exercises by lookang:

activity A

unselect the M2=5.97E24 kg checkbox

drag the red test mass m, on the world side view closer to the Moon.

notice the value of g1 varies according to the distance away from the center of the Moon

since M2 is unselected, gnet = g1 + g2 and g2 = 0

therefore gnet = g1

note down the value of gnet when m =1kg

note down the value of Fnet when m=1 kg

now change the value of m and record down the values of g1 , gnet and Fnet. do this for a few readings.

suggest a relationship between Fnet and gnet.

by manipulating the relationship variables above, write down the form that best describe the concept of a gravitational field as an example of field of force.

hence, derive the meaning that gravitational field strength as force per unit mass

Activity B

reset the simulation if need

unselect the test mass, m and select M2.

notice the green vector drawn on the center of the Moon and Earth.

the readings are as shown as F1= 1.98E20N and F2=-1.98E20N

using the real life data that you can get from textbook, lecture notes or/and the internet, verify the equation

F = G M1M2/r^2

suggest what does F1 represent?

hint: force on ________ exerted by ___________

suggest what does F2 represent?

hint: force on ________ exerted by ___________

drag on the Moon and Earth to move along the horizontal line, observe what happens to the magnitude and direction of the forces F1 and F2.

What observation can be made?

hint: magnitude, direction and different bodies?

What is the name of this physics idea?

What is the meaning of the negative sign on the force that points in the direction opposite to x-axis direction?

Activity C

Given that Newton's law of gravitation in the form F = G M1M2/r^2 and derive the equation for gravitational field strength, g.

hint: select the g field checkbox to reveal the graph of g vs r for a system of M1 alone.

select the M2 checkbox and deduce the relationship when the system is 2 mass, M1 and M2

you may use the data from the applet to verify your equation.

Activity D

apply the equation for gravitational field strength, g = G M/r^2 to the situation of the applet.

write the meaning of g1

write the meaning of g2

hence, suggest what is the net gravitational field strength for the case of a Earth and Moon system.

gnet =

select the gravity g field checkbox

vary the left slider to the bottom to change the scale of the y axis to -1.2 to 1.2 N/kg

notice the shape of the graph of g vs r. sketch it on your worksheet or lecture.

select and deselect the M2 to test your understanding.

Activity E nil

(e) show an appreciation that on the surface of the Earth g is approximately constant and equal

to the acceleration of free fall. another applet perhaps?

Activity F

let the infinity point be i

let the final position of the point be f

write down the energies of a mass m an infinity,

hint: KEi + PEi = 0 + (-G M / infinity) = 0

write down the the energies of a mass m an a point r away from source of gravity field say M.

hint: KEf + PEf = 0 + (-G M / r)

use conservation of energy or otherwise, WDpropulsion + KEi + PEi = KEf + PEf

derive WDpropulsion in terms of G, M and r

define M

define r

hence or otherwise, verify whether you can define potential φ at a point as work done in bringing unit mass from infinity to the point.

write down the equation that shows this clearly.

select the gravity φ potential checkbox

vary the left slider to the bottom to change the scale of the y axis to high value J/kg

sketch the shape of the φ potential vs r.

select and deselect the M2 to test your understanding.

Activity G

solve problems using the equation φ = - G M/r for the potential in the field of a point mass.

for example,

Certain meteorites (tektites) found on the Earth have a composition identical with that of lunar granite. It is thought that they may be debris from volcanic eruption on the Moon. The applet shows how the gravitational potential between the surface of the Moon and the surface of the Earth varies along the line joining their centres. At the point P, the gravitational potential is a maximum.

By considering the separate contributions of earth and Moon to the gravitational potential, explain why the graph has a maximum and why the curve is asymmetrical

State how the resultant gravitational force on the tektite at any point between the Moon and the Earth could be deduced

When a tektite is at P ( drop menu select "Net Force Zero) , the gravitational forces on it due to Moon and Earth are F_M and F_E respectively. State the relation which applies between F_M and F_E.

F_Moon is which color force ?

F_Earth is which color force ?

given that the distance between Earth and Moon used in the applet is 384 403 000 m

determine the distance between test mass m and M1 (moon)

determine the distance between test mass m and M2 (earth)

verify whether the applet is accurate, which the uncertainty error between the 2 values?

If the tektite is to reach Earth, it must be projected from the volcano on the Moon with a minimum speed v0. Making use of appropriate values from the applet, find this speed. Explain your reasoning.

test out your answers against the simulation.

suggest why you cannot use the value derived theoretically, but it should be a value greater or lesser? explain.

Run the simulation with an escape velocity from Moon as v =2500 m/s, Predict and discuss very briefly whether a tektite will reach the Earth’s surface with a speed less than, equal to or greater than the speed of projection v =2500 m/s.

vary the simulation to test out the v =2500 m/s.

what is the value of velocity of test mass impacting earth?

change the values of test mass, m and rerun the sim, what is the velocity of impact on Earth?

by using equation of conservation of energy or otherwise, calculate the velocity of impact on Earth of test mass m.

(h) recognise the analogy between certain qualitative and quantitative aspects of gravitational

and electric fields.

Ejs Open Source Electric Field & Potential of 2 Charged Particles Java Applet

http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1918msg6989;topicseen#msg6989Design an experiment to verify that following table of data

Gravitational Fields Electric Fields

Due to mass interaction, m Due to charge interaction, +q and -q

Only attractive Either attractive or repulsive

Newton’s Law of gravitation Coulomb’s Law

Gravitational Field Strength Electric Field Strength

Gravitational Potential Electric Potential