The height of a projectile at any time during flight is found from y(t) = h + Uyt - 1/2 gt^2; where h is the launch height at time t = 0, Uy is the vertical launch speed, and g is the gravity field. The first term shows y(0) = h. The second term adds to that height as time passes. But the last term, the gravity term, shows that gravity is the force that brings the height downward, the minus sign, as time passes.
So that's how gravity affects the motion of a projectile as it travels over its trajectory. It's the force that causes the projectiles to return to some lower height, which is typically ground level where y(T) = 0 after t = T total flight time. Without that 1/2 g t^2 term, the gravity term, a projectile would just keep climbing as in h + Uy t as time passes. And that, in the shell of a nut, is "how... gravity affect[s] motion."
Gravity can also affect motion along a surface as well. Where there is surface to surface contact, any moving object will encounter friction. And friction in general acts as a braking force to slow the motion down or, at least, to prevent it from speeding up. And friction force F = kN = k W cos(theta) where k is the coefficient of friction, N = W cos(theta) is normal force, and W = mg is the weight of the moving body. And there's g again, the gravity field. Clearly the bigger W is, the more friction there is for a given k. So objects moving where gravity is stronger will tend to be slowed down faster due to the stronger braking action of the friction.
Finally, from the conservation of energy, we learn that PE = mgh = 1/2 mV^2 = KE whenver something loses potential energy in favor of kinetic energy. And there's that g once more. Thus, for a given height h, objects will end up with a faster impact speed V in greater gravity fields than in lesser fields. And this is given by V = sqrt(2gh). Note here and earlier, it's not the mass of the bodies, but the gravity fields acting on those bodies that impact the motion.
So that's how gravity affects the motion of a projectile as it travels over its trajectory. It's the force that causes the projectiles to return to some lower height, which is typically ground level where y(T) = 0 after t = T total flight time. Without that 1/2 g t^2 term, the gravity term, a projectile would just keep climbing as in h + Uy t as time passes. And that, in the shell of a nut, is "how... gravity affect[s] motion."
Gravity can also affect motion along a surface as well. Where there is surface to surface contact, any moving object will encounter friction. And friction in general acts as a braking force to slow the motion down or, at least, to prevent it from speeding up. And friction force F = kN = k W cos(theta) where k is the coefficient of friction, N = W cos(theta) is normal force, and W = mg is the weight of the moving body. And there's g again, the gravity field. Clearly the bigger W is, the more friction there is for a given k. So objects moving where gravity is stronger will tend to be slowed down faster due to the stronger braking action of the friction.
Finally, from the conservation of energy, we learn that PE = mgh = 1/2 mV^2 = KE whenver something loses potential energy in favor of kinetic energy. And there's that g once more. Thus, for a given height h, objects will end up with a faster impact speed V in greater gravity fields than in lesser fields. And this is given by V = sqrt(2gh). Note here and earlier, it's not the mass of the bodies, but the gravity fields acting on those bodies that impact the motion.