Newton 2nd Law

• Today we understand Newton’s Second law and how it can be used to measure mass is a different way.

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

Second Law of Motion: “The Law of Acceleration”

What does this law tell us?•Objects that are not in equilibrium will accelerate.

•Note the difference between a force and a net force. A good analogy is to compare deposits/withdrawals into a bank account with the account balance.

vF mva

“sigma” = sum F and aare vectors

•Net force (sum of all forces) on an object causes acceleration.

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Inertial and Gravitational Mass

F g m

g

Inertial and gravitational masses have been tested and are believed to always be equal in amount. This is why all objects freefall at the same rate of acceleration.

F mra

Relates to how a mass responds to the force of gravity (also called a field force).

Relates to how a mass responds to an external force (also called a contact force).If you push a stalled car into motion you are testing its inertial mass.

If you lift up a stalled car you are testing its gravitational mass.

Inertial mass

Gravitational mass

In the equation for weight, g is no longer considered the acceleration due to gravity, but rather the gravitational field strength, with units of newtons/kilogram.

inertial mass

gravitational mass

Constant acceleration from gravity• Galileo found that balls of

different masses fell at the same rate.

• The force of gravity is stronger for more massive objects.

• But it requires more force to accelerate a more massive object (inertia).

• These two effects cancel each other out.

How does this relate to gravity?• We have already talked object that are in free fall

always fall with a acceleration of 9.8 or 10 m/s2.– Remember the acceleration in the y direction for all of

those fun freefall problems?

• Well this is why they do.

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gmam

FF

gmF

amF

gi

g

gg

i

Mini Lab: Mass Two Ways

• The first way is that you will measure the mass of the car using a triple beam balance.

• What type of mass are you measuring?

• The second way is to plot the Net Force vs Acceleration on a graph.

• Y= x

• ΣF = a• Slope of a F vs a graph

is__________.• What type of mass are

you measuring?

Conclusion

• Are the masses the same?

• What is their percent difference?