A conducting rod of length l, mass m, and resistance R is suspended by two vertical conducting wires of lengths d each. The circuit consists of a battery ε, the horizontal fixed wires, two parallel vertical wires , and the conducting rod. All conducting wires have negligible resistance and mass. There is a conducting long cable. The cable is below the rod and at a distance x.

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# The equation of radioactive decay

The half-life of Molybdenum-93 is 4000 years. A sample of Molybdenum-93 has a mass of 10 mg. When will the mass be reduced to 1 mg?

Image Source: Virtual museum of chemical elements.

# A ball is attached to a string and swung so that it travels in a horizontal circle

A ball of mass 0.2 kg is attached to a massless string 1 m long and swung so that it travels in a horizontal circle of radius 0.5 m.

a) Draw a free-body diagram.

b) Find the force of tension in the string as the ball swings in a horizontal circle.

c) Find the period of the ball’s motion.

# The quantum tunneling phenomenon

The quantum tunneling phenomenon is negligible in the classical mechanics.

Show that the tunneling probability equals 0 for an object of mass 0.007 kg moving at a speed of 0.1 m/s against a solid obstacle of height 0.05 m and width 0.01 m.

# A car moves around a curved banked road

A curved road is banked at an angle β, and there is no friction between the road and the car’s tires. The road has a radius of curvature of 50 m.

A car has a speed of 90 km/h.

Find angle β.

# The car passes over the top of a convex bridge

A car has a mass of 1500 kg and travels with a speed of 5 m/s. The car passes over the top of a convex bridge that has a radius of curvature equal to 10 m. What is the force of the bridge on the car as it passes over the top?

# A C-130 Hercules is traveling toward a cliff

A C-130 Hercules is traveling toward a cliff at the speed of 150 m/s. Its engines emit a tone at frequency f_{0}. We consider that the speed of sound is 340 m/s. What frequency is received by a pilot after reflection from the cliff?

Image Source: U.S. Air Force

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