A 280g block on a 50.0cm -long string swings in a circle on a horizontal, fricti

Question

A 280g block on a 50.0cm -long string swings in a circle on a horizontal, frictionless table at 65.0rpm
What is the speed of the block?
What is the tension in the string?

A 4.00g coin is placed 14.0cm from the center of a turntable. The coin has static and kinetic coefficients of friction with the turntable surface of ?s = 0.860 and ?k = 0.480.
What is the maximum angular velocity with which the turntable can spin without the coin sliding?

A 400g ball moves in a vertical circle on a 1.02m -long string. If the speed at the top is 3.80m/s , then the speed at the bottom will be 7.38m/s .
What is the gravitational force acting on the ball? (N)
What is the tension in the string when the ball is at the top? (N)
What is the tension in the string when the ball is at the bottom? (N)

Explanation / Answer

1) speed of the block is v = r*w = 0.5*65*2*3.142/60 = 3.403 m/sec

T = m*v^2/r = 0.280*3.403^2/0.5 = 6.485 N

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2) The static friction coefficient, Us, determines when it starts sliding.

M*g*Us = M*R*w^2

Solve for w, the angular velocity.

w = sqrt(g*Us/R) =7.75 rad/s

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3) speed at top v2 = sqrt(R*g) = 3.8
speed at the bottom v1 =sqrt(5*R*g) = 7.38 m/sec.....
N_top = m[(v2^2/R)-g] = 0.4[(3.8^2/1.02)-9.8] = 1.742 N...
N_bottom.. = m[(v1^2/R)+g] =
= 0.4 [ (7.38^2/1.02)+9.8 ] = 25.28 N

gravitational force = mg = 0.4*9.8 = 3.92 N

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