# 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 f0. 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