Force Forces, Fields,Potential and Energy Objective: TSW understand and apply the concepts gravitational force, fields, potential and energy.

Gravitational Field: A property of space around a mass that causes forces on other masses. The Gravitational field strength at a point is the force per unit mass on a small mass placed at that point. F F F F g = the gravitational field The gravitational force is always in the same direction as the gravitational field The gravitational field is a vector. (Magnitude and direction)

Equipotential lines: Lines along which the potential is the same. Spacing between equipotential lines increases as the distance from the mass increases.

Equipotential lines are like a topographical map Click to view the Spin and tilt video

The units for a gravitational field are N/kg The gravitational Force = (The mass) x (The Gravitational Field) The units for a gravitational field are N/kg

Let’s zoom in to our physics room: Fg Constant Field

Equipotential line Constant Field

Example 1: Calculate the gravitational field 10000km from the earth, which has a mass of 6x1024kg and a radius of 6400km 10000km

Example 2: Find the final velocity of a 4kg object starting from rest if it is accelerated 25meters through a constant gravitational field of 22N/kg? 4kg 25m Fg = mg = (4)(22) = 88N

Example 2: Solving with energy Find the final velocity of a 4kg object starting from rest if it is accelerated 25meters through a constant gravitational field of 22N/kg? 4kg 25m V = gh V = 0 J/kg

The gravitational potential of a position r is given by: Gravitational potential at a point in a gravitational field is the work done per unit mass in moving a small mass from infinity to that point r R The gravitational potential of a position r is given by: Notice r is not squared The gravitational potential at infinity is zero

Gravitational potential energy at a point is the work done to move a mass from infinity to that point

Graphically V (J/kg) r (m) r (m) The slope (gradient) of the tangent line gives the field strength g. R 2R 3R R = The radius of the mass

Example: With what velocity must a rocket be fired in order to escape the earth’s gravitational field? (Neglect air resistance)