Before the golfer begins
his or her swing, the golf ball is at rest, thus having an initial velocity
of 0.00 m/s. If the golf ball leaves the club face at a speed of
44.7 m/s, the change in velocity must be:
change in velocity = final
velocity - initial velocity
change in velocity = ( 44.7 m/s )
- ( 0.00 m/s )
change in velocity = 44.7 m/s
In order to determine the impulse experienced by the golf ball, one must
determine the change in momentum. Momentum is equal to the product
of the mass of the object and the velocity of the object. Since the
ball is initially at rest, the initial momentum is zero. The final
momentum, however, is:
Momentum = mass *
velocity
Final Momentum = ( 0.0456 kg ) ( 44.7
m/s )
Final Momentum = 2.04 kg m/s
Thus, the change in momentum, which is the impulse experienced by the golf
ball, is:
Momentum Change of Golf Ball = Final Momentum - Initial
Momentum
Momentum Change
of Golf Ball = ( 2.04 kg m/s ) -
( 0.00 kg m/s )
Momentum Change
of Golf Ball = + 2.04 kg m/s
Because the value is positive for the golf ball, the change in momentum
and the impulse are in the same direction.
In order to determine the impulse experienced by the head of the golf club,
one must determine the change in momentum, as performed above. Because
of the idea of "Conservation of Momentum," which states that the total momentum
of the system before the collision is equal to the total momentum of the system
after the collision if no external forces are acting on the system, any impulse
in the positive direction during the collision must have an equal and opposite
impulse in the negative direction during the same collision. This idea
can be used to determine the impulse experienced by the head of the golf
club after the collision with the golf ball.
Momentum Change of Club Head = - ( Momentum Change of Golf Ball)
Momentum Change
of Club Head = - ( 2.04 kg m/s )
Momentum Change
of Club Head = - 2.04 kg m/s
Because the value is negative for the golf club head, the change in momentum
and the impulse are in the opposite direction.
In order to determine the amount of work done by the golf club head on the
golf ball, one must first understand what "Work" actually is and how it relates
to Kinetic Energy. Work the application of a constant force by one object
on another in the direction of the displacement. Kinetic Energy is
the energy that an object has that causes it to move. Work is directly
related to a change in Kinetic Energy.
Net Work =
Final Kinetic Energy - Initial Kinetic Energy
Kinetic Energy = 0.5 (
Mass ) ( Velocity )^2
Because the golf ball is initially at rest, thus the velocity is equal to
zero, the Initial Kinetic Energy of the golf ball is zero. Once the
golf club head makes contact with the golf ball, some kinetic energy is transferred
from the golf club head to the golf ball (in the form of an impulse). Because
the direction of the force is equal to the direction of the displacement,
the Work that the golf club head does on the golf ball is equal the change
in Kinetic Energy that is experienced by the golf ball.
Net Work = Ball's Final Kinetic Energy -
Ball's Initial Kinetic Energy
Net Work = 0.5 ( Mass ) ( Velocity )^2 - 0
Net Work = 0.5 ( .0456 kg ) ( 44.7 m/s )^2
Net
Work = 0.5 ( .0456 kg ) ( 2000 m^2/s^2 )
Net Work = 45.6 J
Since Work is the application of a constant force in the direction of a
displacement, one could use the formula for Work in order to determine the
amount of Force that is applied by the golf club head on the golf ball. The
golf ball, a spherical object, can deform as much as the distance of its
radius. The Force of the golf club head on the ball is applied throughout
this deformation.
Work = (
Force ) ( Displacement )
Work = ( Force ) ( Deformation
)
( 45.6 J ) = ( Force )
( 0.019 m )
Force = 2400 N