(a) 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 with parts b and c because i got 4.62E-10 and got is wrong.
To calculate the gravitational potential energy of a two-particle system, you can use the equation:
Gravitational Potential Energy (PE) = -G * (m1 * m2) / r
Where:
- G is the gravitational constant (approximately 6.674 × 10^-11 N m^2/kg^2)
- m1 and m2 are the masses of the two particles
- r is the separation distance between the particles
(a) Given:
- m1 = 5.4 kg
- m2 = 5.0 kg
- r = 1.3 m
Let's substitute these values into the equation:
PE = -G * (m1 * m2) / r
PE = - (6.674 × 10^-11 N m^2/kg^2) * (5.4 kg * 5.0 kg) / 1.3 m
Now, calculate the value:
PE = - (6.674 × 10^-11 N m^2/kg^2) * (27 kg^2) / 1.3 m
PE ≈ - 1.388 × 10^-9 N m^2/kg
Therefore, the gravitational potential energy of the two-particle system is approximately -1.388 × 10^-9 N m^2/kg.
(b) To find the work done by the gravitational force when the separation between the particles is tripled, we need to calculate the change in potential energy.
The initial potential energy when the separation is 1.3 m is -1.388 × 10^-9 N m^2/kg.
When the separation is tripled to 3 * 1.3 m = 3.9 m, you can calculate the new potential energy:
PE' = -G * (m1 * m2) / r'
PE' = - (6.674 × 10^-11 N m^2/kg^2) * (5.4 kg * 5.0 kg) / 3.9 m
Calculate the value:
PE' = - (6.674 × 10^-11 N m^2/kg^2) * (27 kg^2) / 3.9 m
PE' ≈ - 4.577 × 10^-10 N m^2/kg
To find the work done by the gravitational force, we can use the formula:
Work (W) = PE' - PE
W = - 4.577 × 10^-10 N m^2/kg - (- 1.388 × 10^-9 N m^2/kg)
W = - 4.577 × 10^-10 N m^2/kg + 1.388 × 10^-9 N m^2/kg
Calculate the value:
W ≈ 9.3 × 10^-10 N m^2/kg
Therefore, the work done by the gravitational force between the particles when the separation is tripled is approximately 9.3 × 10^-10 N m^2/kg.
(c) The calculation for the work done by you is not provided in the given question or explanation. Can you please clarify what "you" refers to in this context?