physics 1 midterm exam
how do you add vectors using components?
1. find the components of each vector to be added 2. add the x- and y-components separately 3. find the resultant vector
significant figures example: A tortoise travels at 2.51 cm/s for 12.27 s. How far does the tortoise go?
2.51 cm/s × 12.27 s = 30.8 cm (three significant figures)
1 meter =
3.281 ft
g=
9.81 m/s^2
Does the speedometer in a car measure velocity or speed? a) Velocity b) Speed c) Both d) Neither
b) speed The speedometer clearly measures speed, not velocity. Velocity is a vector (depends on direction), but the speedometer does not care what direction you are traveling. It only measures the magnitude of the velocity, which is the speed.
graphical interpretation of instantaneous velocity
This plot shows the average velocity being measured over shorter and shorter intervals. The instantaneous velocity is tangent to the curve.
instantaneous velocity
evaluate the average velocity over a shorter and shorter period of time; as that time becomes infinitesimally small, we have this.
If the position of a car is zero, does its speed have to be zero? a) yes b) no c) it depends on position
b) no No, the speed does not depend on position; it depends on the change of position. Because we know that the displacement does not depend on the origin of the coordinate system, an object can easily start at x = -3 and be moving by the time it gets to x = 0.
energy =
mass x (velocity)^2
SI unit of length
meter
scalar
number with units
how do you add vectors graphically?
place the tail of the second at the head of the first. The sum points from the tail of the first to the head of the last.
vector
quanitity with magnitude and direction
SI unit of time
seconds
average speed
the total distance traveled divided by the time the trip took •Average speed = total distance/elapsed time •Is the average speed of the red car 40.0 mi/h, more than 40.0 mi/h, or less than 40.0 mi/h?
distance
the total length of travel; if you drive from your house to the grocery store and back, you have covered a distance of 8.6 mi.
unit vectors are dimensionless vectors of ______ ________
unit length
position vector rf and displacement vector (delta)r
- points from the origin to the location in question - points from the original position to the final position
round-off error examples
-$2.21 + 8% tax = $2.3868, rounds to $2.39 -$1.35 + 8% tax = $1.458, rounds to $1.46 -Sum: $2.39 + $1.46 = $3.85 -$2.21 + $1.35 = $3.56 -$3.56 + 8% tax = $3.84
physics
the study of the fundamental laws of nature -These laws can be expressed as mathematical equations -Much complexity can arise from relatively simple laws
what is the standard today for the SI unit the meter?
The distance traveled by light in a vacuum in 1/299,792,458 of a second.
round-off error
The last digit in a calculated number may vary depending on how it is calculated, due to rounding off of insignificant digits
subtracting vectors
The negative of a vector is a vector of the same magnitude pointing in the opposite direction. Here, D=A-B
scalar
a numerical value. May be positive or negative. Examples: temperature, speed, height
vector
a quantity with both magnitude and direction. Examples: displacement (e.g., 10 feet north), force, magnetic field
which of the following is correct? a)If an equation is dimensionally correct, it must be true. If it is not dimensionally correct, it may be true. b)An equation may be true, regardless of whether it is dimensionally correct. c)If an equation is dimensionally correct, it could be true. If it is not dimensionally correct, it cannot be true. d)If an equation is dimensionally correct, it must be true. If it is not dimensionally correct, it cannot be true.
a) If an equation is dimensionally correct, it could be true. If it is not dimensionally correct, it cannot be true.
You throw a ball straight up into the air. After it leaves your hand, at what point in its flight does it have the maximum value of acceleration? a) Its acceleration is constant everywhere. b) At the top of its trajectory c) Halfway to the top of its trajectory d) Just after it leaves your hand e) Just before it returns to your hand on the way down
a) Its acceleration is constant everywhere. The ball is in free fall once it is released. Therefore, it is entirely under the influence of gravity, and the only acceleration it experiences is g, which is constant at all points.
