Question

Fill in the chart with the correct values of F for each change in the system described in questions

Answer 1

Answer:

We know that the gravitational force F between two masses P and Q, that are separated by a distance R is:

$F = G*\frac{P*Q}{R^2}$

Where G is the gravitational constant.

a) Mass P is doubled, then we have 2*P instead of P, the new force is:

$F' = G*\frac{(2*P)*Q}{R^2} = 2*(G*\frac{P*Q}{R^2} ) = 2*F$

b) Now R is doubled, then instead of R, we have 2*R:

$F' = G*\frac{P*Q}{(2*R)^2} = G*\frac{P*Q}{4*R^2} = G*\frac{P*Q}{R^2}*(1/4) = F/4$

c) Now we replace P by 2*P, and Q by 3*Q

$F' = G*\frac{(2*P)*(3*Q)}{R^2} = 2*3*(G*\frac{P*Q}{R^2} ) = 6*F$

d) The entire mass of the system is increased by a factor of 4, then both of the individual masses are increased by a factor of 4.

Then we need to replace P by 4*P, and Q by 4*Q.

$F' = G*\frac{(4*P)*(4*Q)}{R^2} = 4*4(G*\frac{P*Q}{R^2} ) = 16*F$

e) Now we replace R by R/2.

$F' = G*\frac{P*Q}{(R/2)^2} = G*\frac{P*Q}{R^2/4}= 4*G\frac{P*Q}{R^2} = 4*F$