the acceleration vector a is the same as the direction of the force vector F in this case, that is, toward the North Star. As an interesting aside, you might notice that this acceleration is just a little less than the acceleration of gravity at the Earth’s surface, 9.8 m/s 2 . Therefore, a person inside this spacecraft would feel quite at home; there would be an artificial gravitational field produced that would be just about the same strength as the gravity on Earth.

#### Problem 2

According to Newton’s first law, shouldn’t the Moon fly off in a straight line into interstellar space? Why does it orbit the Earth?

#### Solution 2

The Moon is acted on constantly by a force vector that tries to pull it down to Earth. This force is exactly counterbalanced by the inertia of the Moon, which tries to get it to fly away in a straight line. The speed of the Moon around the Earth is nearly constant, but its velocity is always changing because of the force imposed by the gravitational attraction between the Moon and the Earth.

Practice problems of these concepts can be found at: Mass, Force, And Motion Practice Test

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