You drop a rock off a bridge. When the rock has fallen 4 m, you drop a second rock. As the two rocks continue to fall, what happens to their separation? a) The separation increases as they fall. b) The separation stays constant at 4 m. c) The separation decreases as they fall. d) It is impossible to answer without more information.
a) The separation increases as they fall. At any given time, the first rock always has a greater velocity than the second rock. Therefore, it will always be increasing its lead as it falls. Thus, the separation will increase.
You drop a rock off a bridge. When the rock has fallen 4 m, you drop a second rock. As the two rocks continue to fall, what happens to their velocities? a) Both increase at the same rate. b) The velocity of the first rock increases faster than the velocity of the second rock. c) The velocity of the second rock increases faster than the velocity of the first rock. d) Both velocities stay constant.
a) both increase at the same rate Both rocks are in free fall. Thus, they are under the influence of gravity only. That means they both experience the constant acceleration of gravity. Since acceleration is defined as the change of velocity, both of their velocities increase at the same rate.
Does the odometer in a car measure distance or displacement? a) distance b) displacement c) both
a) distance If you go on a long trip and then return home, your odometer does not measure zero, which is the displacement, but it records the total miles that you traveled. That means the odometer records distance.
If the velocity of a car is non-zero (v ≠ 0), can the acceleration of the car be zero? a) Yes b) No c) Depends on the velocity
a) yes Sure it can! An object moving with constant velocity has a non-zero velocity, but it has zero acceleration because the velocity is not changing.
You and your dog go for a walk to the park. On the way, your dog takes many side trips to chase squirrels or examine fire hydrants. When you arrive at the park, do you and your dog have the same displacement? a) Yes b) No
a) yes Yes, you have the same displacement. Because you and your dog had the same initial position and the same final position, then you have (by definition) the same displacement.
velocity =
acceleration x time
an object falling in air is subject to... (and therefore is not free falling)
air resistance
velocity vector is always in the direction of motion; acceleration vector can point ________
anywhere
You throw a ball upward with an initial speed of 10 m/s. Assuming that there is no air resistance, what is its speed when it returns to you? a) More than 10 m/s b) 10 m/s c) Less than 10 m/s d) Zero e) Need more information
b) 10 m/s The ball is slowing down on the way up due to gravity. Eventually, it stops. Then it accelerates downward due to gravity (again). Because a = g on the way up and on the way down, the ball reaches the same speed when it gets back to you as it had when it left.
Which of the following is closest to an order of magnitude estimate of the age of a 35-year-old professor in seconds? a) 108 s b) 109 s c) 1010 s d) 1011 s
b) 10^9 s t = (35 yr)(365 d/yr)(86,400 s/d)= 1.1×109 s (about 109)
Write out 0.0038 g in kg using scientific notation with the correct number of significant figures. a) 3.8×10-3 kg b) 3.8×10-6 kg c) 38×10-4 kg
b) 3.8 x 10^-6 kg 0.0038 g can be expressed as 3.8×10-3 g. There are 1000 g in a kg, so this needs to be multiplied by 1 g/1000 kg, which gives 3.8 ×10-6 kg. Note that there are two significantfigures.
Using the common prefixes, what is the equivalent of 0.0038 g? a) 3.8 cg b) 3800 µg c) 38 mg
b) 3800 µg 0.0038 g can be expressed as 3800 × 10-6 g, which is equivalent to 3800 µg. Of course, a better answer would be 3.8 mg.
The graph of position vs. time for a car is given below. What can you say about the velocity of the car over time? a) It speeds up all the time. b) It slows down all the time. c) It moves at constant velocity. d) Sometimes it speeds up, and sometimes it slows down. e) Not really sure
b) It slows down all the time. The car slows down all the time because the slope of the x vs. t graph is diminishing as time goes on. Remember that the slope of x vs. t is the velocity! At large t, the value of the position x does not change, indicating that the car must be at rest.
A ball is thrown straight upward with some initial speed. When it reaches the top of its flight (at a height h), a second ball is thrown straight upward with the same initial speed. Where will the balls cross paths? a) At height h b) Above height h/2 c) At height h/2 d) Below height h/2 but above 0 e) At height 0
b) above height h/2 The first ball starts at the top with no initial speed. The second ball starts at the bottom with a large initial speed. Because the balls travel the same time until they meet, the second ball will cover more distance in that time, which will carry it over the halfway point before the first ball can reach it.
