Sports Physics: Projectile Motion

Topics: Classical mechanics, Force, Energy Pages: 37 (4351 words) Published: August 9, 2014
Background Information 2

Appendix 119
Appendix 221
Appendix 323
Appendix 425
Appendix 526
Appendix 628
Appendix 730
Appendix 831
Appendix 933
Appendix 1035

Background Information
Sport relies on three major physics concepts: force, acceleration and velocity; many of which involve elastic propulsion and/or projectile motion. Various types of sporting equipment are constructed with springs and elastics, in order to absorb a force or apply a force to another object. In the context of this investigation, the spring is utilised to propel an object. According to Hooke’s law, F = -kx, the distance, x, that a spring is contracted or extended is proportional to the net force being exerted. Springs create a restoring force, so movement implies that potential energy is being converted to kinetic energy (BBC, 2014). Elastic potential energy is defined by Physics: A contextual Approach (2004) as “the energy stored in a compressed or expanded spring. It is proportional to the square of the distance which it is extended or compressed. The proportionality constant is equal to one half of the spring constant.” This can be expressed by the equation Ep = - ½ k x2, where Ep = elastic potential energy (J), k = spring constant (Nm-1) and x = extension or compression of the spring (m). When an object, such as a ball, is propelled by a spring, the spring’s elastic potential energy is translated as the ball’s initial kinetic energy. This is due to the law of inertia, as the object will preserve their velocity and direction until acted upon by an unbalanced force. In the context of this investigation, the unbalanced force in action is gravity (Louviere, 2006). In fact, projectile motion is only dependent on gravitational acceleration (9.8 ms-2). When an object is released at the horizontal, inertia will carry it a short way forward until it begins to follow a downward parabolic motion, under the influence of gravitational acceleration (The Physics Classroom, 2014). The various characteristics of the object’s motion, such as displacement and velocity are entirely dependent on the height of release and force of propulsion. In response, the following investigation aims to design an experiment to investigate the effect that the force of propulsion has on an object’s downward projectile motion. It can be hypothesised that when the height of release and mass of object are constant, increasing the force of propulsion of an object will increase its horizontal displacement and decrease its time of flight.

Desk/small table
30cm ruler
Spring device (see appendix 10 for construction details)
Small ball or other uniformly shaped projectile
Writing implements to record data
Tape measurer
Soft ground surface such as grass or sand
Spring balance
*Side view

1. The spring device was assembled prior to completing the experiment. 2. The ball was weighed, and the weight recorded. The height of release was measured from the ground upward to the spring, and the result recorded. 3. The spring device was placed on the edge of the table and clamped into position. 4. The spring balance hooked onto the loose ends of the strings and was used to measure the compression of the spring at force increment from 1N to the spring’s maximum compression and force. Each increment was marked on the base board underneath the spring, and the measurements recorded. 5. The spring balance was removed and the strings were pulled to the point when the spring compresses to the marked increment indicating 1N of force. The ball was placed in front of the spring and the strings were then released, allowing the ball to travel outward and down. The horizontal distance travelled by the ball was measured with the tape measure and recorded. 6. The process was...

Bibliography: BBC. (2014). Force and Elasticity. Retrieved March 7, 2014, from GCSE Bitesize:
Brodie, R., & Swift, S
Davis, D. (2002). Projectile Motion. Retrieved March 9, 2014, from Eastern Illinois University:
Department of Educationa dn Training
Elert, G. (2014). Springs. Retrieved March 10, 2014, from The Physics Hpyertextbook:
Louviere, G
Madden, D., Stelzer, T., Lindsay, I., Parsons, D., & Gaze, T. (2004). Physics: A Contextual Approach. Melbourne: Harcourt Education.
The graph matched to a quadratic function produced the highest least spares regression value of R2 = 0.9726, therefore it represents the data more accurately than the logarithmic (R2 =0.8851), linear (R2 = 0.9716) and exponential functions (R2 =0.951).
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