A football of mass 550 g is at rest on the ground. The football iskicked with a force of 108 N. The footballer’s boot is in contactwith the ball for 0.3 m.
a)What is the kinetic energy of the ball?
b)What is the ball’s velocity at the moment it loses contact with the footballer’s boot?
a) K.E. = 108 N * 0.3 m = 32.4 J
b) 1/2 m v^2 = 1/2 * .55 kg * v^2 = 32.4 J
... v^2 = 2 * 32.4 / .55 = ? m^2/s^2
Thank you
W=324J=KE
W=1/2mv^2
v=√648/550
V=0.046
To answer these questions, we need to use the principle of work and energy. The work done on an object can be calculated by multiplying the force applied on the object by the distance over which the force is applied. The work done on an object is equal to the change in its kinetic energy.
a) To calculate the kinetic energy of the ball after it is kicked, we need to find the work done on the ball.
Step 1: Calculate the work done. The work done is equal to the force applied multiplied by the distance.
Work = Force × Distance
= 108 N × 0.3 m
= 32.4 Joules
Step 2: The work done is equal to the change in kinetic energy of the ball.
Kinetic Energy = Work Done
= 32.4 Joules
Therefore, the kinetic energy of the ball is 32.4 Joules.
b) To find the velocity of the ball at the moment it loses contact with the footballer's boot, we can use the concept of energy conservation. The initial kinetic energy of the ball is zero because it is at rest, and the final kinetic energy is the value we calculated in part a.
Step 1: Calculate the final kinetic energy.
Final Kinetic Energy = 32.4 Joules
Step 2: Use the formula for kinetic energy to find the final velocity. The formula is:
Kinetic Energy = (1/2) × mass × velocity^2
Rearranging the formula, we get:
Velocity^2 = (2 × Kinetic Energy) / mass
Plugging in the values we know:
Velocity^2 = (2 × 32.4 Joules) / 0.55 kg
Velocity^2 = 118.18 m^2/s^2
Step 3: Find the square root of both sides to get the value of the velocity.
Velocity = sqrt(118.18)
≈ 10.87 m/s
Therefore, the ball's velocity at the moment it loses contact with the footballer's boot is approximately 10.87 m/s.