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Here are some Physics 7B problems to practice on. WARNING – DO NOT ASSUME THAT THE PROBLEMS ON THE REAL FINAL WILL BE “JUST LIKE” THESE. ALL PHYSICS PROBLEMS ARE DIFFERENT AND YOU NEED TO THINK AND ANALYZE TO DO THEM. THESE ARE JUST TO HELP YOU PRACTICE THINKING AND ANALYZING.
1) Consider the circuit show in the diagram at the right. All the bulbs in the circuit have the same resistance.
a. Describe what happens to the brightness of the bulbs A, B, and C, before and after switch S is closed.
b. In which case does the battery provide more power?
2) The curve here illustrates the trajectory of a hockey puck on a frictionless, horizontal surface, as viewed from above. Indicate on the graph the section of the trajectory during which the puck is experiencing an external force, and indicate the approximate average direction of this force during this time.
3) A marble rolls down the track shown in the figure, starting from rest at point A and reaching point B, at which point the track is nearly (but not exactly) vertical. Draw the subsequent trajectory of the marble as accurately as you can. Explain your reasoning.
4) A circuit has two capacitors (both with capacitance C) and one resistor as shown in the figure. Initially the capacitor on the left has voltage V across it, and the one on the right has no voltage. Draw a graph which shows the voltage on the right hand capacitor and the left hand capacitor as a function of time after the switch is closed.
5) A certain refrigerator cost $1000, and costs $10/month to operate. A better refrigerator of the same size and shape costs $1200, but has insulation which has a thermal conductivity half as great as the first refrigerator. If you buy the better one, it costs more but saves you energy. How long does it take before you in fact spend less money with the better refrigerator, including the initial cost and the power cost?
6) A block of mass m=4 kg is on an inclined plane which has an angle of 30 degrees to the horizontal.
a. Draw a complete force diagram in the case where the block is at rest. Label all forces and give their magnitudes.
b. Draw a complete force diagram in the case where the block is accelerating down the plane.
7) A pendulum with a bob of mass m and length l hangs from the
top of a train car. The pendulum makes a constant angle θ of 20 degrees with the vertical. This is because the train is going around a curve of radius 100 m. How fast is the train going? In which direction is the curve (assume the picture shows the train car from behind; it is moving into the page)?
8) A trebuchet is an ancient throwing device that consists of a wooden beam (mass = 3500kg) that can rotate freely about the pivot point shown. The beam has a very heavy object (mass = 35000kg) hanging from one end and something that we want to throw (like a physics teacher) on top of the other end. Initially, there is another weight (mass = 7000kg) hung from a cord on the left side of the pivot point to keep the trebuchet motionless. a) Draw a sketch of the wooden beam. First draw the forces on the beam due to the two hanging masses. Then decide how big the other forces must be and draw those force vectors on the beam also.
b) Referring to your picture in part a), briefly explain how the 7000kg hanging mass is able to keep the beam from rotating (Δ L = 0) even though the 35000kg mass hanging from the other end is 5 times heavier.
c) When it is time to throw the teacher, you just cut the cord holding the 7000kg mass. Soon after you cut the cord, the direction of the angular momentum vector of the beam is (circle the correct answer) left. right. up. down. into the paper. out of the paper. Briefly explain how you use the physics principles we have been talking about to choose this direction.
12) A bowling ball hangs from a wire as shown to the right and swings back and forth. Point I is at the maximum height of the ball during its swinging and point II is the lowest point in the swing. I
II
a) What is the speed of the ball when it reaches point I? Explain.
b) In the space below, draw a reasonable velocity vector for a time just before the ball reaches point I and label this vIi. Also draw a reasonable velocity vector for a time just after the ball leaves point I and call this vIf.
c) In the space below, use your results from part b) to draw a vector representing the net force on the bowling ball near point I. Explain the physics principles you used to arrive at your answer.
d) After leaving point I the ball passes through point II. In the space below, draw a reasonable velocity vector for a time just before the ball reaches point II and call this vIIi. Also draw a reasonable velocity vector for a time just after the ball leaves point II and call this vIIf.
e) In the space below, use your results from part d) to draw a vector representing the net force on the bowling ball near point II. Explain the physics principles you used to arrive at your answer.
13) The picture to the right shows a section of a water circuit similar to the circuit you worked with in DL. The fluid flows from left to right through the pipe at a rate of 10- (^5) m (^3) /s. The center of this section of pipe is larger (cross-sectional area = Acenter = 25 cm^2 ) than either the left or right sides (each has area Aside = 6 cm^2 ). The water in the vertical column on the left is at the level shown. The vertical columns in the center and on the right also have water in them, at a level that you need to determine in parts a) and b). Don’t forget that all real pipes with real water have dissipation.
I
ii)
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iii)
ii)
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a) Three possible water levels are shown for the vertical column connected to the center section. Use the transport equation to figure out which of these three levels is/are possible. Explain your answer thoroughly.
b) The total resistance between the vertical pipe on the left side and the vertical pipe on the right side is known to be 5 x 10^5 Js/m^6. Find the height difference between the water in the vertical pipe on the left side and the water in the vertical pipe on the right side. In this case, is the right side level higher or lower than the left side level?
14) A movie stunt driver is driving a car very fast along a road (shown to the right) with a lot of hills and is being chased by the villains in the movie. The car always stays in contact with the road and the speed of the car is constant.
II
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a) On the picture above , draw the acceleration vector for the car at point I assuming that its speed is constant and that it stays in contact with the road. If a = 0 then just write a 0 on the picture. b) Draw a properly scaled and labeled force diagram for the car at position I. c) Draw a properly scaled and labeled force diagram for the car at position II.
15) Humans are strong enough so that they can lower the pressure in their lungs to about 10,000 Pa less than atmospheric pressure (1 at = 101,000 Pa). Given this fact about your lungs, i) explain the physics of drinking a milkshake through a straw (see picture to the right) and ii) estimate the longest vertical straw that you could use and still be able to get the milkshake up to the top so that you can drink it (ρmilkshake = 1200 kg/m^3 ).
Distance from top of milkshake to top of straw.
Initially at rest
Rolling down ramp
16) A wheel is released from rest (i.e. not moving initially) at the top of a ramp as shown to the right. After being released, the wheel rolls faster and faster down the ramp. Of course, when I say “rolls” I mean that, as it moves faster and faster down and to the right, it is also rotating clockwise faster and faster. a) Draw a reasonable force diagram for the wheel and also draw a reasonable extended force diagram for the wheel.
b) Draw a vector showing the direction of the net force.
c) State the direction of the net torque (clockwise or counterclockwise) about the center of mass of the wheel and explain how it is related to your extended force diagram.
17) Shown to the right is an electric circuit made up of a capacitor, a resistor, and a switch. When the switch is closed, at t = 0, there is a clockwise current in the circuit. The voltage across the resistor, ΔVR, is measured as a function of time and the result is shown on the graph below the circuit.
time (seconds)
Δ V R (Volts)
a) For two times, t = 0.2 s and t = 1.5 s, estimate the rate of change, d(ΔVR)/dt, of the voltage across the resistor and show that the rate of change is approximately (round your numbers to 1 digit) proportional to the voltage itself.
b) Without using any equations, briefly explain why ΔVR decreases as time passes.
18) When a cup of hot coffee is left on a table, it slowly cools to room temperature. For the coffee, ΔT = Tcoffee - Troom changes with time in a form very similar to the graph of the voltage above. Discuss the general similarities between these two transport problems and so explain why the time dependence of Δ VR has a similar shape to the time dependence of Δ T. Again, don’t use any equations.
