A large block P executes horizontal simple harmonic motion as it slides across a frictionless surface with a frequency of f = 1.60 Hz. Block B rests on it and the coefficient of static friction between the two is μs = 0.570.
What maximum amplitude of oscillation can the system have if block B is not to slip?
What maximum amplitude of oscillation can the system have if block B is not to slip?
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If the top block has mass m, it's weight = mg and the normal force, N, on it has magnitude mg.
The top block is accelerated by friction according to F=ma, where F is the frictional force. It will slip at the point where the maximum possible frictional force, μsN, equals ma
μs(mg) = ma
a = μs.g = 0.570 x 9.81 = 5.592m/s²
For SHM |a| = ω²x so maximum magnitude acceleration occurs when x= A(amplitude)
Since ω = 2πf,
5.592 = (2π x 1.60)²A
A = 5.592/(4π²)
= 0.142m
The top block is accelerated by friction according to F=ma, where F is the frictional force. It will slip at the point where the maximum possible frictional force, μsN, equals ma
μs(mg) = ma
a = μs.g = 0.570 x 9.81 = 5.592m/s²
For SHM |a| = ω²x so maximum magnitude acceleration occurs when x= A(amplitude)
Since ω = 2πf,
5.592 = (2π x 1.60)²A
A = 5.592/(4π²)
= 0.142m