What is the gravitational potential energy of a two-particle system with masses 5.4 kg and 5.0 kg, if they are separated by 1.3 m? If you triple the separation between the particles, how much work is done (b) by the gravitational force between the particles and (c) by you?
Please help me. i figured out how to get part a but part b and c i am confused on.
GPE= GM1*M2/distance
when i plugged in the values i got 4.62E10 is that number suppose to be negative or positive?
To solve part a, we can use the formula for gravitational potential energy:
Gravitational potential energy (U) = - G * (m1 * m2) / r
Where:
G is the gravitational constant (6.67430 x 10^-11 N m^2/kg^2)
m1 and m2 are the masses of the two particles
r is the separation between the particles
Let's calculate the gravitational potential energy:
m1 = 5.4 kg
m2 = 5.0 kg
r = 1.3 m
U = - G * (m1 * m2) / r
U = - (6.67430 x 10^-11 N m^2/kg^2) * (5.4 kg * 5.0 kg) / 1.3 m
Using a calculator, we find that the gravitational potential energy is approximately -2.151 x 10^-10 J.
For part b, if we triple the separation between the particles, the new separation (r') will be 3 times the original separation (r).
r' = 3 * r = 3 * 1.3 m = 3.9 m
Now, we can calculate the new gravitational potential energy (U') using the same formula:
U' = - G * (m1 * m2) / r'
U' = - (6.67430 x 10^-11 N m^2/kg^2) * (5.4 kg * 5.0 kg) / 3.9 m
Using a calculator, we find that the new gravitational potential energy is approximately -1.961 x 10^-10 J.
To find the work done by the gravitational force (part b), we need to calculate the change in potential energy (ΔU) using the equation:
ΔU = U' - U
Substituting the values:
ΔU = (-1.961 x 10^-10 J) - (-2.151 x 10^-10 J)
Using a calculator, we find that ΔU is approximately 1.9 x 10^-11 J.
Therefore, the work done by the gravitational force is approximately 1.9 x 10^-11 J.
Now, for part c, the question asks how much work is done by you. Since you are not physically exerting any force on the particles, you do not do any work in this scenario. Work is only done when a force is applied and causes a displacement.