At what point in the swing of a pendulum is the maximum amount of the ball's motion transferred to the object it hits? (I think it's at its lowest swing point but I'm not completely sure.)
And what does this "kinetic energy" depend on?
To determine the point in the swing of a pendulum where the maximum amount of motion is transferred to the object it hits, you are correct that it occurs at the lowest point of the swing. This is because the object's velocity, and hence its motion, is greatest at this point.
Now, let's analyze why this is the case. In a pendulum, the motion is governed by the interplay between potential energy and kinetic energy. When the pendulum reaches its highest point, it has the maximum potential energy and minimum kinetic energy. As it swings downward, the potential energy is progressively converted into kinetic energy, reaching its maximum at the lowest point of the swing. At the lowest point, all the potential energy has been converted, resulting in maximum kinetic energy. This maximizes the transfer of motion upon impact with the object.
Regarding the dependence of kinetic energy, it relies on two factors: mass and velocity. The kinetic energy formula is given by K.E. = (1/2) * mass * velocity^2. As you can see, the kinetic energy is directly proportional to the square of the velocity. This means that doubling the velocity will increase the kinetic energy by a factor of four. On the other hand, increasing the mass of the object will also increase the kinetic energy linearly. Therefore, both velocity and mass play a role in determining the amount of kinetic energy possessed by an object.