Motion of a body - conveyor/catapult/trebuchet design

In summary, the object of mass M1 (kg) traveling around the edge of a rotating wheel at a speed of S1 (m/s) experiences a centrifugal force, gravitational force, and friction force. These forces cause the object to move around the edge of the wheel in a curved path until it reaches the lift point, at which point it continues to move under the effect of gravity.
  • #1
rmf17
6
0
Hello All,
I posted this same question to the classical physics forum - but I'm reckoning it's more ideally suited for a Mechanical Engineer:

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 helping:)

Pqejxxz.jpg
 
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  • #2
</code>This is a very complex problem and it will require a lot of analysis and calculations to solve. It is not something that can be answered in a few simple equations. You will need to start by doing some basic physics calculations in order to determine the forces acting on the object at the lift point. This will involve calculating the centrifugal force, gravitational force, and the friction force between the belt and the wheel. Once you have these values you can use them to calculate the acceleration of the object at the lift point, which will then allow you to calculate the velocity and position of the object after 3 seconds.You will also need to consider the effects of air resistance on the object's motion. For example, if the object is traveling at a high speed, then air resistance will cause the object to slow down over time. You will need to take this into account when calculating the motion of the object.Finally, you may want to consider using numerical simulations to solve the problem. This will give you a more accurate result than using simple equations. There are several software packages available that can be used to simulate the motion of the object, such as MATLAB or COMSOL.Good luck with your project!
 

1. How does the design of a conveyor affect its motion?

The design of a conveyor can greatly affect its motion. Factors such as the materials used, the angle of incline, and the speed of the belt can all impact how smoothly and efficiently the conveyor moves. Additionally, the placement and spacing of rollers or pulleys can also affect the motion of the conveyor.

2. What is the difference between a catapult and a trebuchet?

A catapult and a trebuchet are both types of siege engines used to launch projectiles. However, a catapult typically uses tension or torsion to launch the projectile, while a trebuchet uses a counterweight to swing the arm and launch the projectile. This results in a trebuchet being able to launch heavier projectiles at a longer distance compared to a catapult.

3. How does the weight of the projectile affect the motion of a catapult or trebuchet?

The weight of the projectile is a crucial factor in the motion of a catapult or trebuchet. A heavier projectile will require more force to launch and will also have a greater impact upon landing. However, a heavier projectile may also decrease the maximum distance that can be achieved due to the limitations of the machine's design and the force it can generate.

4. What are some safety considerations when designing a catapult or trebuchet?

Safety should always be a top priority when designing a catapult or trebuchet. These machines can generate a lot of force and launch projectiles at high speeds, so it is important to take precautions to prevent accidents. This may include using strong and durable materials, incorporating safety guards, and ensuring that the machine is operated by trained individuals.

5. How do you calculate the optimal counterweight for a trebuchet?

The optimal counterweight for a trebuchet can be calculated using the principles of energy conservation. The potential energy stored in the counterweight must be equal to the kinetic energy of the projectile at the point of release. By considering the weight of the projectile, the length of the throwing arm, and the distance to the pivot point, the optimal weight of the counterweight can be determined for maximum efficiency and distance.

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