You drive for 30 minutes at 30 mi/hr and then for another 30 minutes at 50 mi/hr. What is your average speed for the whole trip? a) More than 40 mi/hr b) Equal to 40 mi/hr c) Less than 40 mi/hr
b) equal to 40 mi/hr Your average speed is 40 mi/hr. Because the average speed is distance/time and you spend the same amount of time at each speed, your average speed is 40 mi/hr.
The train is traveling at a speed of 45 mph. What is its speed in ft/s? a) More than 66 ft/s b) Equal to 66 ft/s c) Less than 66 ft/s
b) equal to 66 ft/s
Consider the line labeled A in the v vs. t plot. How does the speed change with time for line A? a) Decreases b) Increases c) Stays constant d) Increases, then decreases e) Decreases, then increases
b) increases In case A, the initial velocity is positive, and the magnitude of the velocity continues to increase with time.
Does the displacement of an object depend on the specific location of the origin of the coordinate system? a) Yes b) No c) It depends on the coordinate system.
b) no Because the displacement is the difference between two coordinates, the origin does not matter.
If the average velocity is non-zero over some time interval, does this mean that the instantaneous velocity is never zero during the same interval? a) Yes b) No c) It depends
b) no No! For example, your average velocity for a trip home might be 60 mph, but if you stopped for lunch on the way home, there was an interval when your instantaneous velocity was, in fact, zero.
Alice and Bill are at the top of a cliff of height H. Both throw a ball with initial speed v0; Alice straight down, and Bill straight up. The speeds of the balls when they hit the ground are vA and vB, respectively. If there is no air resistance, which is true? a) vA < vB b) vA = vB c) vA > vB d)Impossible to tell
b) vA = vB Bill's ball goes up and comes back down to Bill's level. At that point, it is moving downward with v0, the same as Alice's ball. Thus, it will hit the ground with the same speed as Alice's ball.
A tortoise travels at 2.51 cm/s for 4.512 s. Which answer gives its total distance using the correct number of significant figures? a) 11.325 cm b) 11.33 cm c) 11.3 cm
c) 11.3 Based on the given speed, there are three significant figures. So, the answer is 2.51 cm/s × 4.512 s = 11.325 cm rounded to 11.3 cm.
How long does it take the turtle to travel 15 cm? Again, use the correct number of significant figures. a) 5.976 s b) 5.98 s c) 6.0 s
c) 6.0 s Based on the distance, there are two significant figures. So, the answer is (15 cm)/(2.51 cm/s) = 5.98 s rounded to 6.0 s.
Alice and Bill are at the top of a building. Alice throws her ball downward. Bill simply drops his ball. Which ball has the greater acceleration just after release? a) Alice's ball b) It depends on how hard the ball was thrown. c) Neither—they both have the same acceleration. d) Bill's ball
c) Neither—they both have the same acceleration. Both balls are in free fall once they are released; therefore, they both feel the acceleration due to gravity (g). This acceleration is independent of the initial velocity of the ball.
A train travels 200 kilometers between two cities. Note that 1.0 km = 0.621 mi. The distance in miles is a) Exactly 200 miles. b) Close to 300 miles. c) Close to 120 miles. d) Greater than 300 miles.
c) close to 120 miles D = (200 km)(0.621 mi/1 km) = 124 miles
The graph of position vs. time for a car is given below. What can you say about the velocity of the car over time? a) It speeds up all the time. b) It slows down all the time. c) It moves at constant velocity. d) Sometimes it speeds up, and sometimes it slows down. e) Not really sure
c) it moves at a constant velocity The car moves at a constant velocity because the x vs. t plot shows a straight line. The slope of a straight line is constant. Remember that the slope of x vs. t is the velocity!
