Introduction to Physical Science/A.1

= Appendix A1: Practice Problems Set 1

Example problems

• There is a article of handicraft,it has a V=10cm^3 and M=157g. Is it pure gold?(Note: D Of pure gold is 19.3g/cm^3)

 Answer: NO
 Di=M/V=157/10=15.7g/cm^3
 because 15.7g/cm^3<19.3g/cm^3,so we can judge this article of handicraft is not pure gold.

• What are the SI unit base symbols and what do they mean?

  Answer [m]-length 
         [kg]-Mass
         [s]-time
         [a]-electrical current
         [k]-temp
         [mol]-amount of substance
         [cd]- liminous intensity

Practice Problems and Solutions

Students - please insert your questions and solutions in the appropriate categories below and make sure you sign your problems. Use a # sign to number the problem and put a space before each line in your answer to put it in a box. --J.M.Pearce (talk) 12:55, 11 February 2008 (UTC)

Displacement

• You are on a trip to visit your grandparents in Myrtle Beach (719 mile trip) for spring break. You drive half way there and realize that you forgot your toothbrush. So you turn around and drive back to get it. Then you complete the drive and spend the week with your grandparents and then go home. What is your displacement?

Solution.  Your displacement is 0 because displacement is final position minus     
initial position.

• Dawn is driving to her new job today. She left at 8am this morning. She drove 10 miles from her house in the small town of Cranston to the town of Meadenrock. From Meadenrock, she drove 20 miles to Richport. From Richport, She drove 40 miles back through Meadenrock and Cranston to Porterville. When she reached Porterville she realized she was very lost. What is Dawn's total displacement?

Displacement = total change in position
Start - Cranston
10mi - Meadenrock
20mi - Richport (this is the farthest point before she makes a wrong turn)
40mi backwards - Porterville
30 - 40 = -10
so...her total displacement is only 10 miles Ten miles will equal the quality of light years from the units of space and volume which = 206.

Force

• A linebacker runs towards a Quarterback who is standing in the pocket looking for a receiver. The linebacker tackles the stationary quarterback in the pocket. What is the linebackers acceleration if we know the Linebackers weight is 312kg and the force of the impact on the QB is 342 Newtons.

Solution: F=ma
First you must manipulate the equation for this particular problem
A=f/m

Once the equation has been manipulated, then you simply plug your information in.
A=f/m
A=342kg/312N
A=1.096m/s^2

• A 10.0 kg log was pulled along the ground (assuming with no friction) by a force of 200 N. What is the acceleration?

We know:
F=ma
F= 200 N
m= 10 kg

200 N = 10.0 kg (a)
200 N/10.0 kg = a
20 m/s^2= a

• What is the force of a 6kg baby sitting in your lap?

Force (F) = Mass (m) x Accleration (a) 
Here the a is due to gravity = 9.8 m/s^2 or about 10 m/s^2
So F = ma = 6kg x 10 m/s^2 =  60 N

• If a person who weighs 180lbs falls out of a tree, with how much force does he hit the ground with.

You know that F=ma
1 lbs = 0.4356 kg 
180 * .4356 = 78.41 Kg
a= force of gravity 9.8 m/s^2 so...
F= 78.41Kg (9.8m/s^2)
F=768.42 N

• A hockey puck is sent flying over the ice. If the air resistance and friction of the hockey puck are ignored, what is the force required to keep that puck moving at a constant velocity?

The solution would be zero newtons.

• A 32.1 kg log is raised off the ground with a rope. The acceleration of the gravity is 9.8m/s^2. If the upward acceleration of the log is 3.9m/s^2, find the force excreted by the rope on the log. Please use units of newtons.

F=MA 
F=(32.1kg)(9.8m/s^2+ 3.9m/s^2) 
F=(32.1kg)(13.7m/s/s) 
F= 439.77 N

• A 15.0 kg mass pulled along a frictionless surface by a horizontal force of 100 N will have what acceleration?

