Mechanics assignment friction
This lab was based on projectile motion and it was to prove the theory that was covered in lecture 5 to be correct. When dealing with projectile motion, it is the theory that when an object has been fired from its starting point into the air, it will come under the influence of gravity and is attracted to ground with an acceleration of g m/s squared.
In the lab a projectile launcher was used to project two steel balls, one in the horizontal direction and one in the vertical direction. The ball that was launched in the vertical direction was ball 1 and the ball that was launched in the horizontal direction was ball 2. The purpose of this experiment was to investigate projectile motion through the use of a vertical acceleration apparatus which shows the independence of vertical acceleration from the horizontal velocity.
Projectile motion is a form of motion in which an object or particle (called a projectile) s thrown obliquely near the earth’s surface, and it moves along a curved path under the action of gravity only. The path followed by a projectile motion called its trajectory. Projectile motion only occurs when there is one force applied at the beginning of the trajectory, after which there is no force in operation apart from gravity. Introduction: Part B Part B of the lab was on Tractive Forces. Tractive force means the force available at the contact between the drive wheel tyres and road is known as ‘tractive effort’ or tractive force’.
As used in mechanical engineering the term tractive force can either efer to the total traction a vehicle exerts on a surface, or the amount of the total traction that is parallel to the direction of motion. The published tractive force value for any vehicle may be theoretical”that is, calculated from known or implied mechanical properties”or obtained via testing under controlled conditions. The example that was taken in the lab was of a train of 3 parts that were coupled together by couples (T 1) and (T2).
The purpose of this lab was to prove the theory covered in lecture 6 was correct and to see the relationship between force, mass and cceleration in tractive forces which comes from Newton’s 2nd law. We know that force = mass x acceleration and we also were giving the conditions to which the train was under. Table 1, Part A: recorded and calculated data Measured time and distance for the vertical ball and the horizontal ball projected from projectile launcher. Test 1st Ball (vertical) 2nd Ball (horizontal) Distance (s) (m) Time of flight (t) 0. 5 0. 93 0. 6 1. 38 0. 4 0. 51 1. 46 0. 43 0. 56 1. 36 0. 35 0. 57 1. 34 0. 60 0. 68 1. 39 0. 0 7 0. 40 0. 54 1 . 45 8 0. 28 1 . 31 9 0. 30 0. 47 10 1. 32 Average values 0. 391 1 . 387 Table 2, part A: Calculated Horizontal velocity, acceleration due to gravity, the % difference in the value of gravity, and the Vertical velocity. Horizontal velocity (Vh) (calculated) 2. 57 rrvs Acceleration due to gravity, g (calculated) 6. 38 m/s squared % difference in the value of g -34. 96% Vertical striking velocity (W) (calculated) 3. 83 rms (Horizontal velocity) S = Vx T therefore S = 1. 39 = 2. 57 m/s T 0. 54 (Acceleration due to gravity) Sv = IJvT – 1 g(t)squared 2 Therefore = 2 (0. 93) squared T squared 0. 54 squared = 1. 86 = 6. 378 = 6. 8 rms 0. 2916 0. 2916 (% difference in the value of g) % difference = Calculated -g x 100 . 81 (Vertical striking velocity) V=U+GXT v = o + 3. 83571 v = 3. 83 rms Discussion part A =6. 38-9. 81 x 100 In this lab that was completed it was shown that the theory behind projectile motion is correct. It was proven that both balls came under the influence of gravity once they left the projectile launcher and that they were both attracted to ground. The two balls were launched from the same vertical height but the ball number 2 that was travelling in the horizontal direction travelled a further distance than ball number 1 in the vertical direction.
Even though ball number 2 travelled a further distance the wo balls will hit the ground at the same time as they both come under the same force of gravity however this was not shown in our table 1 (Fig 1) because their was human errors such as, two people starting the stop watches at different times, the person pressing the trigger mechanism was releasing the balls faster sometimes than other times even though we would start the stop watches on the count of 3. The other factors that had to be taken into consideration is, if the projectile launcher was at any sort of an angle due to the work bench not been balanced or level or an even surface.
However the readings that were taken were still very close to each other so experiment the initial velocity of each ball was O m/s. To calculate the acceleration due to gravity we manipulated the equation to find (g) gravity. When dealing with projectiles, we use the same equations as linear motion but the (a) for acceleration is replaced or substituted with (g) for gravity. The acceleration due to gravity was 6. 38 m/s squared. In theory this acceleration should have been 9. 81 m/ s squared but due to the human errors that occurred during the experiments there was a difference of -3. m/s squared these % errors came from miscalculating of the time taken for the balls to hit the ground and the distance travelled by the horizontal ball. When the steel ball number 2 is projected from the projectile launcher in the horizontal direction, the time it takes for the steel ball to hit the ground is independent of its initial horizontal velocity, the steel ball will continue to move in the horizontal direction with the same horizontal velocity in which it was projected from the projectile launcher with because there is no acceleration so it stays at a constant velocity.
The distance that the steel ball number 2 travels in the horizontal distance before it hits the ground is dependent on the time of flight and the horizontal velocity that it was projected with. Projectile motion only occurs when there is one force applied at the beginning of the trajectory, after which there is no force in operation apart from gravity, this was proven in the experiment as ball number 1 was let fall from a height with no other force applied and ball number two was projected with a horizontal velocity from the projectile launcher and both balls were attracted to ground as they came under the nfluence of gravity.
We found the value of acceleration using the average vertical height in which the ball was projected from and used the average horizontal time in which it took ball number two to hit the ground as ball number two was projected with an horizontal velocity it still should hit the ground at the same time as ball number one does as there both under the same force of gravity. If our measurements and calculations were 100% we should have got an acceleration of 9. 81 m/s squared. The horizontal component of the velocity of the object remains unchanged throughout the motion.
The vertical component of the velocity increases linearly, because the acceleration due to gravity is constant. It is important to note that the Range and the Maximum height of the Projectile do not depend upon mass of the projected body. The Range and Max Height are equal for all those bodies which are thrown by same velocity and direction. Air resistance does not affect displacement of a projectile; this is why we do not take the mass of the balls into consideration or the mass of any objects when dealing with projectiles. This experiment proves and supports the theory behind projectile motion to be correct.
We do not take the mass of the balls or bodies into consideration when dealing with projectile motion as the air resistance does not affect the displacement of the projectile. The range and height are equal for all bodies which are thrown by the same velocity and direction. There was a small difference in calculating the acceleration due to gravity, this was because of the different readings and human errors that took place during the experiment. Both balls come under the influence of the same gravity and are attracted to ground and should hit the ground at the same time.
In theory both balls should hit the ground at the same time, but because there were two people using stopwatches to record the times taking there was going to be a difference in the readings and calculation. The horizontal distance ball number two travels before it hits the ground is dependent of the time of flight and the horizontal velocity of projection. Ball number two will travel at the same horizontal velocity because there is no acceleration or any other force applied. The vertical component of the velocity will increases linearly because the acceleration due to gravity is onstant, so it picks up speed as it is falling from a height.
