Chapter 1 and 2
The mass of a typical adult women is closest to:
75 kg
Ahsoka places a small box at the top of an incline. She releases it from rest and observes that the box has a constant acceleration as it slides down a frictionless incline and has a speed of 3.10 m/s after it has traveled 3.33 m to the bottom of the incline. (A) What is the speed v1 of the box when it is 1.20 m from the top where Ahsoka released it? (B) How long does it take to travel the 1.20 m from part A?
(A) 1.86 (B) 1.29
In the calculation of the area of a rectangle with dimensions of 4.282 m by 0.050 m, which of the following answers has the correct number of significant figures?
0.21 m^2
What is 0.205^(2/3), expressed to the proper number of significant figures?
0.348
The length and width of a rectangle are 1.125 m and 0.606 m, respectively. Multiplying, your calculator gives the product as 0.68175. Rounding properly to the correct number of significant figures, the area should be written as:
0.6982 m^2
Four astronauts are in a spherical space station. If, as is typical, each of them breathes about 500 cm^3 of air with each breath, approximately what volume of air (in cubic meters) do these astronauts breathe in a year? Assume the typical respiratory rate for a healthy adult at rest is 15 breaths per minute. What would the diameter (in meters) of the space station have to be to contain all this air?
1 * 10^4 m^3 30 m
A leaky faucet drips once each second. At this rate, it takes 1 hour to fill a 1-liter graduated cylinder to the 200-cm3 mark. What unit conversion do you need in order to calculate the average volume of a single drop in cm3?
1 hour equals 3600 seconds
The motorcycle engine on a Kawasaki Ninja 1000 has a displacement of 1043 cubic-centimeters (cm^3). In order to calculate its engine displacement in cubic-inches (in^3) what unit conversion factor would you use to multiply the given displacement?
1 in^3 / 16.4 cm^3
A square solar collector measures 6.00 m by 6.00 m and another square solar collector measures 8.000 m by 8.000 m. Using the correct number of significant figures, what is the combined area of both collectors?
1.000 * 10^2 m^2
What is the difference between 103.5 and 102.24 written with the correct number of significant figures?
1.3
If the fastest you can safely drive is 65 mi/h, what is the longest time you can stop for dinner if you must travel 541 mi in 9.6 h total?
1.3 h
What is 1mm^3 in m^3?
10^-9 m^3
How many millimeters are there in one meter?
10^3
Determine the angle between the direction of vectors A = 3.00i+1.00j and vector B = -3.00i+3.00j
117 degrees
The position of an object is given by x = at^3-bt+ct, where a = 4.1 m/s^3, b = 2.2 m/s^2, c = 1.7 m/s, and x and t are in Si units. What is the instantaneous acceleration of the object when t = 0.7 s?
13 m/s^2
A car acceleration from 10.0 m/s to 30 m/s at a rate of 3.00 m/s^2. How far does the car travel while accelerating?
133 m
The position of an object as a function of time is given by x = bt^2-ct, where b = 2.0 m/s^2 and c = 6.7 m/s, and the x and t are in SI units. What is the instantaneous velocity of the object when t = 2.2?
2.1 m/s
A plot of land contains 5.8 acres. How many square meters does it contain? (1 acre = 43,560 ft^2)
2.3 * 10^4 m^2
What is the value of pi(8.104)^2, written with the correct number of significant figures?
206.3
Add the following three numbers and report your answer using significant figures:2.5 cm + 0.50 cm + 0.055 cm = ?
3.1 cm
The human circulatory system is closed - that is, the blood pumped out of the left ventricle of the heart into the arteries is constrained to a series of continuous, branching vessels as it passes through the capillaries and then into the veins as it returns to the heart. The blood in each of the hearts four chambers comes briefly to rest before it is ejected by contraction of the heart muscle. The contraction of the left ventricle lasts 250 ms and the speed of blood flow in the aorta (the large artery leaving the heart) is 0.80 m/s at the end of the contraction. What is the average acceleration of a red blood cell as it leaves the heart?
3.2 m/s^2
Vector A = -1.00i+-2.00j and vector B = 3.00i+4.00j. What are the magnitude and direction of vector C = 3.00A +4.00B?
3.61 in a direction 33.7 degrees counterclockwise from the positive x-axis
In addition to 1 m = 39.37 in., the following exact conversion equivalents are given: 1 mile = 5280 ft, 1 ft = 12 in, 1 hour = 60 min, and 1 min = 60 s. If a particle has a velocity of 8.4 miles per hour, its velocity, in m/s is closest to:
3.8 m/s
Approximately how many times does an average human heart beat in a year?
