A tradesman sharpens a knife by pushing it against the rim of a grindstone. The

Question

A tradesman sharpens a knife by pushing it against the rim of a grindstone. The 50 cmdiameter stone is spinning at 200 rpm and has a mass of 21 kg . The coefficient of kinetic friction between the knife and the stone is 0.20.

Part A

If the stone loses 10% of its speed in 10 s of grinding, what is the force with which the man presses the knife against the stone?

Express your answer to two significant figures and include the appropriate units.

A tradesman sharpens a knife by pushing it against the rim of a grindstone. The 50 cmdiameter stone is spinning at 200 rpm and has a mass of 21 kg . The coefficient of kinetic friction between the knife and the stone is 0.20.

Part A

If the stone loses 10% of its speed in 10 s of grinding, what is the force with which the man presses the knife against the stone?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

wi = 200 rpm = 20.94 rad/s

after 10s it loose 10% of initial speed = 20.94 - 2.094 = 18.8456 rad/s

angular acceleration = (w1-w2)/t = 0.2098 rad/s^2 = 0.21 rad/s^2

moment of inetrial = I = mr^2/2 = 21 * (0.25)^2 /2 = 0.65625 kg-m^2

t = I*alpha = 0.1378125 N-m

t = F.r

F.r = 0.1378125

f*0.25 = 0.1378125

f = 0.55125 N

F = f/mu = 2.75625 N

F = 2.8 N

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