Question

when an athlete holds a barbell overhead, her hands exert an upward force on the bar - bell. at the same time, there is a downward force equal to the weight of the barbell. how do these forces compare in the case where the barbell is moving upward but slow - ing down? 1. it depends on the will of the athlete. 2. the force exerted by the athlete is equal to the weight of the barbell. 3. the force exerted by the athlete is smaller than the weight of the barbell. 4. the force exerted by the athlete is greater than the weight of the barbell

Explanation:

Step1: Analyze the motion of the barbell

The barbell is moving upward but slowing down. According to Newton's second law \(F = ma\), where \(F\) is the net force, \(m\) is the mass of the barbell, and \(a\) is the acceleration. Since the barbell is slowing down while moving upward, its acceleration \(a\) is downward.

Step2: Determine the net force

Let \(F_{athlete}\) be the upward force exerted by the athlete and \(F_{weight}=mg\) (where \(g\) is the acceleration due to gravity) be the downward force (weight of the barbell). The net force \(F_{net}=F_{weight}-F_{athlete}\) (because the net force is in the direction of the acceleration, which is downward). Since \(F_{net}=ma> 0\) (because \(a>0\) in the downward direction), we have \(mg - F_{athlete}>0\).

Step3: Compare the forces

From \(mg - F_{athlete}>0\), we can rearrange the inequality to get \(F_{athlete}

Answer:

1. The force exerted by the athlete is smaller than the weight of the barbell.