Experiment 2 Kinematics

Experiment 2 Kinematics

Topic: Kinematics 

Title: Projectile 

Objective: To study the trajectory of an object subjected to the gravitational acceleration. 

Theory:

When an object is projected at an initial velocity vo at an angle θ to the horizontal, the position (x, y) of the object at some later time t can be specified by two equations.

       

       

where

       

       

By eliminating t in equations (1.1) and (1.2) gives

       

which is of the general mathematical form for a parabola, . From equation (1.3) and (1.4),  

Thus equation (1.5) can be rewritten as

       

Apparatus:

(i)    A 1.0 m aluminium V-track (the V track is being replace by the PVC pipe)

(ii)    A target board (30 cm x 100 cm)

(iii)    Steel ball bearing (about 1 cm)

(iv)     Carbon paper/Carbonised printing paper 

(v)    A metre rule

(vi)    Retort stand

Procedure:

(a)Set-up the apparatus as shown in Figure 1.

Figure 1

(b) Using a suitable method, set the angle 0- 60°.

(c) Place the target board x - 5.0 cm from the table.

How to arrange the target board and carbon paper.

(d) Release the ball bearing at a suitable height h and note the position where it hits the target board.

(e) Measure and record h.

(f) Keeping h constant, increase x in stages and repeat step (d) until the ball strikes the floor.

(g) Measure and record the positions of the hit mark y for the corresponding x. 

(h) Tabulate x, y and y -x tan θ.

(i) Plot a graph of y against x and a graph of y - x tan θ against x2.

(j) Using a suitable graph in (i), determine the initial velocity vo of the ball bearing when it leaves the V-track (PVC pipe).

(k)Using the principle of conservation of energy, calculate vo. Compare and discuss the results.

Data:

Graph :