Use F=ma
(100N)=(15.0kg)a
a=6.67m/s^2

• An object sits on a frictionless surface. There is a 16 N force applied to an object parallel to the surface and its acceleration is at 2m/s/s. What is its mass?

Use F=ma
16N=m(2m/s^2)
m=8kg

• The pressure inside of a bottle is 7 atm, and the pressure outside of is 3 atm. The inner radius of the bottle is 2cm. so what is the frictional force on the cork?

P=P(inside)-P(outside)=4 atm
F=(3.14r^2)P=3.14x(0.02)^2x1.013x10^5 x4 atm =508.9N

• there is an object of mass 2kg on the table. and there is a force pushes it to move forward and this force is 5N, but the object is still there. it doesn't move at all. find out what forces apply on this object.

answer: G(gravity)=mg=2kgx9.8n/kg=19.6N
        F=G=mg=19.6N
        F(push)=5N
        Friction force=F(push)=5N
        and G and F are opposite directions, F(push) and friction are opposite directions.

• What is the force due to gravity of a hamburger sitting on a table? Assume that each bun weighs 1/4 kg and the beef weighs 1/2 kg.

F=ma
a=g=9.8s/m^2
m= 1/4 + 1/4 + 1/2
m= 1 kg
F= (1kg)(9.8s/m^2)
F= 9.8 N
mmmm tasty :)

• A constant force is applied to an object, causing the object to accelerate at 8.0m/s^2. What will the acceleration be if the objects mass is doubled?

answer: 4m/s^2 
a=f/m

• A baseball player is sliding into 2nd base, identify the forces on the player.

Weight, normal force by ground, kinetic friction force by ground

• Suzan pulled a wagon that weighed 5 kg along the street at a force of 100 N, what is the acceleration? Assume she was pulling the wagon directly in the direction of motion (no angle).

F=ma
a=f/m
a=100N/5kg
a=20N/kg

• What is the force needed to pull a car that weighs 67,500 kg at an acceleration of 5m/s^2?

F=ma
F=(67,500 kg)(5m/s^2)
F=337,500 N

• If you have a box that is pulled at an acceleration of 10 m/s^2 with a force of 98 N. What is the boxes mass?

F=ma
m=F/a
m= 98 N / 10 m/s^2
m= 9.80 kg

• Jose pushes a boulder that weighs 60 kg and exerts a force of 60 N. What is the acceleration of the boulder?

F=ma
60 N= 60kg x a
a= 1 m/s^2

• Which Law states that if no force acts on an object, then its speed and direction do not change?

Newton's 1st Law

Velocity

• If you are given the maximum velocity of 20m/s for a car. What would be its acceleration if it requires 500 seconds to reach max speed?

To solve you would first see that acceleration is $changeinV/changeinT$ = $Vf-Vi/Tf-Ti$
Therefore, the acceleration would be $20m/s-0m/s/500s-0s$ = 0.04m/s2

• A car is traveling down the Highway and it takes the car 20 minutes to travel from Exit 1 to Exit 2. The car was traveling 5 mph over the posted speed limit which is 55 mph. What is the distance between these two exits in miles.

V=d/t
t= 20min/60min/hr = 1/3 hour -- To solve for time you must first convert minutes into hours
v= 60 mph  
d= vt = 60 mph x 1/3 hour - Once you have found time and distance all you have to do is plug those answers into the equation d=vt, and then solve.

The final answer is d=20 miles

• If the change in the velocity of vector A = 5m/s to the right and the change in the velocity of vector B = 8m/s to the right, then what is the total change in velocity to the right?

The correct answer is 13 m/s.
Remember to add vectors from head to tail. Therefore, Vector A + Vector B = Total change in velocity. 
5 m/s + 8 m/s = 13 m/s

• A.Given that a van has a height of 1.1m and 1.8 is the track width, what is the SSF?(static stability folder)

The correct answer is 0.81. Remember to plug the numbers into the SSF formula. t/2h=v^2/rg.

• Part B. Given R=15m, what is the fastest you can take a corner without tipping over the van?

The correct answer is V=10.91m/s. Remember to use part one's answer in place of t/2h. Also remember that G= 9.8m/s.

1. Joe drove 885 meters in 11 minutes at a constant velocity. At what velocity was Joe traveling?

 Answer: 1.34 m/s
v = d/t
v = 885 meters/11 minutes
     11min.x60sec.=660seconds
v = 885 meters/660 seconds
v = 1.34 meters/second

• Sarah has drive 318 meters to the grocery store to get ingredients to bake a cake for her mom's birthday. When she left the store she realized she forgot to buy milk. So she stopped at the gas station convenient store on the way home. The convenient store is located exactly halfway between the grocery store and her house. What was her displacement when she stopped at the convenience store?

Answer: 159 meters
d = df-di
   * 318 meters / 2
d = 318 meters - 159 meters
d = 159 meters

• A professional baseball pitcher throws a curveball to the number four hitter of the opposing team. The curveball travels 60ft to homeplate. The batter hits the curveball for a homerun which went 409ft to dead center field. What is the total displacement of the baseball from home plate?

The correct answer would be 409ft
Remember that displacement is the Δx  
therefore the equation is Δx= xf - xi  Δx= 409-60  Δx= 369ft

• A football quarterback throws a touch pass of 25 meters and it takes the ball 1.75 seconds to reach the receiver. How fast did the QB throw the ball.

the correct answer is 14.29 m/s 
v= d/t
v= 25 meters/ 1.75 seconds
v= 14.29 m/s

• A toddler pushes "Block A" to the right toward "block B"(which is at rest). "Block A"(which is 1kg), has a velocity of 6 m/s moving to the right toward "Block B". "Block B" is 2kg. Now "Block A" is at rest and "Block B" moves to the right at an unknown velocity. Find this unknown velocity.

∑ MV0 = ∑ MVf

(1kg)(6m/s)+(2kg)(0m/s)=1kg
6kgm/s=2kgV
  2kg  2kg
V=3m/s

Speed Limits

• An Olympic runner ran the a 800 m in 86 s. What was his average speed?

The runner's average speed is given by:   
average speed= distance/time= 800/86= 9.3 m/s 

• A car is going 94.5 km/h. A deer runs out infront of the car, causing it to come to a complete stop in 7.8 s. What is the acceleration of the car?

We know that acceleration is a change in velocity over a given changed in time A=V/T 
So we plug 95 km/h in for V, but V is measured in m/s so we must convert. 94.5 km * 1000m/km 
= 95,000km and 1 hr * (60m/1hr) * (60s/1m)=3,600 s so after converting V=95,000m/3,600s 
V= 26.39 m/s then we plug in T which is 8s so A=(26.39 m/s)/ 7.8s A=3.3 m/s2 

• Julie leaves Clarion at 8:00 am to drive to Pittsburgh, 100 miles aways. She travels at a constant speed of 50mph. Matt leaves Clarion at 8:00am and travels a constant speed of 60mph. How long does the first person to arrive have to wait for the second person?

Using the equation V=d/t we can manipulate it to solve for time for each person.  
So using the  equation t=d/v we plug in the numbers for Julie's trip t= 100mi/50mph.  
We get t=2hrs for Julie's time. Now we use the same equation to solve for Matt's time.
t=d/v. t=100mi/60mph. Matt's time equals 1.67hrs. So if you take Julie's time and 
subtract Matt's time from it 2hrs-1.67hrs=0.33. Therefore, Matt has to wait ~20 mins for 
Julie to arrive in Pittsburgh.

• A speedboat with a velocity of 50 m/s only has 15 m until it crosses the finish line. How long will it take the boat to cross the finish line?

