Vocab (5.5, 5.9) April 10Vocab (5.5, 5.9) April 10thth, , 2007:2007:

1.1. WeightWeight: F: Fw w ; the amount of ; the amount of gravitational forcegravitational force that the that the earth exerts on an objectearth exerts on an object

2.2. Acceleration due to gravityAcceleration due to gravity: : aagg ; the constant rate of ; the constant rate of acceleration when an object acceleration when an object falls; 9.8 m/sfalls; 9.8 m/s22

Acceleration due to Acceleration due to GravityGravity

PS-5.5: PS-5.5:

Explain how acceleration Explain how acceleration due due to gravity affects the to gravity affects the velocity velocity of an object as it of an object as it falls.falls.

GravityGravity

All objects All objects accelerate as accelerate as they fall because they fall because Earth continually Earth continually exerts a force exerts a force (gravitational (gravitational force) on them.force) on them.

When we drop When we drop something…something…

It accelerates.It accelerates. The direction of the The direction of the forceforce is is

always always downwarddownward.. The acceleration is in the The acceleration is in the

direction of the force so the direction of the force so the direction of direction of accelerationacceleration is is downwarddownward as well. as well.

When we drop When we drop something…something…

It has an It has an initial velocity of ZEROinitial velocity of ZERO.. It will accelerate at a constant It will accelerate at a constant

rate of rate of 9.8 m/s9.8 m/s22..– This means the object will speed up This means the object will speed up

at a constant rate of 9.8 m/s at a constant rate of 9.8 m/s everyevery secondsecond it is falling (in the absence it is falling (in the absence of air resistance).of air resistance).

How velocity is How velocity is affected…affected…

vvi i vvf f

11stst sec sec 0.00.0 m/sec m/sec 9.89.8 m/secm/sec

22ndnd sec sec 9.89.8 m/sec m/sec 19.619.6 m/secm/sec

33rdrd sec sec 19.619.6 m/sec m/sec 29.429.4 m/secm/sec

44thth sec sec 29.429.4 m/sec m/sec 39.239.2 m/secm/sec

55thth sec sec 39.239.2 m/sec m/sec 49.049.0 m/secm/sec

ConclusionConclusion

9.8 m/s9.8 m/s22 ISIS the acceleration of the acceleration of gravity.gravity.

It’s symbol is aIt’s symbol is agg.. Since the object is accelerating Since the object is accelerating

because of Earth’s gravity, the because of Earth’s gravity, the velocity of the object velocity of the object continues to continues to increase in speedincrease in speed and continue in and continue in a downward direction until it hits a downward direction until it hits the ground.the ground.

Motion Diagram Motion Diagram for a falling for a falling

objectobject

Practice Problems—Practice Problems—Show all your work!Show all your work!

1.1. Hallie chased the penguin for 5 meters. It Hallie chased the penguin for 5 meters. It took her 15 seconds to catch it. What was took her 15 seconds to catch it. What was her speed?her speed?

2.2. Duncan slammed on brakes while he was Duncan slammed on brakes while he was driving 50 m/s. It took him 25 seconds to driving 50 m/s. It took him 25 seconds to stop. What was his acceleration?stop. What was his acceleration?

3.3. Daniela lifted her 10kg bookbag with a Daniela lifted her 10kg bookbag with a force of 20 N. With what acceleration did force of 20 N. With what acceleration did she move the bookbag?she move the bookbag?

4.4. Robert grinds the railing of the steps with Robert grinds the railing of the steps with his skateboard but missed it by a his skateboard but missed it by a centimeter. The board goes flying across centimeter. The board goes flying across the pavement, but Robert magically lands the pavement, but Robert magically lands on his feet. Which of Newton’s laws does on his feet. Which of Newton’s laws does this demonstrate?this demonstrate?

The Relationship The Relationship Between Mass and Between Mass and

WeightWeight

PS-5.9 PS-5.9 Explain the relationship Explain the relationship between mass and weight by between mass and weight by using the formula Fusing the formula Fww = ma = magg

The The gravitational forcegravitational force keeps the planets in orbit keeps the planets in orbit

around the Sun. around the Sun.

The Rules of Gravity on The Rules of Gravity on EarthEarth

Objects accelerate as they fallObjects accelerate as they fall The only way that an object can The only way that an object can

accelerate is for a accelerate is for a net forcenet force to to act on it. act on it.