4 * 10^7
The recommended daily allowance (RDA) of the trace metal magnesium is 410 mg/day for males. Express this quantity in μg/day. Express your answer in micrograms per day. For adults, the RDA of the amino acid lysine is 12 mg per kg of body weight. How many grams per day should a 72 kg adult receive? Express your answer in grams per day. A typical multivitamin tablet can contain 2.0 mg of vitamin B2 (riboflavin), and the RDA is 0.0030 g/day. How many such tablets should a person take each day to get the proper amount of this vitamin, assuming that he gets none from any other sources? Express your answer as an integer. The RDA for the trace element selenium is 0.000070 g/day. Express this dose in mg/day. Express your answer in milligrams per day.
4.1 * 10^5 mg/day 0.86 g/day 2 tablets 7.0 * 10^-2 mg/day
A ball rolls across a floor with an acceleration of 0.100 m/s^2 in a direction opposite to its velocity. The ball has a velocity of 4.00 m/s after rolling a distance 6.00 m across the floor. What was the initial speed of the ball?
4.15 m/s
A ball rolls across a floor with an acceleration of 0.100 m/s^2 in a directions opposite to its velocity. The ball has a velocity of 4.00 m/s after rolling a distance 6.00 m across the floor. What was the initial speed of the ball?
4.15 m/s
A test rocket is fired straight up from rest with a net acceleration of 20.0 m/s^2. After 4.00 seconds the motors turns of, but the rocket continues to coast upward with no appreciable air resistance. What maximum elevation does the rocket reach?
487 m
Which of the 8 vectors below shows the vector C minus the vector D(C - D)?
5
Estimate the number of pennies that would fit in a box one foot long wide by one foot tall
5 * 10^4
Vector A , which is shown in the figure, has a magnitude of 10 and a direction angle of 60º. What is the magnitude and direction angle (as measured counterclockwise from the positive x-axis) of −A/2?
5, 240 degrees
The acceleration of an object as a function of time is given by a(t) = (3.00 m/s^3)t, where t is in seconds. If the objects is at rest at time t = 0.00 s, what is the velocity of the object at time t = 6.00 s?
54.0 m/s
Starting from your campsite you walk 3.0 km east, 6.0 km north, 1.0 km east, and then 4.0 km west. How far are you from your campsite?
6.0 km
The radius of the earth is 6,380 kilometers. What is the radius of the earth in centimeters?
6.38 × 10^8 cm
You walk 53 m to the north, then turn 60 degrees to your right and walk another 45 m. Determine the direction of your displacement vector. Express your answer as an angle relative to east.
63 degrees N of E
Vector A has a magnitude of 2.00 m and vector B has a magnitude of 5.00 m. If the direction of each vector is unknown, what is the largest possible value for the magnitude of A − B?
7.00 m
An airplane that is flying level needs to acceleration from a speed 2.00 * 10^2 m/s to a speed of 2.40 * 10^2 m/s while it flies a distance of 1.20 km. What must be the acceleration of the plane?
7.33 m/s^2
If A = +4i-2j-3k and C=-4-2j-3k, which of the following numbers is closest to the magnitude of A-C?
8
A helicopter is flying horizontally with a speed of 444 m/s over a hill that slopes upward with a 2% grade (that is, the 'rise" is 2% of the "run"). What is the component of the helicopter's velocity perpendicular to the sloping surface of the hill?
8.9 m/s
A ball projected upward at time t = 0.0 s, from the point on a roof 90 m above the ground. The ball rises, then falls and strikes the ground. The initial velocity of the ball is 36.2 m/s if air resistance is negligible. The time when the ball strikes the ground is closest to:
9.4 s
Given two vectors A = 3.90i +7.10j and B = 5.30i −1.90j, find the scalar product of the two vectors A and B. Find the angle between these two vectors. Express your answer in degrees.
A * B = 7.18 theta = 80.9 degrees
Which of the following equations correctly expresses the relation between vectors A , B , and C shown in the figure?
A + B + C = 0
Which of the following equations correctly expresses the relation between vectors A, B, C, and D shown in the figure?
