Classical Mechanics Answers

How do you derive the equation τ = k θ for a torsion spring? τ is torque, k is torsion spring’s constant, and θ is displacement in radians. Thanks!  

In an unhealthy, dusty cement mill, there was 2.6x10

9 dust particles (sp g =3.0) per

cubic meter of air. Assuming the particles to be spheres of 2.0 µm diameter, calculate

the mass of dust (a) in a 20mx15mx80m room and (b) inhaled in each average

breath of 400-cm3 volume

A stone has a mass of 5kg. If it takes the stone 4 sec to fall freely to the ground, calculate it's initial height above the ground, and the force with which the stone hit the ground.

The linear density of a thin rod is given by p =cx, where c is a constant and x is the distance

measured from one end. If the rod is of length b, find the center of mass.

A uniform solid ball has a few turns of light string wound around it. If the end of the string

is held steady and the ball is allowed to fall under gravity,what is the acceleration of the

center of the ball? (Assume the string remains vertical.)

Find the center of mass of each of the following:

(a) Athin wire bent into the form of a three-sided, block-shaped "Ll"with each segment of

equal length b

(b) A quadrant of a uniform circular lamina of radius b

(c) The area bounded by parabola y =x2/b and the line y =b

(d) The volume bounded by paraboloid of revolution z = (x2 +y2)/b and the plane z = b

A 1305 kg test car travels around a flat circular track that is 2.15 km long (circumference). If the coefficient of friction between the car’s tires and the track is 1.20 will the car be able to drive a speed of 55.7 m/s and stay on the track?

The emf induced in the armature of a shunt generator is 596 V. The armature

resistance is 0.1Ω

(a) Compute the terminal voltage when the armature current is 460A.

(b) The field resistance is 110Ω. Determine the field current, and the current and power delivered to the external circuit

A shunt motor armature resistance 0.08Ω is connected to 120V mains. With 50A in the armature, what are the back emf and the mechanical power developed within the armature?

1. Determine the discharge over an uncontracted horizontal weir that is 1.5 m high and 4.5 m long. The upstream depth is 2.2 m. Determine the Ink height if the same discharge was desired without exceeding an upstream depth of 1.8 m?

2. Determine the discharge over a standard contracted weir when the upstream water depth is 2.1 m. The weir (one end contraction) is 1.8 m high and has a 1.8 m overflow length. Also determine the approach velocity head in the 4-m-wide channel. Is it significant?