Question

as the ball moves from point a to point b, what happens to the magnitudes of its tangential acceleration, $a_{\text{tan}}$, and centripetal acceleration, $a_c$? assume frictional forces acting on the pendulum are negligible. choose 1 answer: a $a_{\text{tan}}$ increases and $a_c$ increases b $a_{\text{tan}}$ decreases and $a_c$ decreases c $a_{\text{tan}}$ decreases and $a_c$ increases d $a_{\text{tan}}$ increases and $a_c$ decreases

Explanation:

For a pendulum (ball moving from A to B, likely towards the lowest point), tangential acceleration \(a_{\text{tan}}\) is due to the component of gravity tangential to the path: \(a_{\text{tan}} = g\sin\theta\), where \(\theta\) is the angle from the vertical. As the ball moves towards the lowest point, \(\theta\) decreases, so \(\sin\theta\) decreases, thus \(a_{\text{tan}}\) decreases. Centripetal acceleration \(a_c=\frac{v^2}{r}\). As the ball moves down, gravitational potential energy converts to kinetic energy, so speed \(v\) increases. With \(r\) constant, \(a_c\) increases (since \(v\) increases). So \(a_{\text{tan}}\) decreases and \(a_c\) increases.

Answer:

C. \(a_{\text{tan}}\) decreases and \(a_c\) increases