Projectiles: Performance of a Marble Launcher

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Projectiles Practical Report
1. Introduction
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. [1] Velocity can be found many ways through various suvat Equations and their rearranged forms. For example v2=u2+2as in which the square of the final velocity can be found if you know the objects initial velocity, the acceleration and the distance travelled.

Using such formulae makes it possible to test equipment, efficiently and accurately. 2. Aim
The aim of this practical is to build and evaluate the performance of a marble launcher, this is done by first finding the velocity of the marble using the equation v2=u2+2as, this will be done by conducting an experiment to first find the vertical distance (s) the marble travels and acceleration due to gravity (a).

This will then be used to find the time the marble will travel for at angles of 30o, 45o and 60o using the equation v=u=at, rearranging this equation to find the time the marble will travel at will become, . Taking the value and doubling it will give you the time it takes to reach the peak velocity and return to rest. This value is then used to predict the range the marble will travel from a set angle via the rule Distance = Speed X Time. These distances will be compared to actual distances tested and evaluated. 3. Procedure

3.1 Apparatus
• Protractor or set square
• Meter rule
• Small sand pit
• Safety spectacles
• Compression spring
• 1cm diameter plastic conduit
• 1cm diameter rubber bung to fit
• Marble
• Nail

3.2 Method
1. Firstly the assembly of the launcher, after placing the nail through the pre-cut hole transecting the pipe, the marble is placed inside followed by the spring, the bung is fixed securely in the bottom of the pipe causing tension on the spring which is held until the pin is released. 2. Fixing the launcher to a clamp stand secures that during firing of the marble it will remain at the same angle. 3. Start the experiment by firing the marble vertically to find an average result for the distance the marble travels (Table 4.1). 4. After this the results can then be used to find the Velocity of the marble. 5. Using the calculated velocity and suvat equations an estimation for the distance travelled by the marble and the time the marble travelled for can be found for set angles of launch measuring 30o, 45o and 60o. 6. Actual results are then compiled (Table 4.2).

7. And compared to the estimates (Table 4.3).
4.Results
Table 4.1: Table showing the mean height travelled by the marble

Height travelled by marble (cm)
1
129
2
103
3
98
AVERAGE HEIGHT = 110cm or 1.1m

From this result the Velocity can be determined using the equation v2=u2+2as

v2=02+2(9.8x1.1)
v2=21.56
v = 4.64 ms-1

With this result for v the times for each angle can be calculated using the equation v=u=at, rearranging this equation to find the time the marble will travel will become, . and so for the angles 30o, 45o and 60o the calculations are as follows.

600) = = 0.24s to 2 d.p

450) = = 0.33 to 2 d.p

300) = = 0.41 to 2 d.p

To find and estimate a distance from the times found previously the value for time is used to predict the range the marble will travel from a set angle via the rule Distance = Speed X Time, speed we know to be 4.64ms from earlier in the experiment. And time for this calculation is double that of the value found previously because we only worked out the peak velocity, doubling the time compensates for the time taken to reach the peak and the time taken to return to the sand pit. Lm

600) Distance = Speed X Time = 4.64 x Cos60 x 0.48 = 1.93m
450) Distance = Speed X Time = 4.64 x Cos45 x 0.66 = 2.17m
300) Distance = Speed X Time = 4.64 x Cos30 x 0.82 = 1.90m

These values are the estimates for the distance travelled...
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