A + B - C - D = 0
In your physics lab you release a small glider from rest at various points on a long, frictionless air track that is inclined at an angle θ above the horizontal. With an electronic photocell, you measure the time t it takes the glider to slide a distance x from the release point to the bottom of the track. Your measurements are given in (Figure 1), which shows a second-order polynomial (quadratic) fit to the plotted data. You are asked to find the gliders acceleration, which is assumed to be constant. There is some error in each measurement, so instead of using a single set of x and t values, you can be more accurate if you use graphical methods and obtain your measured value of the acceleration from the graph. How can you re-graph the data so that the data points fall close to a straight line? (Hint: You might want to plot x or t, or both, raised to some power.) Select the correct graph with the equation for the straight line that is the best fit to the data points described in the previous part. Use the straight-line fit from the previous part to calculate the acceleration of the glider. Express your answer to two significant figures and include the appropriate units. The glider is released at a distance 1.71 m from the bottom of the track. Use the acceleration value you obtained in part C to calculate the speed of the glider when it reaches the bottom of the track. Express your answer to two significant figures and include the appropriate units.
A plot x versus t^2 should be a straight line. a = 7.6 m/s^2 5.1 m/s
In the study of physics, what distinguishes a scalar from a vector?
A scalar is specified with a single number, but a vector is specified using both a magnitude and a direction.
Vector A has y-component Ay = +18.0 m. A makes an angle of 32.0 ∘ counterclockwise from the +y-axis. What is the x-component of A? Express your answer with the appropriate units. What is the magnitude of A? Express your answer with the appropriate units.
Ax = -11.2 m A = 21.2 m
A race car starts from rest and travels east along a straight and level track. For the first 5.0 s of the car's motion, the eastward component of the car's velocity is given by vx(t) = (0.850 m/s^3)t^2. What is the acceleration of the car when vx = 12.7 m/s? Express your answer with the appropriate units.
Ax = 6.57 m/s^2
Which one of the following graphs could possibly represent the vertical position as a function of time for an object in free fall?
B
Which of the following equations correctly expresses the relation between vectors A→, B→, and C→ shown in the figure?
B = A + C
Vector A has a magnitude of 3.00 and is directed parallel to the negative y-axis and vector B has a magnitude of 3.00 and is directed parallel to the positive y-axis. Determine the magnitude and direction angle (as measured counterclockwise from the positive x-axis) of vector C, if C =A − B.
C = 6.00; theta = 270 degrees
An object moves along the x-axis with constant acceleration. The initial position x0 is positive, the initial velocity is positive, and the acceleration is negative. Which of the following vx-t graphs best describes this motion?
D
A glider in on an inclined, frictionless track. The x-axis points downhill. At t = 0 s the glider is at x = 0 m and moving uphill. After reaching the high point of its motion, it moves downhill and returns to x = 0 m. Which of the following vx -t graphs (graph of the velocity vs time) best matches the motion of the glider?
E
A patient with a dislocated shoulder is put into a traction apparatus as shown in (Figure 1). The pulls A and B have equal magnitudes and must combine to produce an outward traction force of 12.9 N on the patient's arm. How large should these pulls be? Express your answer with the appropriate units.
F = 7.61 N
The speed of a wave pulse on a string depends on the tension F, in the string and the mass per unit length, u, of the string. Tension has SI units of kg * m * s^-2 and the mass per unit length has SI units of kg * m^-1. What combination of F and u must the speed of the wave be proportional to?
F/u
True or False: If all the components of a vector are equal to 1, then that vector is a unit vector.
False
True or False: If two two nonzero vectors point in the same direction, their dot product must be zero
False
True or False: When adding two numbers, the number of significant figures in the sum is equal to the number of significant figures in the least accurate of the numbers being added.
False
If a tree is 15 m tall, its height expressed in feet is x ft, where x is:
Greater than 15
Supposed that a car traveling to the west (the -x direction) begins to slow down as it approaches a traffic light. Which statement concerning its acceleration in the x direction is correct?
Its acceleration is positive but is velocity is negative
The SI base unit for mass is the _______.
Kilogram
Two objects are dropped from a bridge, an interval of 1.0 s apart, and experience no appreciable air resistance. As time progresses, the difference in their speeds:
Remains constant
During your summer internship for an aerospace company, you are asked to design a small research rocket. The rocket is to be launched from rest from the earth's surface and is to reach a maximum height of 910 m above the earth's surface. The rocket's engines give the rocket an upward acceleration so it moves with acceleration of 16.0 m/s^2 during the time T that they fire. After the engines shut off, the rocket is in free fall. Ignore air resistance. Assume that the acceleration due to gravity does not change with the height of the rocket. What must be the value of T in order for the rocket to reach the required altitude? Express your answer with the appropriate units.
T = 6.6 s
A ball is thrown directly upward and experiences no air resistance. Which one of the following statements about its motion is correct?
The acceleration is downward during the entire time the ball is in the air.
The current definition of the standard meter of length is based on:
The distance traveled by light in a vacuum
The current definition of the standard second of time is based on:
The frequency of radiation emitted by cesium atoms
If the eastward component of vector A is equal to the westward component of vector B and their northward components are equal. Which one of the following statements about these two vectors is correct?
The magnitude of vector A is equal to the magnitude of vector B
Which of the following is the basis of the current standard for the meter?
The meter is defined as the distance that light travels in a specified time interval.
Under what condition is |A - B| = A + B?
Vectors A and B are in opposite directions.
An egg is thrown nearly vertically upward from a point near the cornice of a tall building. It just misses the cornice on the way down and passes a point a distance 31.0 m below its starting point at a time 5.00 s after it leaves the thrower's hand. Air resistance may be ignored. What is the initial speed of the egg? Express your answer in meters per second. How high does it rise above its starting point? Express your answer in meters. What is the magnitude of its velocity at the highest point? Express your answer in meters per second. What is the magnitude of its acceleration at the highest point? Express your answer in meters per second squared. What is the direction of its acceleration at the highest point?
Vin = 18.3 m/s h = 17.1 m Vh.p. = 0 m/s a = 9.80 m/s^2 down
Suppose that C = A − B. Under what circumstances is the length of C equal to the sum of the lengths of A and B?
When A and B point in opposite directions.
A gazelle is running in a straight line (the x-axis). The graph in (Figure 1) shows this animal's velocity as a function of time. During the first 12.0 s, find the total distance moved. Express your answer in meters. During the first 12.0 s, find the displacement of the gazelle. Express your answer in meters.
Xpath = 92.0 m Xdisplacement = 92.0 m
An astronaut has left the International Space Station to test a new space scooter. Her partner measures the following velocity changes, each taking place in a 10 s interval. What are the average acceleration in each interval? Assume that the positive direction is to the right. At the beginning of the interval, the astronaut is moving toward the right along the x-axis at 15.7 m/s, and at the end of the interval she is moving toward the right at 5.5 m/s. Express your answer in meters per second squared. At the beginning she is moving toward the left at 5.5 m/s, and at the end she is moving toward the left at 15.7 m/s. Express your answer in meters per second squared. At the beginning she is moving toward the right at 15.7 m/s, and at the end she is moving toward the left at 15.7 m/s. Express your answer in meters per second squared.
a = -1.0 m/s^2 a = -1.0 m/s^2 a = -3.1 m/s^2
Which of the following is a vector?
displacement
On the earth, when an astronaut throws a 0.250-kg upward, it returns to his hand a time T later. On planet X he finds that, under the same circumstances, the stone returns to his hand in 2T. In both cases, he throws the stone with the same initial velocity and it feels negligible air resistance. The acceleration due to gravity on planet x (in terms of g) is:
g/2
A rocket starts from rest and moves upward from the surface of the earth. For the first 10.0 s of its motion, the vertical acceleration of the rocket is given by ay= (3.00 m/s^3)t, where the +y-direction is upward. What is the height of the rocket above the surface of the earth at t = 10.0 s? Express your answer with the appropriate units. What is the speed of the rocket when it is 245 m above the surface of the earth? Express your answer with the appropriate units.
h = 500 m Vy = 93.2 m/s
Two identical objects A and B fall from rest from different heights to the ground and feel no appreciable air resistance. If object B takes TWICE as long as objects A to reach the ground, what is the ratio of the heights from which A and B fell?
hA/hB = 1/4
In the equation z = ct + d, z is measured in meters and t is measured in seconds. What are the dimensions (units) of d?
m
In the equation z = ct + d, z is measured in meters and t is measured in seconds. What are the dimensions (units) of c?
m/s
The period of a pendulum is the time it takes the pendulum to swing back and forth once. If the only dimensional quantities that the period depends on are the acceleration of gravity, g, and the length of the pendulum, l, what combination of g and l must the period be proportional to? (Acceleration has SI units of m * s^-2)
sqrt(l/g)
The figure represents the velocity of a particle as it travels along the x-axis. At what value (or values) of t is the instantaneous acceleration equal to zero?
t = 1 s
A juggler throws a bowling pin straight up with an initial speed of 7.90 m/s. How much time elapses until the bowling pin returns to the juggler's hand? Express your answer with the appropriate units.
t = 1.61 s
A maser is a laser-type device that produces electromagnetic waves with frequencies in the microwave and radio-wave bands of the electromagnetic spectrum. You can use the radio waves generated by a hydrogen maser as a standard of frequency. The frequency of these waves is 1,420,405,751.786 hertz. (A hertz is another name for one cycle per second.) A clock controlled by a hydrogen maser is off by only 1 s in 100,000 years. (The large number of significant figures given for the frequency simply illustrates the remarkable accuracy to which it has been measured.) What is the time for one cycle of the radio wave? Express your answer to three significant figures and include the appropriate units. How many cycles occur in 1.9 h? How many cycles would have occurred during the age of the earth, which is estimated to be 4.6 × 10^9 years? By how many seconds would a hydrogen maser clock be off after a time interval equal to the age of the earth? Express your answer in seconds.
t = 7.04 * 10^-10 s N = 9.7 * 10^12 cycles N = 2.1 * 10^26 cycles t = 4.6 * 10^4 s
A car and a truck start from rest at the same instant, with the car initially at some distance behind the truck. The truck has a constant acceleration of 2.10 m/s^2 and the car an acceleration of 3.40 m/s^2. The automobile overtakes the truck after the truck has moved 60.0 m. How much time does it take the car to overtake the truck? Express your answer with the appropriate units. How far was the car behind the truck initially? Express your answer with the appropriate units. What is the speed of the truck when they are abreast? Express your answer with the appropriate units. What is the speed of the car when they are abreast? Express your answer with the appropriate units. Select the correct x−t graph of each vehicle. Take x=0 at the initial location of the truck.
t = 7.56 s d = 37.1 m Vtruck = 15.9 m/s Vcar = 25.7 m/s
Two identical stones are dropped from rest and feel no air resistance as they fall. Stone A is dropped from height h, and stone B is dropped from height 2h. If stone A takes time t to reach the ground, stone B will take time:
t*sqrt(2)
You are given two vectors A = −3.00i +7.00j and B =6.00i +2.00j. Let counterclockwise angles be positive. What angle θA, where 0 ≤ θA < 360, does A make with the +x-axis? Express your answer in degrees. What angle θB, where 0 ≤ θB < 360, does B make with the +x-axis? Express your answer in degrees. Vector C is the sum of A and B, so C = A + B. What angle θC, where 0 ≤ θC <360, does C make with the +x-axis? Express your answer in degrees.
theta A = 113 degrees theta B = 18.4 degrees theta C = 71.6 degrees
A small block has constant acceleration as it slides down a frictionless incline. The block is released from rest at the top of the incline, and its speed after it has traveled 6.20 m to the bottom of the incline is 3.80 m/s. What is the speed of the block when it is 3.80 m from the top of the incline? Express your answer with the appropriate units.
v = 2.97 m/s
You throw a small rock straight up from the edge of a highway bridge that crosses a river. The rock passes you on its way down, 9.00 s after it was thrown. What is the speed of the rock just before it reaches the water 22.0 m below the point where the rock left your hand? Ignore air resistance. Express your answer with the appropriate units.
v = 48.7 m/s
A small object moves along the x-axis with acceleration ax(t) = −(0.0320 m / s^3)(15.0 s − t). At t = 0 the object is at x = -14.0 m and has velocity v0x = 8.60 m/s. What is the x-coordinate of the object when t = 10.0 s? Express your answer with the appropriate units.
x = 53.3 m
Vector A has magnitude 17.0 m and vector B has magnitude 17.0 m. The scalar product A B is 109 m^2. What is the magnitude of the vector product between these two vectors? Express your answer with the appropriate units.
|A * B| = 268 m^2
For the vectors A and B in the figure (Figure 1), use a scale drawing to find the magnitude of the vector sum A + B. Express your answer in meters. Find the direction of the vector sum A + B. Express your answer in degrees. Find the magnitude of the vector difference A − B. Express your answer in meters. Find the direction of the vector difference A − B. Express your answer in degrees. Use your answers to find the magnitude of −A − B. Express your answer in meters. Find the direction of −A − B. Express your answer in degrees. Find the magnitude of B − A. Express your answer in meters. Find the direction of B − A. Express your answer in degrees.
|A + B| = 9.0 m angle = 34 degrees counterclockwise from +x-axis |A - B| = 22 m angle = 250 degrees counterclockwise from +x-axis |-A - B| = 9.0 m angle = 214 degrees counterclockwise from +x-axis |B - A| = 22 m angle = 70 counterclockwise from +x-axis
