A solid ball is released from rest and slides down a hillside that slopes downwa

Question

A solid ball is released from rest and slides down a hillside that slopes downward at an angle 65.0 degrees from the horizontal.

What minimum value must the coefficient of static friction between the hill and ball surfaces have for no slipping to occur?

Please show all steps, other answers show a 7, but we don't know where that came from. (answer is NOT 2.14)

Any response that does not explain where the 7 comes from through the steps will get a rating of 1. This is the third time I'm asking this question, thank you.

Explanation / Answer

mgsin(65)-fs=ma fs=µsN=µs(mgcos(65)) A solid ball is released from rest and slides down a hillside that slopes downward at an angle 65.0 degrees from the horizontal. therefore, m*g*sin(65) - µs*(m*g*cos(65)) = m*a where, µs is coefficient of static friction force. Normal force = m*g*cos(65) Since it's not slipping, acceleration is zero, thus, m*a = 0 therefore, m*g*sin(65) - µs*(m*g*cos(65))=0 m*g*sin(65) = µs*(m*g*cos(65)) µs = (m*g*sin(65))/(m*g*cos(65)) (m*g) cancels out µs = sin(65))/cos(65) = tan(65) = 2.144

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