Web or In-Class Exercises

This is a collection of exercises to be carried out on the web or on the classroom computers. Their intent is to show you a range of numerical answers associated with different physical phenomena; these are the type of calculations which are carried out in the problem-solving type physics courses. In the case of these exercises, the actual calculations are done by the computer but it is hoped that the exercises will help you become accustomed to the computer as a tool and a source of information.

Note about entering numbers in calculations: When you enter a number in one of the calculations in HyperPhysics, you then just click anywhere outside the box to make sure the transaction is complete and the number is taken. If you need to edit the number, it is usually easiest to just double-click in the data entry box. That will turn the field dark, and any number you type will replace the previous number.
 
 

Exercise 1: Vertical Motion

The items which you can change are in the boxes (launch speed and time). You can calculate the height and speed at any time, and the peak height associated with your chosen launch velocity is displayed.

1. If you toss a ball upward at a speed of 30 m/s, its maximum height will be  _________ meters.
2. For a ball tossed at 30 m/s, the speed after 1 second will be _________ m/s and its height at that time will be __________ meters.
3. After 2 seconds the speed will be __________ m/s and the height ________ m.
4. After 3 seconds the speed will be __________ m/s and the height ________ m.
5. After 5 seconds the speed will be __________ m/s and the height ________ m.
6. After 6 seconds the speed will be __________ m/s and the height ________ m.
 

Exercise 2: Trajectory
The intent of this exercise is to calculate a baseball trajectory by determining the height of the ball at different distances. The scenario is that of a baseball hit at an angle of 45° and a speed of 100 miles/hr (44.7 m/s). The fence is 12 ft (3.7m) high and is200 meters away from home plate. Your task is to plot the trajectory of the baseball at 20 meter intervals, assuming that it was hit at a height of 1 meter, and determine whether it clears the fence.
 
 

Exercise 3: Weight Calculation
 

1. The weight of a 1 kilogram object is _____ newtons = __________ pounds.

2. If an object weighs 50 lbs on the surface of the Earth, its mass is _______kg.

3. If a persons weight is 150 lbs, in metric units it would be ______newtons.

4. The mass unit of the U.S. common sytem is the slug. If an object has a mass of one slug, then it will have a mass of _______kg and would weight ______ lbs.
 
 

Exercise 4: Impulse of Force
 

1. If a mass of 1 kg were traveling at 10 m/s and were brought to rest in 1 second, the average force necessary would be __________ N.

2. If the same mass under the same conditions were brought to rest in one one-hundredth of a sec  (0.01s) the average force necessary would be _______N.

3. If a 0.15 kg baseball traveling toward you at 30 m/s were stopped by your glove in 0.1 s, the average force on your hand would be ________ N.

4. If a 0.15 kg baseball traveling toward you at 30 m/s were struck by your bat and sent outward at 30 m/s in a collision which lasted 0.01 s, the average force on the ball would  be _________ N.  But if you stuck your bat out to bunt the ball and just stopped it in 0.01 s, the force on the ball would be only ______N.
 
 
 
 

Exercise 5: Centripetal force and centripetal acceleration

1. If you were swinging a 0.5 kg mass around your head on a string in a circle of radius 0.5 meters at a speed of 5 m/s, the required tension in the string would be ________N.

2. If you doubled the speed to 10 m/s, the tension would be _______ N.

3. If at a speed of 5 m/s you pulled the string in to a 0.25 m radius,
the tension would be _________ N.

4. On a flat curve of radius 500 m, a 1000 kg car tries to make the curve at 25 m/s (about 56 mi/hr). If the maximum friction force is 80% of the car's weight, can it make the curve? At what maximum speed can it make the curve? (Hint: first calculate the weight of the car.)
 

Exercise 6: Orbit velocity and weight in orbit

1. In an orbit 200 kilometers above the surface of the Earth, the orbit velocity is about ________ mi/hr, and the time to orbit the Earth is about  ______ min.  At that altitude, the force of gravity has fallen to about _______ times the force at the surface of the Earth.

2. To create a geosynchronous satellite (one which stays above the same point on the Earth for communication purposes), you would have to put it out at about _________ x the radius of the Earth. (Hint: If it stays above your head all the time, what is its orbital period?)

3. The 24 satellites of the Global Positioning Service are in orbits about 11000 miles above the Earth (17.7 x 106 meters). These satellites circle the Earth in aobut ________ hours.

4. Joe weighs 220 lb and would like to get down to 200 lb. How high above the Earth would he have to go to decrease his weight by 10%?
 

Exercise 7: Force of the atmosphere

1. The force of normal atmospheric pressure on one square foot of the Earth's surface is ____________ pounds.

2. The force of 1 atmosphere pressure on the top of a car which is 4ft x 4ft is _______ pounds. Why does it not crush the car?

3. The force of 1 atmosphere of pressure on the roof of a house which measures 60ft by 30 ft is ______________ pounds.

4. If a passing tornado lowers the outside air pressure to 13.7 lb/in2 while the pressure inside the above house remains at 1 atmos, what will be the net upward force on the roof of the house? (Hint calculate the force with 1 atmos and then with 13.7 lb/in2 and take the difference.)
 
