Uniform Circualr Motion with Projectile Motion problem (Extremely confusing):

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Homework Help Overview

The problem involves a lump of wet putty moving in uniform circular motion on a wheel, which then flies off at a specific position and height. The task is to determine the height at which the lump strikes a wall located a certain distance away.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the initial position and velocity vector of the lump as it leaves the wheel, with one suggesting the angle and speed at that moment. Others explore how to break down the components of the position and velocity vectors using the geometry of the situation.

Discussion Status

The discussion is active, with participants providing guidance on how to determine the initial conditions for the projectile motion. There is an ongoing exploration of the relationships between the components of motion and the setup of the problem, but no consensus has been reached on a solution.

Contextual Notes

Participants are working with specific values such as the radius of the wheel, the period of rotation, and the initial height of the lump. There is a noted need for clarity on the projectile equations and the relationship between the starting position and the wall's location.

VinnyCee
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A lump of wet putty moves in uniform circular motion of radius 20cm on the rim of a wheel rotating counter clockwise with a period of 5.00 seconds. The lump fly's off the rim at the 5 o'clock position and from a height of 1.20m above the ground and a distance of 2.50m from a wall. At what height on the wall does the lump hit?

I have been stumped by this problem for hours. Please help. :confused:
 
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step 1: What is the position and the velocity vector of the lump as it leaves the wheel?
 
Position is at 60 degrees below the positive x-axis with a velocity of .25 m / ms or 250 m / s, right?
 
I guess the answer is supposed to be 2.64 meters height on the wall that is 2.50 meters away.

But I really need to know how to actually DO the problem!

Please help:)
 
For your projectile, the initial Position Vector (when it leaves the wheel) has an x-component (call it x0) and a y-component (call it y0). (Use your "60 degrees below the positive x-axis" and the wheel radius to determine these components).

The initial Velocity Vector also has an x-component (call it v0,x) and a y-component (call it v0,y). To get these components, first determine its magnitude (the speed) by considering how fast a point on the wheel's rim is traveling... (in one full rotation of wheel, what distance was traveled by a point on the rim in one period of 5 s?). Then determine the direction (the angle of launch) by arguing that the initial velocity vector is tangent to the wheel when it leaves the wheel.

You now have your initial conditions for the projectile.

Now, where is the wall and the floor in relation to your starting position?
At least one of those will determine your final position.

Write down your projectile equations and see what is given and what is unknown.
Formulate an strategy to algebraically solve for your unknowns.
 

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