Question

a golfer hits a ball with a club. which quantities must be equal in magnitude at all times? choose all answers that apply: a the force (f) from the club on the ball and the force from the ball on the club b the net force (σf) on the club and the net force on the ball c the acceleration (a) of the club and the acceleration of the ball

Explanation:

Step1: Analyze Option A

According to Newton's third law, for every action, there is an equal and opposite reaction. The force from the club on the ball and the force from the ball on the club are an action - reaction pair. So, \(F_{club - ball}=F_{ball - club}\) in magnitude at all times.

Step2: Analyze Option B

The net force on the club \(\sum\vec{F}_{club}\) and the net force on the ball \(\sum\vec{F}_{ball}\) are not necessarily equal. The club has forces like the force from the golfer's hand on it, while the ball has only the force from the club (assuming we consider the short - time interaction when they are in contact and neglect air resistance for simplicity during the contact). \(\sum\vec{F}_{club}
eq\sum\vec{F}_{ball}\) in general.

Step3: Analyze Option C

Using Newton's second law \(F = ma\). The mass of the club \(m_{club}\) and the mass of the ball \(m_{ball}\) are different (\(m_{club}\gg m_{ball}\)). Since \(a=\frac{F}{m}\), even if the force between them (during contact) is the same (from Newton's third law), \(a_{club}=\frac{F_{ball - club}}{m_{club}}\) and \(a_{ball}=\frac{F_{club - ball}}{m_{ball}}\), and \(a_{club}
eq a_{ball}\) because \(m_{club}
eq m_{ball}\).

Answer:

A. the force (\(F\)) from the club on the ball and the force from the ball on the club