What Angle Causes a Sphere to Begin Sliding?

AI Thread Summary
To determine the angle at which a sphere begins to slide, the coefficient of static friction is crucial. Initially, an incorrect approach using inverse cosine led to an angle of 87 degrees. However, the correct method involves using the tangent function, resulting in an angle of 26.1 degrees. The discussion also touches on calculating the normal force and frictional force in relation to the mass and gravitational force. Understanding the correct equations is essential for solving this problem accurately.
Paulbird20
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[SOLVED] Sphere: angle to begin sliding

Given a small mass on a sphere. Coef of static friction is .49 what angle would begin sliding.

I thought i would use inverse cos(.49/9.8) and i get 87 degrees but it is wrong any other equations i am missing?
 
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Suppose the mass is m. What is the normal force in terms of m, g, theta?

What is the frictional force... and what is the force that is causing the object to slide...
 
i think i figured it out i went and looked at some other equations and realized i needed to use tan instead of cos and i got the correct answer of 26.1 degrees Thank you for the tip.
 
Paulbird20 said:
i think i figured it out i went and looked at some other equations and realized i needed to use tan instead of cos and i got the correct answer of 26.1 degrees Thank you for the tip.

no prob. you're welcome.
 
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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