force forces, fields,potential and energy
DESCRIPTION
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)TRANSCRIPT
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Force Forces, Fields,Potential and Energy
Objective:
TSW understand and apply the concepts gravitational force, fields, potential and energy.
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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)
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Equipotential lines: Lines along which the potential is the same.
Spacing between equipotential lines increases as the distance from the mass increases.
Equipotential line
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Equipotential lines are like a topographical map
Click to view the Spin and tilt video
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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
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Let’s zoom in to our physics room:
Constant Field
kgNmmgFg 10
Fg
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Constant Field
Equipotential line
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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
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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
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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
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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
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Gravitational potential energy at a point is the work done to move a mass from infinity to that point
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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
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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