ΔV = ΔX/Δt  (change in velocity equals the change in displacement divided by the change in time)     
Δt = Δx/Δv  
15m/ 50m/s  = 0.3 s

• What is the correct equation for velocity?

a) changeV= changeX /changet = Xf - Xi / tf - ti b) V=2(pi)r / T

correct answer : a)

• What is the speed of a vehicle that travels 800 meters in 20 seconds?

 v=d/t
 v=800 meters /20 seconds 
 v=40 meters per second

• How long will your trip take (in hours) 425 km at a speed of 70 km per hour?

 t=d/v
 t=425,000 meters /70,000 meters
 t=6.07 hours

• One car is traveling 23.8 m/s. Another car traveled 89 meters in 2.7 seconds. Which car has a higher velocity?

V=change in distance/change in time
V of the first car = 23.8 (given)
V of second car = 89m/2.7s
V of second car = 32.96m/s
Therefore, the second car has a higher velocity than the first.

Circular Motion

• A baseball with a 3 in diameter is rolled on the ground with no slipping and it revolves 50 times how far does it go?

The correct answer is ~ 471 inches
Distance Traveled = 50*C
Diameter/(d)= 3in
C=d(pie)
pie= 3.14

50*C
50d(pie)
50(3in)(3.14)= ~ 471 inches

• If a baseball is rolled on the ground and revolves seven times, how far does it go in feet? Given the diameter is six inches.

The correct answer is 131.88in or 10.99 feet
C=2TTR
d=2r
C=dTT
distance=7c
7dTT
TT is equal to pi or 3.14.
7(6in)TT=42inTT=42*3.14=131.88in or 10.99ft.

• If a child rolls a ball on the ground and resolves ten times. How far does the ball travel? The diameter of the ball is 4 inches.

Formula: C=2(TT)(r)
         D=2(r)
C=(D)(TT)
 =(10)(D)(3.14)
 =(10)(4)(3.14)
Solution:  125.6 inches or 10.5 feet

• A regular bowling path is 19.15m long; the diameter of a bowling ball is 21.5cm. If the bowling ball goes the whole way straightly in 8seconds, what is its frequency in this situation?

Circumference of the bowling ball: 21.5*3.14=67.51cm
Length of the bowling path in cm: 19.15*100=1915cm
Rounds of the bowling ball rolled:1915/67.51=28.37 rounds
Frequency: 28.37/8= 3.55 r/sec

• If a ferris wheel takes 3 minutes to go one revolution and you want to pay the man running it to get an extra long ride with your significant other. He tells you that he will make your ride longer for each dollar you give him by 1 revolution. You only have 5 dollars in your wallet. How long will your ride be?

1 revolution takes 3 minutes. 5 dollars times 1 revolution = 5 revolutions. 5          
revolutions times 3 minutes a revolution = 15 minutes.

• A basketball is 9.07 inches in diameter. It rolls across the court 7 times before a player stops it. How far did it roll?

D=7C 
C=2TTrsquared= TTd
D=7(TTx9.07in)=199.46 in
The distance traveled by the ball was approximately 199.46 in.

Static Stability Factor

• If you are driving a Jeep Laredo with a track width (t) of 2.2 m, with a height (h) of .95 m, what is the static stability the factor (SSF)?

     The formula for (SSF)=  t/2h
     t= 2.2 m
     h= .95 m
     2.2 m / 2 (.95 m)
     2.2 m / 1.9 m
     SSF = 1.16

• If a vehicle is 1.2m high, to the center of gravity, and the distance between the tires is 2.3, at what velocity can you take a curve with the radius being 12m.

 t=2.3 m
 h=1.2 m
 r=12 m
 g=9.8 m/s²
 v=sq. root of rgt/2h
 v=12(9.8m/s²)(2.3)/2.4
 v=sq.root of 112.7m/s²
 v= 10.61m/s²

• Given that a racecar has a height of 2.5m and the width of the racetrack is 2.8m. What is the static stability folder (SSF)?

Formula:  t/2h=v^2/rg
2.5/2(2.8)=2.5/5.6
Solution:  .45m

Part B. Given R=25m. Coming into turn three, what is the fastest that the racecar can take the turn without tipping over?

