Three identical 50-kg balls are held at the corners of an equilateral triangle, 30 cm on each side. if one of the balls is released, what is the magnitude of its initial acceleration if the only forces acting on it are the gravitational forces due to the other two masses? (g = 6.67 × 10-11 n • m2/kg2)

a= 6.42×10⁻⁸m/s²

Explanation:

Given Data

mass=m=50 kg

angle=α=30°

Gravitational Constant=G=6.67 × 10-11 Nm²/kg²)

To find

acceleration=a=?

Solution

From Gravitational Law " the force of attraction between all masses in the universe; especially the attraction of the earth's mass for bodies near its surface "

F₁ = G×m²/D²

F = 2*F₁*cos30° = 2*G*50²*cos30°/0.3² = 3.21×10⁻⁶N  

a = F/m = 3.21×10⁻⁶/50

a= 6.42×10⁻⁸m/s²

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s