Question

9. A 50 kg halfback is in the process of making a turn on a football field.

The halfback makes 1/4 of a turn with a radius of 15 meters in 2.1 seconds
before being tackled. What is the net force acting on the halfback before
he is tackled?

Answer 1

Net force = 419.5N

Step-by-step explanation:

Given the following data;

Mass = 50kg

Radius = 15m

Time = 2.1 secs

Turns = 1/4 = 0.25

In order to find the net force, we would first of all solve for the speed and acceleration of the halfback.

To find speed;

Speed can be defined as distance covered per unit time. Speed is a scalar quantity and as such it has magnitude but no direction.

Mathematically, speed is given by the equation;

`Speed = (distance)/(time)`

But the distance traveled is given by the circumference of a circle =
`2\pi r`

Since he covered 1/4th of a turn;

`Distance = 0.25 * 2 \pi *r`

Substituting into the equation;

`Speed, v = \frac {(0.25*2*3.142 * 15)}{2.1}`

`Speed, v = \frac {23.565}{2.1}`

Speed, v = 11.22m/s

To find acceleration;

`Acceleration, a = \frac {v^(2)}{r}`

Where, v = 11.22m/s and r = 15m

Substituting into the equation, we have;

`Acceleration, a = \frac {11.22^(2)}{15}`

`Acceleration, a = \frac {125.8884}{15}`

Acceleration, a = 8.39m/s²

To find the net force;

Force is given by the multiplication of mass and acceleration.

Mathematically, Force is;

`F = ma`

Where;

• F represents force.

• m represents the mass of an object.

• a represents acceleration.

Substituting into the equation, we have;

`F = 50 * 8.39`

F = 419.5N

Therefore, the net force acting upon the halfback is 419.5 Newton.