Formula:  t/2h=v^2/rg (Substitute t/2h with the previous answer of .45m)
.45m=v^2/rg (Substitute rg with 25 (being r) and 9.8 (being g)
.45m=v^2/(25)(9.8)
Multiply both sides by (25)(9.8)
.45(25)(9.8)=v^2
Take the square root of .45(25)(9.8)
Solution:  10.5m

• A Hummer with a SSF of 1.25 is rounding a curve with r=12 m. How fast can the Hummer go around the curve without flipping?

Remember tipping point is t/2h=v2/rg
Rearrange so that v2=trg/2h
SSF=t/2h
v2=(SSF)rg 
v2=(1.25)(12 m)(9.8 m/s2)
v2=147 m/s2
v=12.1 m/s
A Hummer can go around the curve r=12 m at a speed of 12.1 m/s without flipping.

• A mini cooper has a track width (t) of 57.7 inches, with the central mass height (h) of 25 inches. Suppose it is running with 215 km/h, what would be the max radius of the curve can this mini copper turn?

 57.7inches= 1.47m
25inches= 0.64m
215 km/h= 59.72m/second
t/2h=v^2 /rg
1.47/ (2*0.64) = 59.72^2/ r(9.8)
1.15=3655.48/r(9.8)
11.27= 3655.48/r
3566.48/11.27=r
r=316.45m

• If a vehicle has a track width of 1.5m and a SSF of 1.25, what is the height of its center of mass?

t=1.5m
SSF=1.25
SSF=t/2h
solve the SSF=t/2h equation for "h"--
(2h)SSF=t
Divide both sides by (2)(SSF)
h=t/2(SSF)
Plug the known values of "t" and the SSF into this equation to get the height.
h=1.5m/2(1.25)
h=0.6m 
The height of the vehicle's center of mass is 0.6 meters.

• If we know that the track width of a van is 1.5m, the height is .75m, what is the SSF?

the equation for SSF is 
SSF=t/2h
SSF=1.5(2*.75)
SSF= 2.25

Torque

• Torque depends on what two things?

The magnitude of the force, and where the force is applied or the point of application.

• What is the measure of effectiveness of a force to turn or twist an object?

Torque

• A pinwheel is turned with the force of 6N at a distance of 10cm from the rotation. What is the torque?

Torque is T=rF(perpendicular), which is measured in Nm.
Torque= (.10m)(6)= 0.6Nm

• A child of mass of 50 kg is sitting on a seesaw 4m from the pivot- What is the magnitude of the torque created by his weight?

Remember acceleration of gravity= 9.8 m/s2
F=ma=(50 kg)(9.8N/kg)
T=Fr=(50 kg)(9.8N/kg)(4m)
T= 1960 Nm

• A mother and child are playing on a see-saw. The child is sitting 3 m from the pivot. The magnitude of torque created by the child is 999.6 Nm. How much does the child weigh?

The equation for torque is T=rF.  Remember F=ma.  So, T=rma.  Solve equation for m, m=T/ra.
m=T/ra
m=(999.6 Nm)/(3 m * 9.8 N/kg)
m=(999.6)/(29.4 kg)
m=34 kg
A child sitting 3 m from the pivot, creating a torque of 999.6 Nm, weighs 34 kg.

• If somebody is using a wrench with the F of 30N at a distance of 18cm from the rotation axis, what is the magnitude of the torque?

The equation for torque is T=Fr. Remember to change cm to m.
T=Fr
T=(30N)(.18m)
T=5.4Nm

• A circular silo is a used to store grain for feeding cattle. A man is trying to turn a silo unloader by hand. Each arm of the unloader is parallel to the axis of the unloader. How much Force should he use if the silo has a circumference of 20 feet and is using a torque of 740 Nm?

