Question

Two particles have a mass of 8kg and 12kg, respectively. if they are 800mm apart, determine the force of gravity acting between them. compare this result with the weight of each particle. g

Answer 1

The force of gravity acting between two particles with masses of 8kg and 12kg, respectively, and a separation of 800mm is approximately 8.01 × 10^-9 N. This is much smaller than the weight of each particle, which is 78.4 N and 117.6 N, respectively.

Step-by-step explanation:

To determine the force of gravity acting between two particles, we can use the equation:

F = G * (m1 * m2) / r^2

where F is the force of gravity, G is the universal gravitational constant, m1 and m2 are the masses of the particles, and r is the distance between their centers.

In this case, we have m1 = 8 kg, m2 = 12 kg, and r = 800 mm = 0.8 m. Plugging these values into the equation, we get:

F = (6.67 × 10^-11 N·m²/kg²) * (8 kg * 12 kg) / (0.8 m)^2

F = 8.01 × 10^-9 N

So, the force of gravity acting between the two particles is approximately 8.01 × 10^-9 N.

To compare this result with the weight of each particle, we can use the equation:

Weight = mass * g

where g is the acceleration due to gravity, which is approximately 9.8 m/s² on Earth.

For the particle with a mass of 8 kg, its weight is:

Weight = 8 kg * 9.8 m/s² = 78.4 N

For the particle with a mass of 12 kg, its weight is:

Weight = 12 kg * 9.8 m/s² = 117.6 N

Thus, the force of gravity between the two particles is much smaller than their individual weights.

Answer 2

The magnitude of the force of gravity acting between the particles is:

`F=G(m_1.m_2)/(d^2)`
The weight of each particle is:

`P=mg`
Now let's plug in the numbers knowing that
`G=6.67*10^(-11)` ,
`g=9.81`,
`d=0.8` and m1 and m2 are already given in kilograms. We get then:

`P_1=m_1.g=78.48`N

`P_2=m_2.g=117.72`N

`F=G(m_1.m_2)/(d^2)=1.00*10^(-8)`N

This results shows us why we don't often see objects being attracted to each other, their mass is too small compared to the earth gravitational pull.