Gravitational Force Lab PDF

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Answer to online simulation...

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Gravitational Interaction Lab 12 Pre – lab questions

Consider two spher following questions:

th indica

s m1, m2 and separation R. Answer

1. Which gravitational force is bigger: force acting on m1 or force acting on m2? Draw the forces on the Figure 1, try to correlate the magnitude of the force with the length of the vector you draw.

Gravitational force is attractive, meaning it tries to pull masses together. Since m1 is heavier than m2 and the two objects are close, the force acting on m2 is bigger because m1 has a large enough force to try to pull it closer than m2 pulling m1 close. 2. If the distance changes to 4 m, by how much would forces change?

By the inverse square law, when the distance is doubled then the gravitational force between two objects is a quarter to what it was. 3. If m2 increases to 200 kg, by how much would forces change?

The law of Universal Gravitation is Fori = (GmM)/R2 , Fori means the object’s original gravitational force (200 kg, 100 kg and 2 m respectively) so when m2 is doubled then the force between m1 and m2 is doubled. It’s like this Fnew  = (G2mM)/R2 to Fnew  = 2((GmM)/ R2 ), Fnew  = 2 Fold 4. If both masses increase twofold, by how much would forces change?

The force increased by a factor of 4. It’s like this Fnew = (G2m2M)/R2 to Fnew = 4((GmM)/ R2 ), Fnew = 4 Fold 5. If masses and separation are the same (200 kg, 100 kg and 2 m respectively), but the radius of first object is 10 times smaller (the object becomes just denser), by how much would the forces change?

Density is a measure of how much mass is concentrated in a given space. However, considering both of the objects are spherical the forces would not change because the first part of Newton’s Shell Theorem says that the gravitational force outside a spherical shell having total mass M is the same as if the entire mass M is concentrated at its center. Therefore if the spherical object has radius r, then the gravitational field inside the object as a distance R < r from the center is the same as if the total mass within a distance R from the center were concentrated at the object’s center. 6. Calculate the forces for the situation shown in Figure 1

Simulation Lab. Go to https://phet.colorado.edu/en/simulation/gravity-force-lab and open the simulation. Set masses and separation as shown in Figure 1. 1. Which gravitational force is bigger: force acting on m1 or force acting on m2?

The force acting on m2 is greater because m1 is heavier in mass thus exerting a stronger gravitational force. 2. If the distance changes to 4 m, by how much would forces change?

The force between the two objects went from 3.32030E-7  N to 8.3381E-8  N. As one object is moving away from the other then the gravitational force decreases. Thus when the distance is doubled, the force decreases by a factor of four. 3. If m2 increases to 200 kg, by how much would forces change?

Force increases by 2. 4. If both masses increase twofold, by how much would forces change?

The forces would increase 4x. 5. Do the forces depend on the radii of object 1 or object 2? To change the radius, check “Constant Radius” field.

No they don’t. Refer back to Newton’s Shell Theorem in question 5. 6. Compare the value of the forces with your calculation.

From the simulation (200 kg, 100 kg and 2 m respectively) = 3.3203E-7  N Calculations: F = (GMm)/R2 , = ((6.67x10-11  )*200*100)/(22) = 3.335E-7  N The difference is .00000000147 or 1.47 E-9  7. If the objects were released from separation of 2m and could move, calculate the acceleration of object 1 and object 2. Give the equation for the acceleration first and then compute the values. Compare a1 to a2 and comment on how and why (if at all) they are different.

acceleration = g = 9.80 m/s2 . M = mass of earth, r = distance to the center of the earth  a1 & a2: F = (GMm)/R2 → mg = (GMm)/R2 → g = (GM)/R2  (N⋅m2 )/kg2 )×((5.98×1024  kg)/(6.38×106 m)2 ) → g = 9.80 m/s2 →g  = (6.67×10−11 a1 and a2 are both falling objects with different masses yet acceleration of a falling object is independent of the object’s mass. Therefore both object’s will be accelerating at the same rate....