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.
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.
To determine the speed, acceleration, and net force acting upon the halfback, we can use the following formulas:
1. Speed = Circumference of the circle / Time taken for a quarter turn
2. Acceleration = (Speed)^2 / Radius of the circle
3. Net Force = (Mass of the halfback) x (Acceleration)
Let's calculate the values step-by-step:
Step 1: Calculate the circumference of the circle
Circumference = 2 x π x radius = 2 x 3.14 x 12 meters = 75.36 meters
Step 2: Calculate the speed
Speed = Circumference / Time taken for a quarter turn
= 75.36 meters / 2.1 seconds
≈ 35.89 meters per second
Step 3: Calculate the acceleration
Acceleration = (Speed)^2 / Radius of the circle
= (35.89 meters per second)^2 / 12 meters
≈ 107.42 meters per second squared
Step 4: Calculate the net force
Net Force = (Mass of the halfback) x (Acceleration)
= 95 kg x 107.42 meters per second squared
≈ 10,207.9 Newtons
The speed of the halfback is approximately 35.89 meters per second.
The acceleration of the halfback is approximately 107.42 meters per second squared.
The net force acting upon the halfback is approximately 10,207.9 Newtons.