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) 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, F net ≠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 F net statement. F net = F g + F n F net = F g, so F n = 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 m/s 2. 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/s 2. 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, F net = F g 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/s 2

Lab

The Plan Max Classes: 7 1.Gravitational field and drawing field lines 2.Apparent weight 3.Deriving g/Lab (g near the surface of the earth) 4.Quiz