Classical Mechanics Answers

Two crossed belts on pulleys of diameters 3.6 m and 2.4 m connect two parallel shafts with centres 4.2 meters apart. The maximum tension in the belts is limited to 1200 N and friction between the belts and the pulley, μ = 0.26. The smaller pulley has a speed of 300 rev/min. 2.1 Find the power that can be transmitted (8) 2.2 What would be transmitted if open belts were used 

A belt of density of 1500 kg/m 3 and cross-sectional area 400 x 10 -6 m 2 transmits 120 kW power at 1800 rev/min through a pulley of diameter 1.6 m. The angle of lap between the belt and the pulley is 240 0 and μ = 0.2. Determine: 3.1 The tensions and the maximum stress in the belt. (10) 3.2 The tensions if a grooved pulley with a groove angle of 50 0 . (

A plate clutch has two disA plate clutch has two discs on driven shaft, each effective on both sides, and of outer and inner radii 280 mm and 140 mm, respectively. It transmits 45 kW at 2400 rev/min and μ = 0.32 for the friction material. Calculate: 4.1 The axial force needed assuming uniform pressure. (7) 4.2 The force that would be needed assuming uniform wear. (5)cs on driven shaft, each effective on both sides, and of outer and inner radii 280 mm and 140 mm, respectively. It transmits 45 kW at 2400 rev/min and μ = 0.32 for the friction material. Calculate: 4.1 The axial force needed assuming uniform pressure. (7) 4.2 The force that would be needed assuming uniform wear. (5)

Two athletes a and b set off from the same point but in opposite directions at a constant speed around a track of circumference 400m.if they meet after 50 s and the speed of a is 1.5 times the speed of b.calculate the speed of each

A belt of density of 1500 kg/m 3 and cross-sectional area 400 x 10 -6 m 2 transmits 120 kW power at 1800 rev/min through a pulley of diameter 1.6 m. The angle of lap between the belt and the pulley is 240 0 and μ = 0.2.

1. Derive and solve the equation of motion of a particle, in a uniform gravitational field, projected with initial horizontal velocity v 0 at a height h.
2. Write the Lagrangian of this particle. Show that the Euler-Lagrange equations of motion for this particle is identical to what one would obtain from Newton’s second law.

Write the Lagrangian of this particle. Show that the Euler-Lagrange equa-

tions of motion for this particle is identical to what one would obtain from

Newton’s second law.

Derive and solve the equation of motion of a particle, in a uniform gravita-

tional field, projected with initial horizontal velocity v 0 at a height h.

A 5.0-{\rm kg} block is suspended from the ceiling by a strong spring and released to perform simple harmonic motion with a period of 0.65 {\rm \;s} . The block is brought to rest, and the length of the spring with the block attached is measured. By how much is this length reduced when the block is removed?