Newton's Second Law of Motion 3.26.12
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.
Acceleration = Force / Mass
Force = Mass * Acceleration
Force = Mass * Acceleration
- Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced.
- The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.
- The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object.
- As the force acting upon an object is increased, the acceleration of the object is increased.
- As the mass of an object is increased, the acceleration of the object is decreased.
- 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.
- This verbal statement can be expressed in equation form as follows: a = Fnet / m
- The above equation is often rearranged to a more familiar form as shown below. The net force is equated to the product of the mass times the acceleration. Fnet = m * a
- 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 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.
- Consistent with the above equation, 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 is often used in algebraic problem solving.
- Acceleration is directly proportional to net force.
- 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.
1. Determine the accelerations that result when a 12-N net force is applied to a 3-kg object and then to a 6-kg object.
A 3-kg object experiences an acceleration of 4 m/s/s. A 6-kg object experiences an acceleration of 2 m/s/s.
2. A net force of 15 N is exerted on an encyclopedia to cause it to accelerate at a rate of 5 m/s2. Determine the mass of the encyclopedia.
Use Fnet= m * a with Fnet = 15 N and a = 5 m/s/s. So (15 N) = (m)*(5 m/s/s) And m = 3.0 kg
3. Suppose that a sled is accelerating at a rate of 2 m/s2. If the net force is tripled and the mass is doubled, then what is the new acceleration of the sled?
Answer: 3 m/s/s. The original value of 2 m/s/s must be multiplied by 3 (since a and F are directly proportional) and divided by 2 (since a and m are inversely proportional)
4. Suppose that a sled is accelerating at a rate of 2 m/s2. If the net force is tripled and the mass is halved, then what is the new acceleration of the sled?
Answer: 12 m/s/s. The original value of 2 m/s/s must be multiplied by 3 (since a and F are directly proportional) and divided by 1/2 (since a and m are inversely proportional
A 3-kg object experiences an acceleration of 4 m/s/s. A 6-kg object experiences an acceleration of 2 m/s/s.
2. A net force of 15 N is exerted on an encyclopedia to cause it to accelerate at a rate of 5 m/s2. Determine the mass of the encyclopedia.
Use Fnet= m * a with Fnet = 15 N and a = 5 m/s/s. So (15 N) = (m)*(5 m/s/s) And m = 3.0 kg
3. Suppose that a sled is accelerating at a rate of 2 m/s2. If the net force is tripled and the mass is doubled, then what is the new acceleration of the sled?
Answer: 3 m/s/s. The original value of 2 m/s/s must be multiplied by 3 (since a and F are directly proportional) and divided by 2 (since a and m are inversely proportional)
4. Suppose that a sled is accelerating at a rate of 2 m/s2. If the net force is tripled and the mass is halved, then what is the new acceleration of the sled?
Answer: 12 m/s/s. The original value of 2 m/s/s must be multiplied by 3 (since a and F are directly proportional) and divided by 1/2 (since a and m are inversely proportional
- The elephant has more mass and more force from gravity.
- The mouse has less mass and less force from gravity.
- Because of this force of both objects is offset by the objects mass.
- This causes acceleration of both objects to be the same.
- Both will hit the ground at the same time.