 
 
 

Exercise 8: Forces in a car crash.

1. If a 3200 lb car traveling at 30 mi/hr strikes the tree and stops in a distance of 1 foot, the average impact force on the car would be  ______ tons.

2. If the car above were built more sturdily so that it stopped in 0.5 feet, the average impact force on the car would be ______ tons.

3. The average force on a 160 lb driver who was stopped with the car in part 1 above in a distance of 1 foot, the force on the driver would be _______ tons. (Hint: Put in 160 lb in the box labeled Weight of Car - it works on any weight.)

4. If the 160 lb driver, traveling at 30 mi/hr, had no seatbelt on so that he was stopped by the steering column and windshield in a distance of 0.2 feet, the average force on the driver would be ________ tons.
 
 
 

Exercise 9: Temperature scales
 

If you double-click on any of the closed boxes and change the number, then clicking outside the box will calculate the equivalent temperatures in the other scales.

1. The temperature of this room has typically been 21°C lately. That is ______°F

2. Standard body temperature is 98.6°F. That is _______°C.

3. The temperature of liquid nitrogen is 77K. That is _______°F.

4. Absolute zero  (0 K) is equal to  __________°C   and ________°F.

5. There is a temperature at  which the Celsius temperature is equal to the Fahrenheit temperature. At that temperature   ________°C = ________°F.   (Hint: Find it by plugging in different numbers and changing them until the temperatures approach each other.)
 
 
 

Exercise 10: Heat and specific heat.
 
 

1. If in the lab you heated 400 grams of copper from 20°C to 95°C, and the specific heat of copper is 0.092 cal/gm°C, the heat required is Q =  _______cal.

2. If you put that amount of heat into 100 grams of water at 20°C, it will raise its temperature by _________°C.

3. If you heat 100 grams of water from 20°C to  21°C, the heat required is Q=_______ calories.
 
 

Exercise 11: The Ideal Gas Law
 

Set the initial and final volumes to 1 liter, and the initial and final pressures to 1 atmosphere.

1. If the initial temperature is 0°C and the final temperature is 20°C, then in absolute temperature the initial and final values will be  _____K  and   _____K.

2. If the pressure is constant at 1 atmos, you start with 1 liter and you increase the temperature from 0 to 20°C, the final volume will be ______liters.

3. If both initial and final temperatures are 0°C, initial volume 1 liter, initial pressure 1 atmosphere, then the increase of pressure from 1 to 2 atmospheres will result in a final volume of _______ liters.

4. If you keep the volume of gas at 1 liter and start with  1 atmosphere of pressure at 0°C, a temperature of  _____K  =  ______°C  will be required to raise the pressure to 2 atmospheres.
 
 

Exercise 12: Maximum efficiency allowed by the Second Law of Thermodynamics: the Carnot cycle.
 

1. If a coal-fired power plant operated at a temperature of 650 K and exhausted its waste heat at 300 K,  then its maximum efficiency would be ________%.

2. If you operated near the softening point of the steel reactor vessel at 850K, the ideal efficiency is increased to _______%.

3. If an ocean thermal generator makes use of the fact that surface seawater is at about 300 k and deeper water is at about 290 K, the maximum efficiency of the generator would be ________%.

4. If exhaust fumes from your car are at 310 K, and the environment is at 300 K, then you could judge the maximum efficiency of any energy reclamation project for the energy in the exhaust would be at most   ________% efficient.
(Hint: The higher temperature is considered to be the source of the energy and the lower temperature is the temperature of the cold reservoir in the heat engine model.)
 

Exercise 13: Electric circuits
 

1. If 120 volts is applied to a 60 ohm resistor, the current will be _______ amps.

2. In order to double the current, the resistance will have to be changed to ____ ohms.

3. To get 5 amperes of current to flow through an 8 ohm loudspeaker coil, you will have to apply ________ volts.

4. If you have 0.1 ohms of resistance at your car's battery terminals because of accumulated corrosion and your car's starter causes a current of 85 amperes to flow, how much of the 12 volt battery's voltage is dropping across the corrosion at the terminal?  (Hint: The 0.1 ohms is in series with the starter motor, and any voltage drop across that resistance is subtracted from the voltage applied to the starter.)
 
 
 
 
 
 

Exercise 14: Electric power.
 

Assume standard household AC voltage of 120 volts in the following:

1. The amount of power which can be obtained from a household circuit which has a 20 ampere breaker is _________ watts.

2. If you want to limit the power to your stereo amplifier to 500 watts, you should put in a fuse to limit the current  to _______ amperes.

3. Using 15 ampere fuses in your house will limit the power from each circuit to ________ watts.

4. If you wanted to supply 40 watts of power to a toy train which operated off a 6 volt transformer, the required current would be  _________ amps.
 
 
 
 
 

Exercise 15: Series and Parallel Circuits
 

Assume 120 volts supply in the following

1. If you placed a 10 ohm resistance in series with a 40 ohm resistor, the voltage across the 10 ohm resistor would be  ________ volts. But if you put it in parallel with the 40 ohms, the voltage would be _______ volts.

