free body diagrams

Frank and Alex in a tug-of-war
• Draw the free body diagram on the back of your sheet or your notes for Frank winning (accelerating away) a tugof-war with Alex

– Draw Frank and Alex as separate objects, with forces acting on each
– How many forces are there on each?
– Identify Newton’s 3rd law pairs
– Identify Newton’s 2nd law relationships

1

Frank and Alex in a tug-of-war
• Draw the free body diagram on the back of your sheet or your notes for Frank winning (accelerating away) a tugof-war with Alex
FN1

Ff1

FN2

Frank

FT
Fg1

Ff1 - FT = m1a

FT

Alex

Ff2

Fg2
FT - Ff2 = m2a
2

Worksheet – Elevator Physics
Sketch three free-body diagrams, for the situation of you inside an elevator, with the whole system at rest.
- Be sure to note that the ‘system’ always includes both you and the elevator

Forces that belong on a free-body diagram
Only forces that are being applied to the object should appear on that object’s free-body diagram. We should include a downward normal force, applied to the elevator by you.
Yes, mg is numerically equal to this normal force in this case. When the system has an acceleration, however, these forces are no longer equal.

The system has a constant velocity directed up
When the system of you and the elevator is moving up with a constant velocity, what do we need to change on the freebody diagrams?

1.

An extra force, directed up, needs to be added to each free-body diagram.

2.

One or more of the existing forces needs to change in magnitude.

3.

No changes are necessary.

Constant velocity
No changes are required – the forces must still all balance. (“As far as forces are concerned, at rest and constant velocity are the same thing.”)

The system has a constant acceleration directed up
When the system of you and the elevator has a constant acceleration directed up, what do we need to change on the free-body diagrams?

1.

An extra force, directed up, needs to be added to each free-body diagram.

2.

One or more of the existing forces needs to change in magnitude.

3.

No changes are necessary.

Constant acceleration
In this case, each free-body diagram needs to show a net force directed up. This is achieved by making appropriate adjustments to the tension in the cable, and the normal force associated with the interaction between you and the elevator. The circled forces increase in magnitude when the elevator has an upward acceleration. Two boxes
You accelerate a system of two boxes to the right by pushing on the green box with a 15 N force directed right.
The green box has a larger mass than the blue box.
Sketch the three free-body diagrams asked for on the worksheet. The boxes are on a frictionless table.

Which box applies a larger force to the other?
Consider magnitudes of forces only.
1.

The green box applies more force to the blue box than the blue box applies to the green box.

2.

The blue box applies more force to the green box than the green box applies to the blue box.

3.

The green box applies a force to the blue box that has the same magnitude as the force the blue box applies to the green box.

What did we learn from the “Forces between Carts” experiment?

Which box experiences a larger net force?
The two boxes accelerate as one unit.
1.

The green box experiences a larger net force.

2.

The blue box experiences a larger net force.

3.

The net forces are equal.

Apply Newton’s Second Law
The net force is equal to the product of the mass multiplied by the acceleration.
How do the accelerations compare?
The boxes have the same acceleration.
How do the masses compare?
The green box has a larger mass. ma for the green box is larger than ma for the blue box - the green box has a larger net force on it.

Calculate the acceleration of the system
Let’s choose positive to be to the right.
Which of the three free-body diagrams should we use? Find the acceleration

The simplest is the free-body diagram of the two-box system. Apply Newton’s Second Law.
The vertical forces cancel, so we can neglect them.

Find the force the green box applies to the blue box.
Which free-body diagram should we use?

Find the force the green box applies to the blue box.
Let’s use the free-body diagram of the blue box.

Apply Newton’s Second Law - again, the vertical forces cancel. The net force on the blue box is the force the green box applies to the blue box, 6.0 N to the right.

Find the force the blue box applies to the green box.
Which free-body diagram should we use?

Find the force the blue box applies to the green box.
In this case, let’s use the free-body diagram of the green box.
Apply Newton’s Second Law
(vertical forces cancel).


∑ F = mG a = 3.0 kg × (+3.0 m/s 2 ) = +9.0 N
The net force is the vector sum of the 15 N force directed right, and the force the blue box exerts

to the left.

15.0 N + FN ,B→G = +9.0 N

FN ,B→G = +9.0 N − 15.0 N = −6.0 N

This agrees with Newton’s third law.