A football player kicks a ball of mass 1.534 kg across the field using a constant force of 13.4 N over a distance 30.0 m. How much work does the football player do? If the ball was initially stationary, what is its final speed?
Work = force * distance
= 13.4 *30 = 402 Joules
(1/2) m v^2 = 402
1.524 v^2 = 804
v = 22.9 m/s
To calculate the work done by the football player, we can use the formula:
Work (W) = Force (F) * distance (d) * cosine(theta)
where theta is the angle between the force and the direction of motion. In this case, the force is applied parallel to the ground, so the angle between the force and the direction of motion is 0 degrees.
So, plugging in the values:
Force (F) = 13.4 N
Distance (d) = 30.0 m
theta = 0 degrees
Work (W) = 13.4 N * 30.0 m * cos(0 degrees)
= 402 N*m or 402 Joules
Therefore, the football player does 402 Joules of work.
To determine the final speed of the ball, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
The initial kinetic energy of the ball is zero since it was initially stationary. Therefore, the work done by the football player is equal to the final kinetic energy of the ball.
The equation to calculate the kinetic energy of an object is:
Kinetic Energy (KE) = 1/2 * mass (m) * velocity^2
Rearranging the equation to solve for velocity:
velocity = sqrt(2 * KE / m)
Plugging in the values:
Mass (m) = 1.534 kg
Work (W) = 402 J
Velocity = sqrt(2 * 402 J / 1.534 kg)
= sqrt(524.02 m^2/s^2)
= 22.91 m/s
Therefore, the final speed of the ball is approximately 22.91 m/s.