Calculating Speed of a motion of a Circular Object

AI Thread Summary
To calculate the speed of a ball in a conical pendulum, the radius of the circular motion is determined using the formula R = L * sin(θ), where L is the string length and θ is the angle. Given L = 1.70 m and θ = 37.0°, the radius is calculated as approximately 1.02 m. The circumference of the circular path is then found using the formula C = 2πR, resulting in a value around 6.3 m. The speed is calculated by dividing the circumference by the time for one revolution, yielding a speed of approximately 2.7 m/s. Various calculations provided by participants indicate slight variations in results, but the method remains consistent.
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Homework Statement



A conical pendulum is made of a ball on the end of a string, moving in circular motion as represented in the figure below. The length L of the string is 1.70 m, the angle θ is 37.0o, and the ball completes one revolution every 2.30 s.

Calculate the speed of the ball, by first deriving a symbolic equation and then inserting the
numbers.

Homework Equations





The Attempt at a Solution



I sort of know how to do this problem without the degrees.
 
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I can't see the picture, but I presume that it is rotating in a horizontal plane.

First of all you know that the ball is describing a circle that has a radius of L*Sin37°.

You know the time to complete a revolution ...
 
Alright, here is what I got

R=L*sin(37)

R=1
Diameter=2
Circumference=pi(2)

Circumference=6.3

Speed=Distance Traveled/Time

Speed=6.3m/2.3s

= 2.7m/s

Is that right?
 
Looks about right.

I get 1.02 m

and 6.41 and 2.79.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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