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

In summary: The projectile leaves the wheel at a height of 2.64 meters above the ground and hits the wall at a height of 2.50 meters from the wall.
  • #1
VinnyCee
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0
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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  • #2
step 1: What is the position and the velocity vector of the lump as it leaves the wheel?
 
  • #3
Position is at 60 degrees below the positive x-axis with a velocity of .25 m / ms or 250 m / s, right?
 
  • #4
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:)
 
  • #5
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.
 

1. What is the difference between uniform circular motion and projectile motion?

Uniform circular motion is the motion of an object along a circular path at a constant speed. Projectile motion, on the other hand, is the motion of an object through the air under the influence of gravity, with a parabolic trajectory.

2. How do you calculate the velocity of an object in uniform circular motion?

The velocity of an object in uniform circular motion can be calculated by dividing the circumference of the circle by the time it takes to complete one full revolution.

3. How does the angle of projection affect the range of a projectile?

The range of a projectile is directly affected by the angle of projection. The maximum range is achieved when the angle is 45 degrees, and the range decreases as the angle increases or decreases from this optimal angle.

4. Can an object be in both uniform circular motion and projectile motion at the same time?

Yes, an object can be in both uniform circular motion and projectile motion at the same time if it is projected at an angle from a circular path. This is known as a combination of both motions.

5. How does air resistance affect projectile motion?

Air resistance can affect projectile motion by slowing down the object's horizontal velocity and causing it to fall to the ground at a shorter distance. However, this effect is typically only significant for objects with larger surface areas, such as feathers or parachutes.

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