2. A pair of 40 ohm resistors is placed in parallel where they draw ______ amps of current from the power supply. If they are placed in series they will draw only ______ amps.

3. A 40 ohms resistor by itself will draw _______ amps of current from the 120 volt supply. If you put a 2 ohm resistor in series with it the total current will be _______ amps. If you put a 2 ohm resistor in parallel with it the total current will be _______ amps.
 
 

Exercise 16: Wave calculation

1. What is the wavelength in meters of the electromagnetic carrier wave transmitted by the radio station WSB AM at 750 kHz? 1 kHz =10³ Hz and the speed of light is 3 x 10⁸ m/s.

2. What is the wavelength in meters of the electromagnetic carrier wave transmitted by GSU's WRAS at 88.5 MHz ? 1 MHz = 10⁶ Hz

3. If a sound is produced at the orchestra standard frequency of 440 Hz, at a temperature where the speed of sound is 345 m/s, what is the wavelength of the sound produced?

4. If the limits of human hearing are 20 Hz to 20,000 Hz, what are the sound wavelengths associated with these extremes. You may use 345 m/s for the speed of sound.
 
 
 

Exercise 17: Open air column resonance
1. If a flute constitutes an open air column, how long must the air column be if it is to produce a frequency at middle-C, 261 Hz?
 

2. An open-ended organ pipe is to be constructed to sound the note A= 55 Hz, one octave above the bottom note on the piano. How long must the air column be?
 
 

Exercise 18: Closed air column resonance

1. A clarinet acts as a closed-ended air column. If its bottom note has a frequency of 130 Hz, how long is the column?

2. The ear canal responds most strongly to frequencies around 3700 Hz because that is the lowest resonant frequency of the canal. If the canal acts like a closed-ended cylinder, how long is the ear canal?

3. If the top resonance of the water tube resonance unit is at a column length of 8 cm when a tuning fork of frequency 1024 Hz , what is the corresponding speed of sound?
 

Exercise 19: Formation of real images
1. If a camera lens has a focal length of f = 5 cm, at what image distance from the lens must the film be placed to form an image of an object which is 500 cm from the lens?

2. If the object is moved closer to the camera lens ( to 100 cm) what is the distance to the film from the lens?

3. If you want to take a picture of a flower at only 20 cm from the lens, what lens-to-film image distance would be required? (This probably would require and extension tube).

4. In a slide projector the slide is placed very close to the focal length of the lens. If you want to project an image 5 meters away from a f=5cm slide projector lens, where would you have to put the slide (object distance)?
 

Exercise 20: Formation of virtual images

1. If you are looking through a divergine lens of focal length f = -20 cm at an object which is 40 cm away from the lens, at what distance from the lens would the image appear to be?
 

Exercise 21: More virtual images

If the object distance is smaller than the focal length of  a magnifying lens, then the image will be virtual, on the same side of the lens as the object and further away.

1. If you use a magnifier of focal length f=10 cm to look at an object which is at 5 cm from the lens, where will the image appear to be? What will be the magnification?

2. If you put the object closer to the focal length, at 9 cm from the lens, where will the image be and what is its magnification?

Exercise 22: Atomic Spectra
Radiation of all the types in the electromagnetic spectrum can come from the atoms of different elements. A rough classification of some of the types of radiation by wavelength is:
Infrared   > 750 nm
Visible   400 - 750 nm
Ultraviolet   10-400 nm
Xrays   < 10 nm
(An approximate classification of spectral colors: Violet (380-435nm), Blue(435-500 nm), Cyan (500-520 nm), Green (520-565 nm), Yellow (565- 590 nm), Orange (590-625 nm), Red (625-740 nm).
1. If the electron in a hydrogen atom (Z=1) makes a transition from n=2 to n=1, the wavelength of the radiation will be  _______ nm, which is in the __________ part of the electromagnetic spectrum.
2. If the electron in a hydrogen atom (Z=1) makes a transition from n=3 to n=2, the wavelength of the radiation will be  _______ nm, which is in the __________ part of the electromagnetic spectrum.
1. If the electron in a hydrogen atom (Z=1) makes a transition from n=4 to n=3, the wavelength of the radiation will be  _______ nm, which is in the __________ part of the electromagnetic spectrum.
1. If the electron in a oxygen atom (Z=8) makes a transition from n=2 to n=1, the wavelength of the radiation will be  _______ nm, which is in the __________ part of the electromagnetic spectrum.

Exercise 23: Radioactive half-life
1. If the half-life of a certain radioisotope is 1 year, what fraction of it will remain after 3 years?  _____________
2. For carbon-14 with a half-life of 5730 years, how long will it take to decay to one-tenth of its original activity? _____________
3. Iodine-131 has a half-life of 8 days. If a given contamination is considered tolerable when it has decayed to one-thousandth (0.001) of its original value, how long would that take? _____________
4. Cesium-137, the most insidious of the contaminants released at Chernobyl, has a half-life of 30 years. If it must reduce to one-thousandth of its initial value, how long would that take? _____________