Suppose you are standing on top of a hemisphere of radius r and you kick a soccer ball horizontally such that it has velocity v.
what is the minimum v that ensures the ball will not hit the hemispherical surface. in this case, how far does the ball land from the base of the hemisphere?
Minimizing the initial velocity of the soccer ball would minimize the amount of mechanical energy it has. It shall maintain a minimal gravitational potential possible at all time. It should therefore stay to the ground as close as possible. An elliptical trajectory would thus be unfavorable; the ball shall maintain a uniform circular motion as it orbits the planet.
<em>Equation 1</em> (see below) relates net force the object experiences, to its orbit velocity and its mass required for it to stay in orbit :
<em>(equation 1)</em>
The soccer ball shall experiences a combination of gravitational pull and air resistance (if any) as it orbits the planet. Assuming negligible air resistance, the net force acting on the soccer ball shall equal to its weight, where the gravitational acceleration constant. Thus
<em>(equation 2)</em>
Substitute equation 2 to the left hand side of <em>equation 1</em> and solve for ; note how the mass of the soccer ball, , cancels out:
<em>(equation 3)</em>
<em>Equation 4 </em> gives the value of gravitational acceleration, , a point of negligible mass experiences at a distance from a planet of mass (assuming no other stellar object were present)
Newtons first law states that if an object is at rest it will stay at rest only if an unbalanced force acts on it. As well as if an object is in motion it will stay in motion unless an unbalanced force acts on it.
Ps- The object will stay moving in the same speed and direction.
Explanation:the atom consists of a tiny nucleus at its center which is surrounded by a moving electrons. The nucleus contains a positively charged proton equal in size with the negatively charged electrons . The nucleus also may contain neutrons which have the same mass with the protons but no charge is neutral.