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Honors Physics Sample Problems

Columbus Academy

Section I:
Mechanics

Mechanics Sample

Two small blocks, each of mass m, are connected by a string constant of lenght 4h and negligible mass. Block A is placed on a smooth tabletop as shown above, and block B hangs over teh edge of the table. The tabletop is a distance 2h about teh gloor. Block B is then released from rest at a distance h above the floor at time t = 0. Express all algebraic answers in terms of h, m, and g.

(a)

Determine the acceleration of block B as it descends.


(b)

Block B strikes the floor and does not bounce. Determine the time t1 at which block B strikes the floor.


(c)

Describe the motion of block A from time t = 0 to the time when block B strikes the floor.


(d)

Describe the motion of block A from the time block B strikes the floor to the time block A leaves the table.


(e)

Determine the distance between the landing points of the two blocks.







Section II:
Electricity and Magnetism

Electrical Picture

In the circuit shown above, A, B, C, and D are identical lightbulbs. Assume that the battery masintains a constant potential difference between its terminals (i.e. the internal resistance of the battery is assumed to be negligible) and the resistance of each lightbulb remains constant.

(a)

Draw a diagram of the circuit in the box below, using the following symbols to represent the components in your diagram. Label the resistors A, B, C, and D to refer to the corresponding lightbulbs.


symbols

Answer Box

(b)

List the bulbs in order of their brightness, from brightest to least bright. If any tow or more bulbs have the same brightness, state which ones. Justify your answer.


(c)

Bulb D is then removed from its socket.

i.

Describe the change in brightness, if any, of bulb A when bulb D is removed from its socket. Justify your answer.

ii.

Describe the change in brightness, if any, of bulb B when bulb D is removed from its socket. Justify your answer.






Section III:
Light and Optics

Optics Problem


A transmission diffraction grating with 600lines/mm is used to study the line spectrum of the light produced by a hydrogen discharge tube with the setup shown above. The grating is 1.0 m from the source (a hole at the center of the the meter stick). An observer sees the first-order red line at a distance yr = 428 mm from the hole.


(a)

Calculate the wavelength of the red line in the hydrogen spectrum.


(b)

According to the Bohr model, the energy levels of the hydrogen atom are given by
En = -13.6eV/n2, where n is an integer labeling the levels. The red line is a transition to a final level with n = 2. Use the Bohr model to determine the value of n for the inital level of the transition.


(c)

Qualitatively describe how the location of the first-order red line would change if a diffraction grating with 800 lines/mm were used instead of one with 600 lines/mm.



Columbus Academy