Question

A block of mass M slides on a thin film of oil. The film thickness is h and the area of the
block is A. When released, mass m exerts tension on the cord, causing the block to accelerate.
Neglect friction in the pulley and air resistance. Develop an algebraic expression for
the viscous force that acts on the block when it moves at speed V. Derive a differentia]
equation for the block speed as a function of time. Obtain an expression for the block
speed as a function of time. The mass M = 5 kg, m — I kg, A = 25 cm2, and h = 0.5 mm.
If it takes 1 s for the speed to reach 1 m/s, find the oil viscosity /x. Plot the curve for V(t).

Answer 1

Answer:

A block of mass M=12 kg slides on a thin film of oil. The film thickness is h=2 mm and the area of the block is A=0.5 m2 A = 0.5 m 2 . When released mass m=1 kg exerts tension on the cord, causing the block to accelerate. Neglect friction in the pulley and air resistance.

Answer 2

An algebraic expression for the viscous force that acts on the block when it moves at speed V.

Explanation:

A block of mass M slides on a thin film of oil. When released, mass m exerts tension on the cord, causing the block to accelerate.

• film thickness is h= 0.5 mm
• area of the block is A =25 cm
• mass is M=5 kg
• friction in the pulley is neglected
• air resistance is neglected
• speed is V
• m= 1 kg

An algebraic expression for the viscous force that acts on the block when it moves at speed V.

F = µ VA / h

V = (mgh / µA )(1 - exp [ - µAt / )(M + m)h ])

µ = 1.29 Ns/m²