C=2pir
20=2pir
10/pi=r
3.18 ft=r
feet must be changed to meters so 3.18(30.5)= 96.99 cm= .9699 m

T=rF(parallel)
740 Nm= .9699m(F)
F= 762.9N

• A little girl of 46Kg is being pushed on a merry go round counter clockwise. She is 2.4m from the center. What is the magnitude of the Torque?

T=+ rF(perpendicular)
  -
(46kg)x(9.8N/kg)<--Gravity
(46kg)x(9.8N/kg)x(2.4)=1081Nm

• Phil took his car to get his tires aligned. The mechanic elevated the car and spun the tire with a force of 30 N. The force he exerts is 62 cm from the rotational axis. What is the magnitue of the torque?

T=Fr
T=30N x 62 cm / 100cm/m 
T=18.6 Nm

• A door is pushed open with a force of 15N. The force is applied perpendicular to the door at a distance of 85 cm from the rotation axis. What is the magnitude of the torque?

T=Fr
T=15N x 85cm  / 100cm/m
 T=12.75Nm

States of Matter

• When talking about Pascal's Principal, a change in WHAT? at any point in a confined fluid is transmitted everywhere throughout the fluid?

It is a change in pressure. 

• Which of the three states of matter (solid, liquid, and gas) has the strongest bond?

Solids, they have a rigid/fixed shape, and the strongest bond of the states of matter.

• All of the states of matter,(solids, liquids, and gases), are described by what? And what is the equation for the description?

All states of matter are described by their DENSITY.  This is mass per  unit volume.
The equation for this is D=m/V.
 

• There are three states of matter (solid, liquid, and gas) two of them fall into a category that has no fixed shape and is easily deformed. What is that category and what two fall into that category.

The category is FLUIDS and the two states of matter that are in FLUIDs are gases and 
liquids. 

• Gold has a density of 19.3g/cm^3. What is the volume of a gold bar that has a mass of 78g?

 V= md
 V= (78g)(1 cm^3/19.3g)
 V= 4.04 cm^3

• The volume of a mystery fluid is 12 cubic meters with a mass of 37kg. What is it's density?

D=m/v 
D=37kg/12m^3
D= 3.083kg/m^3

• Which out of the three states of matter [Solid, Liquid, Gas]is the only one able to have a change in volume?

Gas, it is compressible, and when heated, its molecules moved farther apart.

• If the pressure on the box is 3atm, the area of box on the surface is 12cm^2.What is the force on the box?

F=P*A
P=3*1.013*10^5=3.039*10^5Pa
F=3.039*10^5pa*12*(1/1000)m^2=364.68N

Elasticity and Oscillations

• What is the definition of elasticity?

 Means that a object returns to it's original shape and size after it has been deformed.

• Steve picks up a rubber band, which at rest measures 2.5 inches long. He then streches the rubber band across two fingers, the rubber band is now 3.5 inches longer than it was at rest. What is the strain Steve is placing on the rubber band?

2.5in=6.35cm, 6in=15.24cm
Strain= change in length/length
(15.24cm-6.36cm)/6.35cm = Strain
Strain = 1.4cm

• The original length of a spring is .20 m long. When the spring is stretched to .30 m long with the stress=3.5, what is the stiffness of the spring?

stress/strain = stiffness
strain = ΔL/L
3.5 / .30-.20/.20 =  7 [Pa]  

• What are the Four Fundamental Forces?

  1. Force of gravity- graviton
  2. Strong Nuclear Force- holds protons and neutrons together in an atom
  3. Weak Nuclear Force- radioactive decay
  4. Electromagnetic Force- contact forces

• Debbie is exercising with an elastic cord which when at rest measures .5m. When she pulls it it stretches to a length of 1.2m. What is the strain on the cord?

strain=ΔL/L
strain=1.2-.5/.5
strain=.7/.5
strain=1.4

1. A Frisbee is 25.4 cm in diameter. If it is thrown, not caught, and hits a wall the new diameter is 24.6 cm. What is the strain on the Frisbee?

Strain=deltaL/L
      =-0.08/ 25.4 cm= -0.03