Assignment 4, solutions

Problem 1:

An ideal battery is connected to a 200 kΩ and a 300 kΩ resistor in series.
A voltmeter is used to measure the voltage across the battery and the 200 kΩ resistor.
Its readings are Vbattery = 6.0 V,  V200kΩ = 2 V.
What is the value is the internal resistance of the voltmeter and what will the voltmeter read if it is used to measure the voltage across the 300 kΩ resistor?

Solution:

Problem 2:

A long straight wire is connected to an ideal battery.  When the room temperature is 20.0 oC, the established temperature of the wire is 22.0 oC.
The wire is disconnected and one-third of it is cut off.  The remaining piece of the wire is then connected to the same battery in the same room.
What is the new established temperature of the wire?
Assume Newton's law of cooling applies, i.e. the rate at which a system transfers heat to its environment is proportional to the temperature difference between the system and its environment.

Solution:

Problem 3:

imageA long cylindrical solenoid of radius R and length L >> R is tightly wound with a single layer of wire.  The number of turns per unit length is N/L.  The wire breaks when the tension in the wire is greater than T.  Find the maximum current the wire can carry before breaking.

Solution:

Problem 4:

imageA hollow ball with a volume V is held in place in a tank under water by a wire under a sloped plank as shown in the figure.  The water density is ρ and average ball density is ρ/5.  The plank makes an angle α with the horizontal, with tan(α) = 1/3.   What is the tension in the wire if the whole system is accelerating horizontally with acceleration a = g/6.

Solution:

Problem 5:

imageA glass is filled to height h0 with a volume of water V0 with density ρ.  A straw with uniform cross sectional area A is used to drink the water by creating a pressure at the top of the straw (Ptop) that is less than atmospheric pressure (PAtm).  The top of the straw is a distance htop above the bottom of the glass.

(a)  Determine the pressure (Ptop) at the top of the straw as a function of the height (h) of the water in the glass so that the velocity of water coming out of the top of the straw remains constant at a value of vtop.
(b)  How much work is done by the person in order to drink all the water in the glass with the constant velocity vtop?
(c)  How much time does it take to drink all the water in the glass with the constant velocity vtop?

Solution: