Purpose: To determine the relationship, or discrepancy in the speed of the club head and golf ball in a chip shot. Materials: 1. Golf Ball 2. Chipping Wedge 3. High Speed Camera 4. Tracker Procedure: 1. Hit golf ball 2. Put video in tracker 3. ANALYZE
Mass of Golf Ball = .05 kg
Definition: Velocity is a vector measurement of the rate and direction of motion or, in other terms, the rate and direction of the change in the position of an object. The scalar (absolute value) magnitude of the velocity vector is the speed of the motion. In calculus terms, velocity is the first derivative of position with respect to time. Velocity = V=d/t X direction - 2.9 m/s/s or 6.5 mph Y direction - 3.9 m/s/s or 8.7 mph
The top line is the Velocity in the Y direction and the Second line from the top is the velocity in the X direction. Definition: Acceleration is the rate of change of velocity as a function of time. It is vector. In calculus terms, acceleration is the second derivative of position with respect to time or, alternately, the first derivative of the velocity with respect to time.
Acceleration = A=d = 1/2(v_{f} + v_{i})t
X direction - 11.5 m/s/s or 25.7 mph
Y direction - 3.73 m/s/s or 8.3 mph
Definition: Force is a quantitative description of the interaction between two physical bodies, such as an object and its environment. Force is proportional to acceleration. In calculus terms, force is the derivative of momentum with respect to time. Force=ma(average of two accelerations) Force = (.05)(7.6) Force = .38 N
Definition: Momentum is the product of an object's mass and velocity. It is a vector. The SI units of momentum are kg * m/s. p=mv(average of velocities) momentum of golf ball - p=(.05)(3.4) p= .17 (kg)(m/s/s)
Definition: Work is defined (in calculus terms) as the integral of the force over a distance of displacement. In the case of a constant force, work is the scalar product of the force acting on an object and the displacement caused by that force. Though both force and displacement are vector quantities, work has no direction due to the nature of a scalar product (or dot product) in vector mathematics. This definition is consistent with the proper definition, because a constant force integrates to merely the product of the force and distance. W=F x D W(x direction)=(.38)(1.5) W(x direction)= .57 J W(y direction)=(.38)(2) W(y direction)=.76 J
Definition: Torque is the tendency of a force to cause or change rotational motion of a body. Torque is calculated by multiplying Force and distance, so the SI units of torque are newton-meters, or N*m (even though this is the same as joules, torque isn't work or energy, so should just be newton-meters). The club experiences torque momentarily at the top of the backswing when the club flexes. It experiences torque again when the ball comes in contact with the ground and flexes again.
Conclusion: Before we started this experiment we assumed that the harder the club was swung, the further the ball would travel. After testing both the ball, and club head in the Tracker program, we discovered that there was a discrepency between the speed of the club head and the speed of the ball. On Jake's chip shot, he swung the club with enough velocity to cause flex in the iron shaft, yet the ball traveled a total of 12 yards. |