September 10September 10

AP physicsAP physics

Two forces act on a 6.00-kg object. One of Two forces act on a 6.00-kg object. One of the forces is 10.0 N. If the object the forces is 10.0 N. If the object accelerates at 2.00 m/saccelerates at 2.00 m/s22, what is the , what is the greatest possible magnitude of the greatest possible magnitude of the other force?other force?

  

a. 1.0 Na. 1.0 N

b. 2.0 Nb. 2.0 N

c. 22.0 Nc. 22.0 N

d. 34.0 Nd. 34.0 N

  

Objective:Objective:To To understandunderstand::

– Forces and pulleysForces and pulleysFree body diagramsFree body diagramsSum of the forcesSum of the forcesTensionTensionAccelerationAcceleration

Success CriteriaSuccess CriteriaBe able to solve pulley problemsBe able to solve pulley problems

Pulley systemPulley system

Set up #1: Equal masses: Draw a Set up #1: Equal masses: Draw a diagram:diagram:

Examine the pulley system.Examine the pulley system.– What do you notice?What do you notice?

Set up #2: Set up #2: ΔΔm=50gm=50g– What do you notice?What do you notice?

Set up #3: Set up #3: ΔΔm=100gm=100g– What do you notice?What do you notice?

Set up #4: Set up #4: ΔΔm=50g total mass m=50g total mass increasedincreased– What do you notice?What do you notice?

What can we say about What can we say about pulleys?pulleys?

Forces and pulleysForces and pulleys

Pulley rules:Pulley rules:

Pulleys only change the direction of Pulleys only change the direction of the forces.the forces.

Pulleys are frictionlessPulleys are frictionlessThe do not add any force to the The do not add any force to the

systemsystem

Strings don’t stretchStrings don’t stretchThe acceleration of one body is the The acceleration of one body is the

same as the other body only same as the other body only negativenegative

Strings only pullStrings only pullThe direction of the force is always The direction of the force is always

away from the object.away from the object.

Strings have no mass.Strings have no mass.

Steps to solve a pulley Steps to solve a pulley problem:problem:1.1. Draw a free body diagram of each Draw a free body diagram of each

mass.mass.

2.2. Sum the forces on each body Sum the forces on each body separatelyseparately

3.3. Solve for acceleration of each body.Solve for acceleration of each body.

4.4. Set the two accelerations equal and Set the two accelerations equal and opposite.opposite.

5.5. Solve for TensionSolve for Tension

6.6. Re-substitute to get accelerationRe-substitute to get acceleration

mm11=4 kg=4 kg

mm22=8 kg=8 kg

What is the tension?What is the tension?

What is the acceleration?What is the acceleration?

Solve for Tension Solve for Tension

and accelerationand acceleration

50 kg

35 kg

Practice: pulleysPractice: pulleys

Out:Out:

m1=4.5kg

Draw a free body diagram of each mass:

What is the tension in the string?

What is the acceleration of the system?

m2=1.5kg