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(Requested by Merjan)

Q – Two cars were moving on parallel lanes in one direction. One car had speed 60 km/hour, while the other had speed of 65 km/hr. At time 8:30 AM, the distance between the cars was 8 km. 

(a)  How far a way from each another the were at 9:20 AM that day?

(b)  At what time the cars moved side by side?

Ray Optics: Refraction

Q- Red light (n = 1.520) and violet light (n = 1.538) traveling in air are incident on a slab of crown glass. Both colors emerge from the glass at the same angle of refraction. The red light has an angle of incidence of 35.96°. What is the angle of incidence of the violet light? Give your answer to four significant figures.

Solution:

Speed of Bullet

Q- A bullet is shot through two cardboard disks attached a distance D apart to a shaft turning with a rotational period T, as shown. Derive a formula for the bullet speed v in terms of D, T and a measured angle θ between the position of the hole in the first disk and that of the hole in the second. Both of the holes lie at the same radial distance from the shaft.

Solution:

Errors: Measuring Speed of Light

Q- Galileo attempted to measure the speed of light by measuring the time elapsed between his opening a lantern and his seeing the return light from his assistant’s lantern, which is opened when the assistant sees the light from Galileo’s lantern. What distance d must separate Galileo from his assistant in order for the human reaction time Δt = 0.2 s, to introduce no more than 15% error in the measured speed of light?

Harmonic Oscillations

Q- A harmonic force F0 sin(ωt) is applied to mass m1 which in turn is coupled to springs of spring constants k1, k2 and k3. Let x1 and x2 ­be the deviations from equilibrium for m1 and m2, respectively.  The blocks moves on a horizontal frictionless table.

(a) Write the equations of motion for the two blocks. Use x1 and x2 as your variables.

(b) Find the normal frequencies of the system, that is, when the external force is absent. Assume for this part and the remainder of the problem the springs are the same and the masses are equal.

(c) Solve for the steady state motion with the force, that is find x1 and x2 as functions of time.

Solution:

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