Classical Mechanics Answers

A drain has a rectangular profile. W is the width of the drain in meters, and

D is the depth of the water in meters.

In the case that the depth is much less than the width the amount of water that flows per second through a rectangular drain is given by the following formula:

Q = (A/n)*(D^2/3)*(S^1/2) ------------- (1)

In which:

- Q is the volume of water that

flows per second through the

drain (in m3/s);

- A = W×D, the cross-sectional

area of the drain up to the level

of the water (in m2)

- n is a parameter describing the

resistance to the flow of water;

- S is the gradient of the river

(in m/m).

Use formula 1 to derive the units of n.

A boy throws a ball straight into the air. It reaches the highest point of its flight in 4 seconds. How fast was the ball going when it left the boy’s hand?

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

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?

With block C placed on top of B. the system undergoes simple harmonic motion with an amplitude of 0.12 m. Block B has a speed of 0.22 m/s at a displacement of 0.075 m from its equilibrium position. Determine the period of the motion. Express your answer with the appropriate units. What minimum value for the coefficient of static friction mu_s between B and C is needed if C is never to slip? Ignore any friction between B and the horizontal surface.