A 95-kg halfback makes a turn on the football field. The halfback sweeps out a path that is a portion of a circle with a radius of 12-meters. The halfback makes a quarter of a turn around the circle in 2.1 seconds. Determine the speed, acceleration and net force acting upon the halfback.

Answer 1

First, let's find the distance the halfback travels during the quarter turn:

Circumference of the circle = 2πr
Circumference of the quarter circle = (1/4) * 2πr = (1/4) * 2π * 12m = 9.42m

Therefore, the distance the halfback travels during the quarter turn is 9.42 meters.

Next, let's find the linear speed of the halfback:

Speed = distance/time = 9.42m / 2.1s = 4.49 m/s

The linear speed of the halfback is 4.49 m/s.

Now, let's find the centripetal acceleration of the halfback:

Centripetal acceleration = (linear speed)^2 / radius = (4.49 m/s)^2 / 12m = 1.67 m/s^2

The centripetal acceleration of the halfback is 1.67 m/s^2.

Finally, let's find the net force acting upon the halfback:

Net force = mass * centripetal acceleration = 95 kg * 1.67 m/s^2 = 159.65 N

The net force acting upon the halfback is 159.65 N.