Download Topic 6-1 Gravitational Force and Field

IB Physics
Topic 6 Fields and Forces
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6.1 Gravitational Force and Field (2 hr)
Activity 611 Measuring Gravitational Force between two objects (NB)
Activity 612 Investigating Gravitational Field around a mass (NB)
Activity 613 Investigating the local gravitational acceleration (NB)
Read Tsokos pp 127-130
Read Cutnell pp 96-103(force) G-acc pp 44, 47, 147-151 (artificial G)
Assignment A611 Tsokos pp130,131#1 to 8
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6.1 Gravitational Force and Field
The Newton’s universal law of gravitation
“Newton proposed that the attractive force of gravitation
between two point masses is directly proportional to the
product of the masses of the particles and inversely
proportional to the square of the distance between them.
The direction of the force is along the line joining the two
masses. ” (Newton’s Principia)
Important details:
Equation:
Where m1, m2 are masses of the particles,
r is the separation between them, and
G is the Newton’s constant of universal gravitation,
G = _____________________________
Summary
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<Sample Questions>
Q1 Find the attractive force between the sun and the earth.
(mearth = 5.98x1024 kg. msun = 1.99x1030 kg. the average
distance between earth and sun is 1.5x1011 m)
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Q2 If the distance is doubled, what happen to the
gravitational force between them?
How happens if the distance is tripled or halved?
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Summary
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Weight and Gravitational Force
<Sample questions>
Q3 Find the acceleration due to gravity (or gravitational field
strength) on a planet 10 times as massive as the earth and
the radius 20 times as large.
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Q4 Find the acceleration due to gravity at a height of 300
km from the surface of earth. (The average radius of the
earth is rE = 6.378x106 m)
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Summary
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The Gravitational Field Strength
The magnitude of a gravitational field is known as
Gravitational Field Strength. This is defined as the
gravitational force that acts on per unit mass, or on each
kilogram, of a body in the field.
(The gravitational field strength at a certain point is the force per
unit mass experienced by a small point mass m at that point.)
The force experienced by a small point mass m placed at
distance r from a mass M is
So the gravitational field strength (F/m) of the mass M is
The unit of gravitational field strength is Nkg–1 or ms2
Gravitational Field Diagrams:
(1) Gravitational Field around a point mass is radial
(2) Gravitational field above a flat surface
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Graphing the Gravitational Field caused by a non-point mass
What do you see in this graph?
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Derive an expression for gravitational field strength at the
surface of a planet, assuming that all its mass is
concentrated at its centre.
Summary
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The inverse square law
Gravitational Field vs. position
Equation of the curve
Summary
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Q5 Two stars have the same density but star A has double the
radius of star B. Determine the ratio of the gravitational
field at the surface of each star.
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Q6 Show that the gravitational strength at the surface of a
planet of density  has a magnitude given by 𝑔 =
4𝑔𝜋𝜌𝑅
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Determine the Gravitational Field that is due to one or more point masses
1. A 50 kg piece of space junk is falling towards Earth from a height of 1 000
km above the Earth’s surface (mass of Earth is 5.98x1024 kg, radius is
6.38x106 m). Ignoring air resistance, determine:
a. The gravitational field strength at this high
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b. The direction of the gravitational field at this location
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c. The acceleration of the space junk at this height as it falls
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d. The value of the ratio
𝑓𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑎𝑡 500 𝑘𝑚 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒
𝑓𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑎𝑡 500 𝑘𝑚 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒
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2. A 10.0 kg watermelon falls a short distance to the ground. If the Earth has a
radius of 6.38x106 m (6 380 km)and a mass of 5.98x1024 kg, calculate:
a. The gravitational force that the Erath exerts on the watermelon.
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b. The gravitational force that the watermelon exerts on the Earth.
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c. The acceleration of the watermelon toward the Earth
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d. The acceleration of the Earth toward the Watermelon
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3.
Three identical 8-kg point masses m1, m2 and m3 are placed on x = -2, 0, and +8
respectively on a linear coordinate system that is located somewhere in space far away from
all other space objects.
a. Draw a free-body diagram (force diagram) and determine the net
gravitational force exerting on m1.
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b. Draw a free-body diagram (force diagram) and determine the net
gravitational force exerting on m2.
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4.
Three identical 5-kg point masses m1, m2 and m3 are placed on (0,0), (0,3) (4,3)
respectively on a plane coordinate system that is located somewhere in space far away from
all other space objects.
a. Draw a free-body diagram (force diagram) and determine the net
gravitational force exerting on m1.
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b. Draw a free-body diagram (force diagram) and determine the net
gravitational force exerting on m2.
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Summary
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Activity 611 Measuring Gravitational Force between two objects (Lab NB)
Newton proposed that the attractive force of gravitation between two point
masses is directly proportional to the product of the masses of the particles and
inversely proportional to the square of the distance between them. The
direction of the force is along the line joining the two masses.
Essential Question: How do you determine the gravitational force or gravitational
attraction between two objects at your choice?
1. Identify the chosen ones.
2. Decide the procedure and divide the work among partners
3. Carry it out collaboratively
4. Check your findings and analyze it.
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Activity 612 Investigating Gravitational Field around a Mass (Lab NB)
The Gravitational Field vs. Position graph shows the progression
of the gravitational field along a line between the center of the
field creator and the center of the object in the field.
Data Table
Distance
RE), R
in between m and M (in
RE
2 RE
3 RE
4 RE
5 RE
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Gravitational Field Strength,
g, Nkg-1 or ms-2
9.8
2.5
1.1
0.6
0.4
(1) Design a data table to show the Linearization of the Curve
(2) Plot the graph with the data (include the title, the axes,
the units, and a brief description of the graph)
(3) Write the equation for the line
(4) What information may be found with the Extrapolate and
Interpolate methods? Describe the significance.
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Activity 613 Investigating the local gravitational acceleration (Lab NB)
The gravitational field is expressed with the gravitational acceleration which includes
magnitude and direction.
Essential Question: How do you determine the gravitational field near the surface of
earth?
5. Identify the location.
6. Decide the procedure and divide the work among partners
7. Carry it out collaboratively
8. Check your findings and analyze it.
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Extended Questions:
(1) How to create an artificial gravitational field?
(2) How to create a zero-gravity (microgravity)
environment?
(3) How does Einstein’s model differ from Newton’s model?
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