What about objects in freefall?What about objects in freefall?– the net force acting on falling the net force acting on falling

objects = objects = gravitational forcegravitational force exerted exerted by Earth. (neglecting air resistance) by Earth. (neglecting air resistance)

– amount of force by Earth depends amount of force by Earth depends on the object’s masson the object’s mass

Gravity on Earth: MASSGravity on Earth: MASS

The The greatergreater the mass, the the mass, the greatergreater the gravitational force.the gravitational force.

The amount of gravitational force The amount of gravitational force that the earth exerts on an object that the earth exerts on an object is called is called weightweight..

Newton’s 2Newton’s 2ndnd Law Rewritten Law Rewritten

FFww = ma = magg

FFw w = Weight of object = Weight of object m = mass of the object (….kg)m = mass of the object (….kg) aagg = acceleration of gravity for all = acceleration of gravity for all

objects = 9.8m/sobjects = 9.8m/s22

This formula is sometimes written This formula is sometimes written as as w = mgw = mg

ExamplesExamples

Austin measures the mass of an Austin measures the mass of an apple to be 0.15 kg. What is it’s apple to be 0.15 kg. What is it’s weight?weight?

What is the mass of Noell’s car if it What is the mass of Noell’s car if it weighs 9800 N?weighs 9800 N?

A satellite with a mass of 230 kg A satellite with a mass of 230 kg experiences a gravitational force of experiences a gravitational force of 1380 N. What is the acceleration due 1380 N. What is the acceleration due to gravity at the altitude where the to gravity at the altitude where the satellite is orbiting?satellite is orbiting?

ExamplesExamples

A high school student has a mass A high school student has a mass of 60 kg. What will be the of 60 kg. What will be the student’s weight on the moon, student’s weight on the moon, where the acceleration due to where the acceleration due to gravity is 1/6 that of the Earth’s gravity is 1/6 that of the Earth’s gravity?gravity?

How much gravitational force is How much gravitational force is exerted on Joey’s bookbag, exerted on Joey’s bookbag, which has a mass of 18 kg?which has a mass of 18 kg?

Calculating aCalculating agg

Calculate the acceleration due to Calculate the acceleration due to gravity from your measurements gravity from your measurements of Fof Fww and mass, using the and mass, using the balance and the spring scale.balance and the spring scale.

You must do this for 10 objects You must do this for 10 objects of your choosing that are less of your choosing that are less than 0.4 kg (400g).than 0.4 kg (400g).

Find an average value for aFind an average value for agg..

Data TableData Table

Organize your work in a nice summary that Organize your work in a nice summary that includes: Question, Hypothesis, Data Table, includes: Question, Hypothesis, Data Table, Answers to follow up questions, Conclusion.Answers to follow up questions, Conclusion.

You must attach a sheet which shows your You must attach a sheet which shows your calculations in the correct format!calculations in the correct format!

Object DescriptionObject Description FFww mm aagg

Follow Up QuestionsFollow Up Questions Do objects accelerate as they fall?Do objects accelerate as they fall? What must act on an object for an What must act on an object for an

object to accelerate?object to accelerate? What is the relationship between mass What is the relationship between mass

and weight?and weight? What is the relationship between mass What is the relationship between mass

and gravitational force?and gravitational force? If two objects have the same mass, will If two objects have the same mass, will

they have the same weight? Why?they have the same weight? Why? Suppose two identical objects were Suppose two identical objects were

subjected to different accelerations due subjected to different accelerations due to gravity, would they still have the to gravity, would they still have the same weight? Why?same weight? Why?

Calculating HeightsCalculating Heights

• From careful measurements of time and using ag = 9.8 m/s2, you will calculate the height of the stadium bleachers.

• We will be going outside, so be on your best behavior, or else you will be written up and receive a ZERO for the lab exercise!

• You will calculate x - the height of the bleachers. Everyone must do their own work!

Instructions:Instructions:

• Copy the data table on the next slide.

• Perform the procedure.

• Record the results.

• Knowing vi, calculate d - the height of the bleachers. Everyone must do their own work!

• Answer the follow up questions.

Data TableData Table

• Organize your work in a nice summary that includes: Question, Hypothesis, Data Table, Answers to follow up questions, Conclusion.

ag (m/s2) t (s) vi (m/s) x (m)

Follow Up QuestionsFollow Up Questions

• Draw a motion diagram of the ball falling, include scaled arrows to indicate changes in velocity.

• How does the velocity and displacement of an object vary with time as the object falls? Be specific.

• Explain what it means when we say that the acceleration due to gravity is constant.

• Suppose the true height of the bleachers was 1 meter taller than what you calculated, what could account for this error?

• How could a skydiver calculate the height of the airplane he jumped from?