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 line

Equipotential lines are like a topographical map

Click to view the Spin and tilt video

The gravitational Force = (The mass) x (The Gravitational Field)

mgFg

2rmMGF e

g

mF

rMGg ge 2

The units for a gravitational field are N/kg

Let’s zoom in to our physics room:

Constant Field

kgNmmgFg 10

Fg

Constant Field

Equipotential line

Example 1:

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

10000km2rMGg

23

2411

)1010000(1061067.6

g

kgNg 0.4

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) = 88N222

)4(88

sma

amaF

smv

v

xavv o

2.33

)25)(22(2

22

22

Example 2: Solving with energyFind 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 = 0 J/kg

V = gh

smv

v

ghv

mvmgh

mvmV

KU g

2.33

)25)(22(2

22121

2

2

r

The gravitational potential of a position r is given by:

rMGV

Notice r is not squared

The gravitational potential at infinity is zero

R

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

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

rMGV

Graphically

V

(J/kg)

0r (m)

R 3R2R

R = The radius of the mass

The slope (gradient) of the tangent line gives the field strength g.

rVg

Example:

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

RGMv

RGMmmv

RGMmmv

mVmv

UKUK

EWE

ffoo

f

221

021

021

2

2

2

0

smv

v

11000

1038.6)1098.5)(1067.6(2

6

2411