# Newton's Second Law?

1 What is the acceleration of a 12 kg object if a force of 450 N to the right acts on it?

2 what is the acceleration if an additional force of 160 N to the left is applied while the first force is still acting?

3 For a skydiver falling at high speeds through air, air friction (also called air drag) is actually quite strong. The Force of Gravity on the skydiver is -800 Newtons (the force of gravity is better known as the _____ of the skydiver, and it is negative because the force is pointed -? direction-). Air drag exerts 200 N upward, what is the acceleration of the 80.0 kg skydiver?

4 If an object has a net force of 100 N on it, and it accelerates at 16 m/s2, what is it's mass?

5 If an object has a mass of 60 kg, and it accelerates at 10 m/s2, what is the net force on it?

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• Anonymous

Here you go.

Newton's second law of motion can be formally stated as follows:

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

In terms of an equation, the net force is equated to the product of the mass times the acceleration.

Fnet = m * a

In this entire discussion, the emphasis has been on the "net force." The acceleration is directly proportional to the "net force;" the "net force" equals mass times acceleration; the acceleration in the same direction as the "net force;" an acceleration is produced by a "net force." The NET FORCE. It is important to remember this distinction. Do not use the value of merely "any 'ole force" in the above equation; it is the net force which is related to acceleration. As discussed in an earlier lesson, the net force is the vector sum of all the forces. If all the individual forces acting upon an object are known, then the net force can be determined. If necessary, review this principle by returning to the practice questions in Lesson 2.

The above equation also indicates that a unit of force is equal to a unit of mass times a unit of acceleration. By substituting standard metric units for force, mass, and acceleration into the above equation, the following unit equivalency can be written.

The definition of the standard metric unit of force is stated by the above equation. One Newton is defined as the amount of force required to give a 1-kg mass an acceleration of 1 m/s/s.

The Fnet = m a equation can also be used as a "recipe" for algebraic problem-solving. The table below can be filled by substituting into the equation and solving for the unknown quantity. Try it yourself and then use the "pop-up menus" to view the answers.

Net Force

(N) Mass

(kg) Acceleration

(m/s/s)

1. 10 2 Depress mouse.a = 5 m/s/sa = F/ma = 10 N/2 kga = 5 m/s/s

2. 20 2 Depress mouse.a = 10 m/s/sa = F/ma = 20 N/2 kga = 10 m/s/s

3. 20 4 Depress mouse.a = 5 m/s/sa = F/ma = 20 N/4 kga = 5 m/s/s

4. Depress mouse.F = 10 NF = m aF = 2 kg x 5 m/s/sF = 10 N 2 5

5. 10 Depress mouse.m = 1 kgm = F/am = 10 N/10 m/s/sm = 1 kg 10

The numerical information in the table above demonstrates some important qualitative relationships between force, mass, and acceleration. Comparing the values in rows 1 and 2, it can be seen that a doubling of the net force results in a doubling of the acceleration (if mass is held constant). Similarly, comparing the values in rows 2 and 4 demonstrates that a "halving" of the net force results in a "halving" of the acceleration (if mass is held constant). Acceleration is directly proportional to net force.

Furthermore, the qualitative relationship between mass and acceleration can be seen by a comparison of the numerical values in the above table. Observe from rows 2 and 3 that a doubling of the mass results in a "halving" of the acceleration (if force is held constant). And similarly, rows 4 and 5 show that a "halving" of the mass results in a doubling of the acceleration (if force is held constant). Acceleration is inversely proportional to mass.

The analysis of the table data illustrates that an equation such as Fnet = m*a can be a guide to thinking about how a variation in one quantity might effect another quantity. Whatever alteration is made of the net force, the same change will occur with the acceleration. Double, triple or quadruple the net force, and the acceleration will do the same. On the other hand, whatever alteration is made of the mass, the opposite or inverse change will occur with the acceleration. Double, triple or quadruple the mass, and the acceleration will be one-half, one-third or one-fourth its original value.

As stated above, the direction of the net force is in the same direction as the acceleration. Thus, if the direction of the acceleration is known, then the direction of the net force is also known. Consider the two ticker tape traces below for an acceleration of a car. From the trace, determine the direction of the net force which is acting upon the car. Then depress the mouse on the "pop-up menu" to view the answer. (Review acceleration from previous unit.)

Depress mouse for answer.The net force is to the right sincethe acceleration is to the right.An object which moves to theright and speeds up has arightward acceleration.

Depress mouse for answer.The net force is to the left sincethe acceleration is to the left.An object which moves to theright and slows down has aleftward acceleration.

In conclusion, Newton's second law provides the explanation for the behavior of objects upon which the forces do not balance. The law states that unbalanced forces cause objects to accelerate with an acceleration which is directly proportional to the net force and inversely proportional to the mass.

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