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Work and Energy Problems

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Questions:

Work and Energy Review Problems (Answers are at the bottom of this document)

1. From the given list, select a possible pair for the value of coefficient of static and kinetic frictions μs and μk (There may be more than one choice)
a. (2.61, 2.00) b. (2.00, 2.61) c. (0.261, 0.150) d. (0.150, 0.261)

2. A runner has a kinetic energy of 750 J. What will be his/her kinetic energy if
(a) his/her mass is doubled.
(b) his/her speed is doubled.

3. Three objects were thrown from top of a building. First one was thrown with 20 m/s horizontally. The second one was thrown vertically upward with an initial speed of 20 m/s. The third object was thrown at an angle 30o to the horizontal. When the objects reach the ground, which object will have the highest speed?

4. A 2.5 x 103 kg car starts from rest at the top of a 20 m rough slope inclined at 30o with the horizontal. If the average frictional force experienced by the car is 3.2 x 103 N, find the speed of the car at the bottom of the slope.

5. The electric motor of a toy car accelerates the car from rest to 0.5 m/s in 0.030 s. If the mass of the toy car is 3.0 kg, find the average power delivered to the car during its acceleration.

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Answers.

1. Coefficient of friction can only assume values between 0 and one. i.e.
0 ≤ μs ≤ 1 0 ≤ μk ≤ 1. Further, coefficient of static friction is larger than coefficient of kinetic friction. i.e. μs > μk
So the only possible choice is choice C.

2. Formula for kinetic energy is: K = ½ m v2
Note that K is proportional to m. Hence if we double the mass, kinetic energy also should double. So the new kinetic energy must be 2 x 750 = 1500 J
Note that K is proportional to v2 ...

Solution Summary

This document contains five problem on the topic of 'Work and Energy'. First three problems test the conceptual understanding of this topic while the other two tests the problem solving skills. I have provided detailed step-by-step solution to all the problems. I also have included colorful clear labeled diagrams to further clarify the problems at hand. I created these problem set for my college level students for review and I believe these will benefit you as well.

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Problems

(See attached file for full problem description and diagrams)

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3.
The filament of a light bulb has a resistance of 580 Ω. A voltage of 120 V is connected across the filament. How much current is in the filament?

13.
A cylindrical copper cable carries a current of 1200 A. There is a potential difference of 1.6 X 10-2 V between two points of the cable that are 0.24 m apart. What is the radius of the cable?.

25.
A blow-dryer and a vacuum cleaner each operate with a voltage of 120 V. The current rating of the blow-dryer is 11 A, and that of the vacuum cleaner is 4.0 A. Determine the power consumed by (a) the blow-dryer and (b) the vacuum cleaner. (c) Determine the ratio of the energy used by the blow-dryer in 15 minutes to the energy used by the vacuum cleaner in one-half hour.

35.
An electric furnace runs nine hours a day to heat a house during January (31 days). The heating element has a resistance of 5.3 Ω and carries a current of 25 A. The cost of electricity is $0.10/kWh. Find the cost of running the furnace for the month of January.

41.
A 36.0-Ω resistor and an 18.0-Ω resistor are connected in series across a 15.0-V battery. What is the voltage across (a) the 36.0-Ω resistor and (b) the 18.0-Ω resistor?

67.
A new "D" battery has an emf of 1.5 V. When a wire of negligible resistance is connected between the terminals of the battery, a current of 28 A is produced. Find the internal resistance of the battery.

75.
Two batteries, each with an internal resistance of 0.015 Ω, are connected as in the drawing. In effect, the 9.0-V battery is being used to charge the 8.0-V battery. What is the current in the circuit?

83.
A galvanometer with a coil resistance of 12.0 Ω and a full-scale current of 0.15 mA is used with a shunt resistor to make an ammeter. The ammeter registers a maximum current of 4.00 mA. Find the equivalent resistance of the ammeter.

87.
Determine the equivalent capacitance between A and B for the group of capacitors in the drawing.

95.
The circuit in the drawing contains two resistors and two capacitors that are connected to a battery via a switch. When the switch is closed, the capacitors begin to charge up. What is the time constant for the charging process?

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(See attached file for full problem description and diagrams)

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