You drive 4 miles at 30 mi/hr and then another 4 miles at 50 mi/hr. What is your average speed for the whole 8-mile trip? a) More than 40 mi/hr b) Equal to 40 mi/hr c) Less than 40 mi/hr
c) less than 40 It is not 40 mi/hr! Remember that the average speed is distance/time. Because it takes longer to cover 4 miles at the slower speed, you are actually moving at 30 mi/hr for a longer period of time! Therefore, your average speed is closer to 30 mi/hr than it is to 50 mi/hr.
using dimensional analysis, what does v^2/x equal? a) t b) a c) v d) x
c) v Writing the term out in terms of dimension is as follows:
When throwing a ball straight up, which of the following is true about its velocity v and its acceleration a at the highest point in its path? a) Both v = 0 and a = 0 b) v ≠ 0, but a = 0 c) v = 0, but a ≠ 0 d) Both v ≠ 0 and a ≠ 0 e) Not really sure
c) v = 0, but a ≠ 0 At the top, clearly v = 0 because the ball has momentarily stopped. But the velocity of the ballis changing, so its acceleration is definitely not zero! Otherwise, it would remain at rest!
displacement
change in position; If you drive from your house to the grocery store and then to your friend's house, your displacement is -2.1 mi, and the distance you have traveled is 10.7 mi. The displacement is negative as it is to the left.
before describing motion, you must set up a _______ _______- define an origin and a positive direction
coordinate system
Which of the following is a vector and not a scalar? (1) Wind blowing N/NW at 20 mph (2) A temperature of 90º Fahrenheit (3) A mass of 200 kg (4) A block moving at 30º above the floor a) 1 and 2 b) 1 and 3 c) 2 and 4 d) 1 and 4
d) 1 and 4 A vector has magnitude and direction. Only 1 and 4 have both magnitude and direction. Both 2 and 3 are scalars, as they only have magnitude.
the average velocity points the same direction as the...
displacement
average velocity
displacement/elapsed time - if you return to your starting point, your velocity is zero
Consider the line labeled B in the v vs. t plot. How does the speed change with time for line B? a) Decreases b) Increases c) Stays constant d) Increases, then decreases e) Decreases, then increases
e) Decreases, then increases In case B, the initial velocity is positive but the magnitude of the velocity decreases toward zero. After this, the magnitude increases again, but becomes negative, indicating that the object has changed direction.
You drop a rubber ball. Right after it leaves your hand and before it hits the floor, which of the plots below represents the v vs. t graph for this motion? (Assume your y-axis is pointing up).
graph C The ball is dropped from rest, so its initial velocity is zero. Because the y-axis is pointing upward and the ball is falling downward, its velocity is negative and becomes more and more negative as it accelerates downward.
You drop a very bouncy rubber ball. It falls, and then it hits the floor and bounces right back up to you. Which of the graphs below represents the v vs. t graph for this motion?
graph D Initially, the ball is falling down, so its velocity must be negative (if UP is positive). Its velocity is also increasing in magnitude as it falls. Once it bounces, it changes direction and then has a positive velocity, which is also decreasing as the ball moves upward.
You toss a ball straight up in the air and catch it again. Right after it leaves your hand and before you catch it, which of the plots below represents the v vs. t graph for this motion? (Assume your y-axis is pointing up).
graph D The ball has an initial velocity that is positive but diminishing as it slows. It stops at the top (v = 0), and then its velocity becomes negative and becomes more and more negative as it accelerates downward.
how can we resolve vector?
into two perpendicular components using a two-dimensional coordinate system?
what is magnitude in a vector?
its length
what is the standard SI unit for mass?
kg
SI unit of mass
kilogram
Number of significant figures after multiplication or division is the number of significant figures in the ________________ __________
least-known quantity
if the acceleration is constant, the velocity changes....
linearly avg velocity =
instantaneous velocity vector is _________ to the path
tangent
what is direction in a vector?
the angle relative to the x-axis
average acceleration vector is the direction of...
the change in velocity
free fall
the motion of an object subject only to the influence of gravity, The acceleration due to gravity is constant, g.
multiplying unit vectors by scalars
the multiplier changes the length, and sign indicates the direction
significant figures
the number of digits in a quantity that are known with certainty
graphical interpretation of avg velocity
the same motion, plotted one-dimensionally and as an x-t graph
deceleration
velocity and acceleration have opposite signs
distance =
velocity x time