There are several divisions of machine mechanics and kinematics is one of them, which deals with and explains the acceleration of a body caused by something. The physical quantities such as position, acceleration, and velocity are its parameters and how they differ over time. When the body moves in a unidimensional way, which is around the x-axis, at a velocity that is constant vx, the fundamentals of gestures happen. The linear equation describes the uniform displacement, as stated above, along a straight line. x=x0 + vxt ……………… (i)
where x0 is the initial position at time t=0.
Where displacement is plotted against time, a straight line is gotten and its slope is vx, the intercept occurs at x0 (x – intercept).
But to complicate the motion slightly, which is where a body moves in a straight line along y axis this time but its velocity changes at a constant rate. The acceleration achieved becomes ay. The following becomes the kinematic equation, where a position y is a function of time accounting for the change in velocity.
y= y0 + v0yt + ………………………………. (ii)
Where: y0 is the initial position, v0y is the initial velocity. The graph of the position vs time of a constant accelerated motion gives a curve in the shape of a parabola. Therefore, instantaneous velocity at a specified time gives a slope of the tangent to the parabola/curve at a specified time.
When a body’s movement is influenced by gravity only, there will be an acceleration downwards, represented as; ay = -g = – 9.80 m/s2 ………………………………. (iii)
This object or body will experience a free – fall represented by the following equation (similar to (ii))
y=y0 + v0yt – ………………………………… (iv)
The aim of the experiment is to determine or to observe the linear motion and a constant speed and to determine or observe the linear motion of a free fall object or body.
Small or medium sized ball
Figure 1:Set of materials needed for the experiment
The first procedure is to install the software in a computer that will help analyse the motions of the determining the motion with constant velocity.
Stretch or lay out the measuring tape, to a known length
Set the digital camera, to view either on the top or sideview, it should be perpendicular to the motion, turn it on to record the motion
Push the ball carefully, so that it rolls in a straight line in a moderated speed.
Figure 2:The layout of the set of materials for the experiment
The video when imported into the tracker, it can be played and paused at appropriate moments(see Figure 3). These appropriate moments are the time, that shall be set from t=0 to say t=0.60(see Table 1)
Table 1:For the Distance (displacement) time recordings
The length of the scale is set, the adjustments made help set the motion of the ball along the x – axis. The data will be collected in the same software. If the ball rolls along the x – axis, ignore the y values in your table. Then these values can be plotted automatically of the position versus the time. When “curve fits” is selected, a window appears where “Fit Name to Line” can be selected. The “Fit Equation” is x=A*t+B the values of A and B are therefore displayed.
Figure 3:Indications of the golf ball analysed using the Tracker software
Analysis and Discussions
Kindly make the recordings and check if the ball moves in a constant velocity. Also, use the (i) on the values recoded. The values shall not produce a straight line, but determine the best fit (the line with many points), get the gradient and determine vx. One error you are likely to note is the frictional force, though negligible, but will cater for the theoretical differences, this error can be solved by making sure the place is very smooth. Another source of error, was the distance, that we were able to cover with the measuring instrument, a longer distance would have given a workable range of recorded values.
In the experiment, we determined the relationship between the position of an object and its velocity, being displaced in one dimension, along a straight line. The experiment was carried out with limiting friction taken into account and that there was no force acting on the body. Initial final velocities of the ball that was made to roll was in an interval measured or recorded by the software installed to accurately determine the set times. The theoretical results were expected, but different ones were found, majorly because of friction.
Kindly use the formula in (i) to answer the first question, going by your values.