Suppose the object's mass is 41.0 g, with mu_s = 0.750 and mu_k = 0.400 . Determine a_min.?

Question

Try this! Hold your right hand out with your palm perpendicular to the ground, as if you were getting ready to shake hands. You can't hold anything in your palm this way because it would fall straight down. Use your left hand to hold a small object, such as a ball or a coin, against your outstretched palm, then let go as you quickly swing your hand to the left across your body, parallel to the ground. You'll find that the object stays against your palm, without slipping or falling, if your hand maintains a certain minimum acceleration a_min."

Suppose the object's mass is 41.0 g, with mu_s = 0.750 and mu_k = 0.400 . Determine a_min.

Answer 1

model the object as a FBD in the vertical at the threshold of breaking static friction downward:

f=m*g
where f is friction:
N*0.750
N is the normal force.

Looking at a FBD in the horizontal
N=m*a
where a is a_min
m*a_min*.750=m*g
a_min=g/.75
or a force that is 4/3 times gravity

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