Projectile Trajectory - as influenced by multiple factors

In summary, the conversation discusses a scenario involving an object of mass M1 approaching a rotating wheel at a speed of S1 along a belt at an angle of Th1. The object travels around the outer edge of the wheel until it reaches the lift point, after which it continues to move under the influence of gravity for 3 seconds. The speaker is creating a spreadsheet to calculate the object's location, velocity, and acceleration leading up to and after the lift point. They plan to use motion equations and Newton's Laws of Motion to solve the problem and plot the object's trajectory curve using a spreadsheet or software.
  • #1
rmf17
6
0
Hello All,
I'm currently working through a scenario in which the following occurs :
  • An object of mass M1 (kg) approaches a rotating wheel at a speed of S1 (m/s) along a belt
  • The belt is at an angle Th1 (degrees) to the horizontal axis
  • The rotating wheel has a linear velocity equal to S1 (m/s), and a diameter of D1 (m)
  • The object of mass M1 (kg) has a centre of mass of distance X1 (m) above the belt surface
  • The mass travels around the outer edge of the wheel until such a point as its combined velocity, acceleration and mass components cause it to leave the surface of wheel - this is the tangent or lift point of the object
  • The mass then continues to travel under the effect of gravity (assuming no air resistance), proscribing an arc for 3 seconds. After 3 seconds we are no longer interested in its position or characteristics.
I'm creating a spread sheet that for any M1, S1, Th1, D1, X1 the relative location, velocity, acceleration can be found for any moment leading up to the lift point and in the 3 seconds after.
I hope to have the spread sheet plot this trajectory curve - not ideal but I'm limited at work as to what software I can use. I hope to build a VisSim model of it later.

While I have motion equations these are only in affect from the point of lift, this point is highly variable based on the mass, velocity, angel etc.

Can anyone please help me to get the correct relationships and equations in order?

Thanks for reading :)

http://imgur.com/Pqejxxz
 
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  • #2
This diagram might help to explain the scenario better.In order to solve this problem, you will need to use the equations of motion for rotational and linear motion. The equations of motion for rotational motion are: Angular velocity (w) = angular acceleration (alpha) * time + initial angular velocity (w0) Angular displacement (theta) = angular acceleration (alpha) * time2 / 2 + initial angular velocity (w0) * time + initial angular displacement (theta0) The equations of motion for linear motion are: Velocity (V) = acceleration (a) * time + initial velocity (V0) Displacement (s) = acceleration (a) * time2 / 2 + initial velocity (V0) * time + initial displacement (s0) Using these equations, you can calculate the velocity, acceleration and displacement of the object at any given time. You will also need to use Newton's Laws of Motion to calculate the force on the object due to the belt and the wheel. To do this, you will need to calculate the mass, velocity and acceleration of the object, as well as the torque on the wheel due to the belt and the wheel. Once you have all of the necessary variables, you can then use the equations of motion to calculate the position, velocity and acceleration of the object. You can then plot the trajectory curve of the object using a spreadsheet or other software.Hope this helps!
 

1. What factors influence the trajectory of a projectile?

The trajectory of a projectile is influenced by multiple factors, including the initial velocity, the angle of projection, the mass of the projectile, the air resistance, and the gravitational force.

2. How does the initial velocity affect the trajectory of a projectile?

The initial velocity, or the speed at which the projectile is launched, determines how far the projectile will travel and how high it will go before reaching the ground. A higher initial velocity will result in a longer horizontal distance and a higher peak height.

3. Why is the angle of projection important in determining the trajectory of a projectile?

The angle of projection, or the angle at which the projectile is launched, affects both the horizontal and vertical components of the projectile's motion. A smaller angle will result in a shorter horizontal distance but a higher peak height, while a larger angle will result in a longer horizontal distance but a lower peak height.

4. What role does air resistance play in the trajectory of a projectile?

Air resistance, or drag, reduces the speed and alters the direction of a projectile as it travels through the air. This can cause the projectile to deviate from its intended trajectory and land at a different point than expected.

5. How does the mass of a projectile impact its trajectory?

The mass of a projectile affects its trajectory by influencing the amount of force needed to launch it and the amount of air resistance it experiences during flight. A heavier projectile will require more force to launch and will experience more air resistance, resulting in a shorter horizontal distance and a lower peak height.

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