What Is the Angle Between the Pendulum and the Vertical?

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AI Thread Summary
To find the angle between the pendulum and the vertical, the tension in the rope and the weight of the pendulum bob are analyzed. A free-body diagram is suggested to visualize the forces acting on the pendulum. The calculation involves using the tangent function, resulting in an angle of approximately 8.13 degrees. The tension in the rope is confirmed to be horizontal, affecting the pendulum's angle. Understanding the relationship between the forces is crucial for solving the problem accurately.
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Homework Statement


A pendulum bob of mass 24.5 N is pulled aside by a horizontal rope. If the tension in the rope is 3.50 N, what's the angle between the pendulum and the vertical?


Homework Equations


Vectors


The Attempt at a Solution


tan^-1(3.50/24.5) = 8.13 degrees?
 
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draw a free-body diagram

the rope pulling from the left, the weight down, and Tension at an angle to the upper right
 
it duznt seem like it is necessary
 
And it means the tension is the horizontal rope
 
Last edited:
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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