# Solving for Example Physics Problems

1. Two charges are placed at opposite ends of a meter stick. Approximately where could a third charge be placed so it would be in equilibrium?

2. A 2 C charge and a 8 C charge repel each other with 10 N of force. How much will a 4 C charge and a 4 C charge repel each other when placed the same distance apart?

A. 40 N B. 20 N C. 10 N D. 8 N

5. Consider a 75 W light bulb connected to a 120 V outlet.

a. Find the resistance of the light bulb when lit.

b. The tungsten filament (wire) in the light bulb has a diameter of 1.8x10-5 m2 and a resistivity of 8.2x10-8 W.m at the operating temperature. Find the length of the filament.

6. Find the equivalent resistance of the circuit shown below. (R1 is on the top left, R3 and R4 are on the right side of the square on the same line and R2 is down the middle line.)

R2 =14 W

R1 = 12 W

R4 = 10 W

R3 = 16 W

7. If a current of 80.0 mA exists in a metal wire, how many electrons flow past a given cross section of the wire in 10.0 min? In what direction do the electrons travel with respect to the current?

8. An electric heater carries a current of 13.5 A when operating at a voltage of 1.20 x 10^2 V. What is the resistance of the heater?

9. Nichrome wire of cross-sectional radius 0.791 mm is to be used in winding a heating coil. If the coil must carry a current of 9.25 A when voltage of 1.20 x 10^2 V is applied across its ends, find (a) the required resistance of the coil and (b) the length of wire you must use to wind the coil.

10. Suppose your waffle iron is rated at 1.00 kW when connected to a 1.20 x 10^2 V source. (a) What current does the waffle iron carry? (b) What is its resistance?

11. What minimum of 75-W light bulbs must be connected in parallel to a single 120-V household circuit to trip a 30.0-A circuit breaker?

12. Three 9.0 Ώ resistors are connected in series with a 12-V battery. Find (a) the equivalent resistance of the circuit and (b) the current in each resistor. (c) Repeat for the case in which all three resistors are connected in parallel across the battery.

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#### Solution Preview

Please refer to the attachment.

1. Two charges are placed at opposite ends of a meter stick as shown in the fig.. Approximately where could a third charge be placed so it would be in equilibrium?

F1 F2

q1= -2.5μC q2 = -8.5μC

x Q

1 m

Solution: Let the third charge +Q be placed at a distance x from q1 for it to be at equilibrium.

Then from Coulomb's law magnitude of force on Q due to q1 is given by:

F1 = kq1Q/x2 where k = 1/4Πε0

F1 = k(-2.5x10-6)Q/x2

Taking force acting towards right as +ve and that towards left as -ve, the direction of F1 is negative. Hence,

F1 = - k(-2.5x10-6)Q/x2 ..........(1)

Force on Q due to q2 = F2 = kq2Q/(1 - x)2 = k(-8.5x10-6)Q/(1 - x)2

As F2 acts towards right, it is taken as +ve.

For equilibrium, vector sum of F1 and F2 must be zero. Hence,

- k(-2.5x10-6)Q/x2 + k(-8.5x10-6)Q/(1 - x)2 = 0

+2.5/x2 - 8.5/(1 - x)2 = 0

2.5(1 - x)2 - 8.5x2 = 0

1 + x2 - 2x - 3.4x2 = 0

2.4x2 + 2x - 1 = 0

____________ ______

Solving for x: x = [-2 + √22 - 4(2.4)(-1)]/2(2.4) = [-2 + √4 + 9.6]/4.8

x = (-2 + 3.69)/4.8

Taking + sign: x = 0.352 m

Taking - sign: x = - 1.18 m

As Q must lie between the two charges, x must be +ve, x = 0.352 m is the correct solution.

2. A 2 C charge and a 8 C charge repel each other with 10 N of force. How much will a 4 ...

#### Solution Summary

This solution provides assistance with the physics problems attached.

Solving Physics Questions

1. Give an example of a situation in which there is a force and a non-zero displacement, but the force does no work. Explain why it does no work.

2. What is a conservative force?

3. (a) Calculate the work done on a 1500 kg elevator by its cable to lift it 40.0 m at constant speed, assuming friction averages 100 N. (b) What is the work done on the elevator by gravity in this process? (c) What is the total work done on the elevator?

4. A shopper pushes a grocery cart 20.0 m at constant speed on level ground, against a 35.0 N frictional force. He pushes in a direction 25.0 degrees below the horizontal. (A) What is the work done on the cart by friction? (B) What is the work done on the cart by gravity? (C) What is the work done on the cart by the shopper? (Remember the Work-Kinetic Energy Theorem.) (D) Find the force the shopper exerts, giving both the x- and y-components, and the magnitude of the force. (E) What is the total work done on the cart?

5. Compare the kinetic energy of a 20,000 kg truck moving at 110 km/h with that of an 80.0 kg astronaut in orbit moving at 27,500 km/h.

6. (a) Calculate the force needed to bring a 950 kg car to rest from a speed of 90.0 km/h in a distance of 120 m. Use the work-kinetic energy theorem (b) Suppose instead the car hits a concrete abutment at full speed and is brought to a stop in 2.00 m. Calculate the force exerted on the car and compare it with the force found in part (a).

7. Suppose a bicycle rolls down a hill, starting from rest. It drops an altitude of 4.0 m, ending up on level ground. The mass of the bicyclist plus bike is 70.0 kg. Assume that friction can be ignored. (A) Find the potential energy lost by the bicycle and rider. (B) Find the speed of the bicycle when it reaches level ground. (C) Repeat (B), assuming that this time the bicycle starts with an initial speed of 4.0 m/s. (D) Suppose frictional forces dissipate 400 J of energy while the bike rolls down the hill. Find the speed of the bicycle when it reaches level ground in this case. (Again, assume an initial speed of 4.0 m/s.)

8. A 60.0-kg skier with an initial speed of 12.0 m/s coasts up a 2.5-m-high hill as shown. (A) Find his final speed at the top, assuming no friction is involved. (Use energy methods, not the equations for constant acceleration.) (B) Now suppose the coefficient of friction between skier and snow is 0.08. Again find his speed at the top of the hill. (Don't worry about energy lost on the flat at either end --- just find the energy dissipated by friction on the 35-degree slope and use this in your calculations.)

9. A cart is rolling without friction on a platform, hooked to a hanging mass with a string which runs over a pulley, as shown in the diagram. The mass m_c of the cart is 0.35 kg, and the hanging mass is 0.050 kg. (A) How much work does the force of gravity do on the system when the hanging mass moves from a height of 0.80 m to a height of 0.30 m? (B) Assuming it starts from rest, find the speed of the cart after 0.50 m of travel. Use the information from part (A), and energy considerations. Do not use Newton's laws.

10. Suppose we have a spring whose force as a function of compression is shown in the graph. We place a ball of mass 0.600 kg on top of the spring and compress it by 0.25 m from its relaxed length. We then let the ball go. When the ball is released, its height above the floor is 0.10 m.

(A) Find the spring constant of the spring.

(B) Determine the potential energy of the spring when compressed.

(C) Find the highest point the ball reaches in its flight.

(D) Determine the velocity of the ball just as it leaves the spring: that is, just as the spring is fully relaxed.