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 og 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
To determine the speed, acceleration, and net force acting upon the halfback, we can use the following formulas:
1. Speed: v = 2πr / T
2. Acceleration: a = v^2 / r
3. Net Force: F_net = m * a
Where:
- v is the speed
- r is the radius of the circle
- T is the time it takes to make a complete turn around the circle
- a is the acceleration
- F_net is the net force acting upon the halfback
- m is the mass of the halfback
Given values:
Mass of the halfback (m) = 95 kg
Radius of the circle (r) = 12 meters
Time to make a quarter turn (T) = 2.1 seconds
1. Speed:
v = 2πr / T
v = (2 * 3.14159 * 12) / (2.1)
v ≈ 18.05 m/s
2. Acceleration:
a = v^2 / r
a = (18.05)^2 / 12
a ≈ 27.23 m/s^2
3. Net Force:
F_net = m * a
F_net = 95 * 27.23
F_net ≈ 2586.85 N
Therefore, the speed of the halfback is approximately 18.05 m/s, the acceleration is approximately 27.23 m/s^2, and the net force acting upon the halfback is approximately 2586.85 N.
To determine the speed, acceleration, and net force acting upon the halfback, we need to use the formulas of circular motion.
1. Speed:
The speed of an object moving in a circle is given by the formula:
Speed = (2πr) / T
where r is the radius of the circle and T is the time taken to complete one full revolution.
In this case, the halfback makes a quarter turn in 2.1 seconds. Since one complete revolution is equivalent to four quarter turns, the time taken for one full revolution (T) can be found by multiplying the quarter turn time by four:
T = 4 * 2.1 seconds = 8.4 seconds
Now we can calculate the speed using the formula:
Speed = (2*π*12) / 8.4 seconds
2. Acceleration:
The acceleration of an object moving in a circular path is given by the formula:
Acceleration = (v^2) / r
where v is the velocity (speed) and r is the radius of the circle.
Using the speed we just calculated, along with the radius of the circle (r = 12 meters), we can calculate the acceleration:
Acceleration = (Speed^2) / r
3. Net Force:
The net force acting upon a body moving in a circular path is given by the formula:
Net Force = (mass * (velocity^2)) / radius
where mass is the mass of the body, velocity is the speed, and radius is the radius of the circular path.
Using the given mass of the halfback (95 kg) and the velocity we calculated earlier, we can find the net force:
Net Force = (mass * (Speed^2)) / r
Now, plug in the values into the respective formulas to calculate the speed, acceleration, and net force acting upon the halfback.
lkjn
v = (2 pi R/4) / 2.1 = pi R/(4.2)
Ac = v^2/R
F = mAc = m v^2/R