103: Physics Lecture 28 Review I
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Physics 103, Spring 2005, U. Wisconsin
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Problem Solving in Physics (Science!?)
Identify the physical significance of the situation The concepts that are present and relevant. Translate the situation described to physics equations Perhaps, the situation is best clarified by a diagram (make one) Analyze the details of the situation to determine which concepts are needed Jot down the numbers (and unit) associated with those given Identify what is asked and what can be easily obtained Choose the appropriate relationship between the concepts. (equation) Obtain the answer Check - does the answer make sense? Check - are the units consistent? Techniques Try to work out the problem as far as possible algebraically You should not complete the arithmetic solution from the outset You SHOULD try the problems out before looking at the choices provided to get maximum benefit.
12/14/05
Physics 103, Spring 2005, U. Wisconsin
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Preflight 1
The decibel intensity level of a jackhammer is 130 dB. Decibel intensity level of two jackhammers operating side by side is: 65 dB 130 dB 133 dB 144 dB
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260 dB
I1
I2 = 2I1
I1 log AB = log A + log B = 10log = 130db 1 I0 2I I = 10log 1 = 10log 1 + 10log2 = 130db + 3db = 133db 2 I0 I0
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Preflight 2
A string on a piano is tuned to produce middle C (f=261.63 Hz) by carefully adjusting the tension in the string. For a fixed wavelength, what is the frequency when this tension is doubled? 130.08 Hz 185.00 Hz 370.00 Hz 446.63 Hz 523.26 Hz
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f =
v
=
1
F F(Tension) Qv = (Linear mass density) f 2 = f1 2 = 370Hz
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f2 = f1
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F2 F1
Physics 103, Spring 2005, U. Wisconsin
Preflight 3
An European sports car dealer claims that his product will accelerate at a constant rate from rest to a speed of 100 km/hr in 8s. What is the speed after first 5 s of acceleration? 17.4 m/s 53.2 m/s 44.4 m/s 34.7 m/s 28.7 m/s
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v = v 0 + at (for constant acceleration) v v 0 100km /hr 0 100000 /3600 = = m /s2 a= 8s 8 t 100000 /3600 After 5 seconds : v = 0 + m /s2 5s = 17.4m /s 8
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Preflight 4
A rope of length L is clamped at both ends. Which one of the following is not a possible wavelength for the standing waves on this rope? 2L/3 2L L 4L
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L/2
Both ends must have nodes Length must equal an integral multiple of L=n 2 4L 2 L for n = 1,2,3K n (means n = 1/2!) =
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2
12/14/05
Physics 103, Spring 2005, U. Wisconsin
Preflight 5
How much power is needed to lift a 75-kg student vertically upward at a constant speed of 0.33 m/s? 25 W 12.5 W 243 W 115 W 230 W
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Work Force Distance Power = = = Force Speed Time Time Power = mgv = 75kg 9.8m/s2 0.33m/s = 243W
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Physics 103, Spring 2005, U. Wisconsin
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Preflight 6
Two gliders of unequal mass mA<mB are placed on a frictionless air track. Glider A is pushed horizontally as shown so that the gliders accelerate together to the right. Let FhA represent the magnitude of the force of the hand on the glider A. Let FBA represent the magnitude of the force exerted by the glider A on the glider B.
Which one of the following is true? FhA < FBA FhA = FBA FhA > FBA
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Newtons Second Law: Net external, FhA-FBA, is causing block A to accelerate to the right. FBA = FAB < FhA
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Physics 103, Spring 2005, U. Wisconsin
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Preflight 7
Two gliders of unequal mass mA<mB are placed on a frictionless air track. Glider A is pushed horizontally as shown so that the gliders accelerate together to the right. Let FhA represent the magnitude of the force of the hand on the glider A. Let FBA represent the magnitude of the force exerted by the glider A on the glider B.
Which one of the following is true? FBA < FAB FBA = FAB FBA > FAB
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Newtons Third Law
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Physics 103, Spring 2005, U. Wisconsin
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Preflight 8
Two gliders of unequal mass mA<mB are placed on a frictionless air track. Glider A is pushed horizontally as shown so that the gliders accelerate together to the right.
How does the net force on glider B (FB) compare to the magnitude of the net force on glider A (FA)? FB < FA FB = FA FB > FA
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Given : mA < mB and aA = aB Second Law : FA = mA aA and FB = mB aB FB mB = FB > FA FA mA
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Physics 103, Spring 2005, U. Wisconsin
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Preflight 9
Suppose a box sits next to you on the floor of an elevator. During which of the following situations is the normal force exerted on the box by the floor of the elevator smallest? When the elevator is accelerating upward. When the elevator is moving upward with constant speed. When the elevator is stationary. When the elevator is moving downward with constant speed. When the elevator is accelerating downward.
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Preflight 10
Now suppose the box next to you on the floor of an elevator is annoying you, and you want to push it out of the way. Because of static friction, you need to push the box with a minimum force F before it will start to move. During which of the following situations is the force F required to move the box smallest? When the elevator is accelerating upward. When the elevator is moving upward with constant speed. When the elevator is stationary. When the elevator is moving downward with constant speed. When the elevator is accelerating downward.
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Physics 103, Spring 2005, U. Wisconsin
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Preflight 11
The picture below shows three different ways of using a wrench to loosen a stuck nut. Assume the applied force F is the same in each case. In which case is the torque on the nut the biggest? Case 1
= F d sin Case 2 Longest lever arm, d Case 3 90o angle
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Preflight 12
The picture below shows three different ways of using a wrench to loosen a stuck nut. Assume the applied force F is the same in each case. In which case is the torque on the nut the smallest?
