Gravitational Fields

Physics 30S

Outcomes• The student will be able to:• S3P-4-01: Define the gravitational field

qualitatively as the region of space around a mass where another point mass experiences a force.

• S3P-4-02: Diagram the Earth’s gravitational field, using lines of force.

• S3P-4-03: Define the gravitational field quantitatively as a force per unit mass.

• S3P-4-04: Compare and contrast the terms “mass” and “weight.”

Outcomes Continued

• S3P-4-05: Describe, qualitatively and quantitatively, apparent weight changes in vertically accelerating systems. Examples: elevators, spacecraft…

• S3P-4-06: Derive the acceleration due to gravity from free fall and Newton’s laws.

• S3P-4-07: Perform an experiment to calculate g near the surface of the Earth.

• S3P-4-08: Solve free-fall problems.

Gravitational Fields

• What is a field?• A field is a region in space where an object

would experience a force.• The field type is determined by the type of

force– A gravitational field is an area in space where an

object would experience a gravitational force– An electric field is an area in space where an

object would experience an electric force

What is Gravity?

• Gravity is an inherent attraction between two objects with mass.

• Gravity is rare in that it is only an attractive force – it cannot repel

• All matter has mass, and therefore is affected by gravity

Drawing Fields

• Michael Faraday (experimental physicist known for his contributions to electricity) determined a method to represent fields symbolically

• Fields around an object are indicated by arrows• A greater number of arrows per unit area

indicates a stronger field• Arrow head indicates direction of field

(direction of the force experienced by a test mass.

Example 1

• Draw the gravitational field for a 1 kg round mass.

Example 2

• Draw the gravitational field for Earth.

• It’s exactly the same!!!

What about Size?

• The field diagrams for a 1 kg mass and Earth show no difference, but the fields obviously have different strengths.

• There are no moons orbiting the 1 kg mass• Qualitative definition:• The strength of a gravitational field is the force

experienced by an object in that field per unit mass.

• Units: N/kg

Example 3

• A 50.0 kg mass experiences a 490.0N gravitational force down. Find the strength of the gravitational field.

• G = 9.8 N/kg

Example 4

Robert lifts a 10.0 kg medicine ball. Could he be on Earth if he lifts the ball with a:

a) 50.0 N force?b) 500.0 N force?a) No b) Yes

Homework

1. Suppose you needed a formula to calculate the gravitational force on a 1 kg mass on the surface of another planet. What factors would need to be taken into account?

2. Suppose you needed a formula to calculate the gravitational force on a 1 kg mass floating in space due to another planet. What factors would need to be taken into account?

Apparent Weight

• Mass: a measure of the amount of matter in an object

• Weight: the amount of gravitational force acting on an object.

• Is your weigh always the same? When could it change?

Apparent Weight

• Apparent weight is when the normal force acting on a body is different from the gravitational force acting on a body.

• From the FBD, Fnet ≠0• Occurs when the reference frame is

accelerating• Examples: rollercoaster, swings, elevator,

spacecraft, etc.

Example 1

• Suppose you are riding in the elevator when the cable is cut. If the elevator is freefalling, draw your free body diagram and come up with an Fnet statement.

• Fnet = Fg + Fn

• Fnet = Fg, so Fn = 0• This is what the physics is behind

weightlessness.

Example 2

• Suppose Sam (m = 60.0 kg) is riding in the elevator and the elevator accelerates upwards at 0.150 m/s2. If Sam were standing on a scale, what would it read?

• The scale would read 600. N.

Example 3

• Suppose Sam (m = 60.0 kg) is riding in the elevator when the cable is cut. Suppose the elevator accelerates downwards at 1.50 m/s2. If Sam were standing on a scale, what would it read?

• The scale would read 498N.

Homework

• Physics Concepts and Conceptions• Pg. 171 #1

Derivation of g

Imagine a mass free falling towards earth. The only forces acting on the object are gravity and air resistance. Assuming no air resistance,

Fnet = Fg

a = g

g

• Ever heard of pulling 2g through a bend?• What it means is that the apparent weight on

you is twice the force of gravity.• You are accelerating at 19.6 m/s2

Lab

The Plan

• Max Classes: 71. Gravitational field and drawing field lines2. Apparent weight3. Deriving g/Lab (g near the surface of the

earth)4. Quiz