Four masses m1 = 1kg, m2 = 2kg, m3 = 3kg and m4 = 4kg are at the corners of a
square of sides 4cm. What is the gravitational potential energy of the system?
Remember potentials add.
bring m1 into .04 m from m2 and m4 and .04*sqrt 2 from m3
get Pe remember G MM'/d
then do m 2 in between the other 3
then m3 , then m4
then add
Please help me the answers of that question
To calculate the gravitational potential energy of the system, we need to find the potential energy between each pair of masses and then sum them up.
The gravitational potential energy between two masses can be calculated using the formula:
PE = G * (m1 * m2) / r
where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.
In this case, we have four masses arranged at the corners of a square. Let's label them as follows:
m1 = 1kg (top-left corner)
m2 = 2kg (top-right corner)
m3 = 3kg (bottom-right corner)
m4 = 4kg (bottom-left corner)
The side of the square is given as 4cm, which means that the distance between adjacent masses is also 4cm.
Now, we can calculate the potential energy for each pair of masses:
PE12 = G * (m1 * m2) / r12
PE23 = G * (m2 * m3) / r23
PE34 = G * (m3 * m4) / r34
PE41 = G * (m4 * m1) / r41
where r12, r23, r34, and r41 are the distances between each pair of masses.
Since the masses are at the corners of a square, the distances between them are equal. Therefore:
r12 = r23 = r34 = r41 = 4 cm
Now, let's plug in the values and calculate the potential energies:
PE12 = G * (1 kg * 2 kg) / (4 cm) = G * 2 / 4
PE23 = G * (2 kg * 3 kg) / (4 cm) = G * 6 / 4
PE34 = G * (3 kg * 4 kg) / (4 cm) = G * 12 / 4
PE41 = G * (4 kg * 1 kg) / (4 cm) = G * 4 / 4 = G
Finally, we can sum the potential energies of all pairs:
PE_total = PE12 + PE23 + PE34 + PE41 = G * 2 / 4 + G * 6 / 4 + G * 12 / 4 + G = G * (2 + 6 + 12 + 1) / 4
Therefore, the gravitational potential energy of the system is G * 21 / 4.