= F d sin Case 2 Short lever arm, d Reduced 45o angle
Case 1 Case 3
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Physics 103, Spring 2005, U. Wisconsin
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Preflight 13
The picture below shows two people lifting a heavy log. Which of the two people is supporting the greatest weight? The person on the left The person on the right Both are supporting the same weight
FL
dL dR
FR mg
For static equilibrium
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Net force is zero, FL+FR = mg Net torque must be zero, dL FL = dR FR, considering an axis of rotation at midway point of the heavy log. Person to left has shorter lever arm - therefore, FL > FR
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Physics 103, Spring 2005, U. Wisconsin
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Kinematics
Two stones are released from rest at a certain height, one after the other. (a) Will the difference in their speeds increase decrease stay the same? (b) Will their separation distance increase decrease stay the same? (c) Will the time interval between the instants at which they hit the ground be smaller than, equal to, or larger than the time interval between the instants of their release?
Equal to
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Motion in Gravity
A rock is thrown straight up from the Earths surface. Which one of the following statements concerning the net force acting on the rock at the top of its path is true? It is equal to zero for an instant. It is equal to the force used to throw it up but in opposite direction It is equal to the weight of the rock Its direction changes from up to down Its magnitude is equal to the sum of the force used to throw it up and its weight
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Physics 103, Spring 2005, U. Wisconsin
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Forces
You are riding your bike along a country flat road. Both the brake and the pedals work on the rear wheel; there is no brake on the front wheel. Indicate the direction and relative magnitude of the frictional forces on the front and rear tires in the following situations: (a) you are accelerating; (b) you are pedaling along at a steady pace; (c) you are braking.
12/14/05
Physics 103, Spring 2005, U. Wisconsin
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Forces
A horse is pulling a wagon at constant velocity over a flat, horizontal road. Draw a free-body diagram of all the forces acting on the horse and another one of all the forces acting on the wagon. Indicate the relative magnitude of the forces Identify any third-law force pairs. Identify forces of equal magnitude that are not third-law pairs.
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Physics 103, Spring 2005, U. Wisconsin
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Forces
A monkey clings to a rope that passes over a pulley. The monkeys weight is balanced by the mass m of a block hanging at the other end of the rope; both monkey and block are motionless. In order to get to the block, the monkey climbs a distance L (measured along the rope) up the rope. (a) Does the block move as a result of the monkeys climbing? (b) If so, in which direction and by how much?
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Physics 103, Spring 2005, U. Wisconsin
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Friction
A block is placed on a planar sheet that is pivoted at one end. The free side of the sheet is then raised very slowly, as shown. When the sheet is first raised, friction between block and sheet keeps the block from moving. At a certain angle, however, the block begins to slide down the inclined sheet. (a) If the sheet is kept at this angle, will the acceleration of the block be zero, constant, or neither? (b) If the condition k < s were not true, what would happen to the block?
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Physics 103, Spring 2005, U. Wisconsin
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Work
A boy swings a mass m tied to a string in a horizontal circle about his head. (a) How much work is done by the tension in the string? (b) If he swung it in a vertical circle, how much work is done by the tension in the string?
12/14/05
Physics 103, Spring 2005, U. Wisconsin
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Energy
A package of mass m is released from rest and slides along a track as shown. The coefficient of sliding friction between the package and the track is 0.33. (assume the package changes direction smoothly at the junction.) To what height will the package rise?
H 45o 45o
12/14/05
Physics 103, Spring 2005, U. Wisconsin
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Energy
What is the cost of continuously running a 500 W space heater per day, if the cost of electricity is 9 cents per kWh?
cost is $0.09 per KWH = $2.16 per KW day heater is 0.5 KW cost is $1.08 per day
12/14/05
Physics 103, Spring 2005, U. Wisconsin
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Power
Estimate the maximum power consumed by an elevator motor if it can carry no more than 10 people vertically upward at a constant speed of 0.33 m/s. (Assume that an average adult weighs about 150 lbs and that the elevator itself weighs as much as its maximum load.) about 2200 W. about 10000 W. about 15000 W. about 21500 W. about 80000
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Physics 103, Spring 2005, U. Wisconsin
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Collisions
A moving object collides with an object initially at rest. 1. Is it possible for both objects to be at rest after the collision?
NO YES
1. Can one of them be at rest after the collision? 2. Is it possible to have a collision in which all kinetic energy is lost?
YES
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Physics 103, Spring 2005, U. Wisconsin
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Statics
A sign of mass M is hung 1 m from the end of a 4 m long beam (mass m) as shown in the diagram. The beam is hinged at the wall. What is the tension in the guy wire?
wire = 30 1m SIGN
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Physics 103, Spring 2005, U. Wisconsin
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solution
N F mg
T 300
Mg
r F =0 ;
r
=0
0
2Mg + 3mg = T sin 30 T = 2g(2M + 3m)
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Physics 103, Spring 2005, U. Wisconsin
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Rotational Motion
A boy is whirling a stone around his head by means of a string. The string makes one complete revolution every second, and the tension in the string is T. The boy then speeds up the stone, keeping the radius of the circle unchanged, so that the string makes two complete revolutions every second. What happens to the tension in the string? The tension increases to four times its original value. The tension increases to two times its original value. The tension is unchanged. The tension reduces to one half its original value. The tension reduces to one fourth its original value.
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Physics 103, Spring 2005, U. Wisconsin
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Elasticity
A mass of 100 tonnes (105 kg) is lifted on a steel rod two cm in diameter and 10 m in length. (Youngs modulus is 210 109 N/m2) (a) How long does the rod stretch?
stress F / A E= = strain L /L F mgL L= L= = 0.15...