PHY101 Midterm (ch. 2-7)
Consider a baseball player batting a ball. (a) Identify the action-reaction pairs when the ball is being hit and (b) while the ball is in flight.
(a) Action; bat hits ball. Reaction; ball hits bat. (b) While in flight there are two interactions, one with the Earth's gravity and the other with the air. Action: Earth pulls down on ball (weight). Reaction: ball pulls up on Earth. And, action: air pushes ball, and reaction: ball pushes air.
For each of the following interactions, identify action and reaction forces. (a) A hammer hits a nail. (b) Earth gravity pulls down on a book. (c) A helicopter blade pushes air downward.
(a) Action; hammer hits nail. Reaction; nail hits hammer. (b) Action; Earth pulls down on you. Reaction; you pull up on the Earth. (c) Action; helicopter blade pushes air downward. Reaction; air pushes helicopter blade upward. (In these examples, action and reaction may be reversed—which is called which doesn't matter.)
Identify the action-reaction pairs of forces for the following situations: (a) You step off a curb. (b) You pat your tutor on the back. (c) A wave hits a rocky shore.
(a) Action; your foot pushes curb. Reaction; the curb pushes your foot. (b) Action; your hand pats tutor's back. Reaction; your tutor's back "pats" your hand. (c) Action; waves exert forces on rocky shore. Reaction; rocky shore exerts forces on waves.
You hold an apple over your head. (a) Identify all the forces acting on the apple and their reaction forces. (b) When you drop the apple, identify all the forces acting on it as it falls and the corresponding reaction forces. Neglect air drag.
(a) Two force pairs act; Earth's pull on apple (action), and apple's pull on Earth (reaction), Hand pushes apple upward (action), and apple pushes hand downward (reaction). (b) With no air drag, one force pair acts; Earth's pull on apple, and apple's pull on Earth. If air drag counts, then air pushes upward on apple (action) and apple pushes downward on air (reaction).
A boxer punches a sheet of paper in midair and brings it from rest up to a speed of 25 m/s in 0.05 s. (a) What acceleration is imparted to the paper? (b) If the mass of the paper is 0.003 kg, what force does the boxer exert on it? (c) How much force does the paper exert on the boxer?
(a) a = m∆v/∆t = (25 m/s)/(0.05 s) = 500 m/s2. (b) F = ma = m∆v/∆t = (0.003 kg)(25 m/s)/(0.05 s) = 1.5 N, which also is about 1/3 pound. (c) By Newton's third law, the same amount, 1.5 N.
Calculate the resultant of the pair of velocities 100 km/h north and 75 km/h south. Calculate the resultant if both of the velocities are directed north.
100 km/h - 75 km/h = 25 km/h North 100 km/h + 75 km/h = 175 km/h North
In the simplest sense, a force is a push or a pull. In a deeper sense, what is a force?
A force is an interaction between one thing and another.
Can a pair of vectors with unequal magnitudes ever add to zero? Can three unequal vectors add to zero? Defend your answers.
A pair of vectors can cancel only if they are equal in magnitude and opposite in direction. But three unequal vectors can combine to equal zero
Cite three examples of a vector quantity and three examples of a scalar quantity.
A vector is a quantity that specifies both a magnitude and a direction. Examples: displacement, velocity, acceleration, force and electric field A scalar is a quantity that is completely specified by its magnitude and has no direction. Examples: mass, volume, distance, energy, and time
The newton is a unit of A) force. B) inertia. C) density. D) mass.
A) force.
A cannon fires a cannonball. While the cannonball is accelerating within the cannon, the magnitude of the acceleration of the cannonball is _________ that of the cannon. A) greater than B) equal to C) less than
A) greater than Although the forces are equal and opposite, the acceleration is greater since the cannonball's mass is much lower.
A rock weighs 30 N on Earth. A second rock weighs 30 N on the moon. Which of the two rocks has the greater mass? A) the one on the moon B) the one on Earth C) They have the same mass.
A) the one on the moon
Suppose that two carts, one twice as massive as the other, fly apart when the compressed spring that joins them is released. What is the acceleration of the heavier cart relative to that of the lighter cart as they start to move apart?
As in the preceding exercise, the force on each cart will be the same. But since the masses are different, the accelerations will differ. The twice-as-massive cart will undergo only half the acceleration of the less-massive cart.
A fireman pushes on a closed door. What force makes a reaction pair with the force exerted by the fireman onto the door? A) The force exerted on the ground by the fireman. B) The force exerted on the fireman by the door. C) The force exerted on the fireman by the ground (due to friction).
B) The force exerted on the fireman by the door. Due to Newton's 3rd law, these two forces are equal and opposite.
While a bullet is being fired within the rifle, how does the force exerted on the bullet compare to the force exerted on the rifle? A) The magnitude of the force acting on the bullet is just a little big greater than that acting on the rifle. B) The magnitude of the force acting on the bullet is equal to that acting on the rifle. C) The magnitude of the force acting on the bullet is much larger than that acting on the rifle.
B) The magnitude of the force acting on the bullet is equal to that acting on the rifle. Due to Newton's 3rd law, the reaction force on the rifle is equal and opposite to the action force on the bullet.
A player catches a ball. Consider the action force to be the impact of the ball against the player's glove. The reaction to this force is the A) player's grip on the glove. B) force the glove exerts on the ball. C) muscular effort in the player's arms. D) friction of the ground against the player's shoes. E) none of these
B) force the glove exerts on the ball.
A person pushes a large crate across the room from left to the right. Friction acts on the crate as well as on the person's feet. If the person pushes with a force greater than the force of friction between the crate and floor, the net force on the crate A) is directed to the left. B) is directed to the right. C) is zero, since all forces cancel with their reaction pair partner.
B) is directed to the right. The net force on the crate is equal to the force exerted on it by the person minus the force of friction.
In which case would you have the largest mass of gold? If your chunk of gold weighed 1 N on the A) Earth. B) moon. C) planet Jupiter
B) moon.
As seen from above, a stubborn stump is pulled by a pair of ropes, each with a force of200 N, but at different angles as shown. From greatest to least, rank the net force on the stump.
B, A, C
Here we see a top view of an airplane being blown off course by wind in three different directions. Rank the speeds of the airplane across the ground from fastest to slowest.
B, A, C
Ken and Joanne are astronauts floating some distance apart in space. They are joined by a safety cord whose ends are tied around their waists. If Ken starts pulling on the cord, will he pull Joanne toward him, or will he pull himself toward Joanne, or will both astronauts move? Explain.
Both will move. Ken's pull on the rope is transmitted to Joanne, causing her to accelerate toward him. By Newton's third law, the rope pulls back on Ken, causing him to accelerate toward Joanne.
The rope is repositioned as shown and still supports the 50-N lantern. Is the tension in the rope less than, equal to, or more than 50 N? Use the parallelogram rule to defend your answer.
By the parallelogram rule, the tension is greater than 50 N.
A large man is playing a game of tug-o-war with a small child. The man causes the child to skid towards the man as the man is walking backwards. Which person is pulling on the rope harder? A) The child is pulling harder. B) The large man is pulling harder. C) The two are pulling equally hard on the rope.
C) The two are pulling equally hard on the rope. Even though the large man is stronger, he can't pull harder than the tension of the rope, which is the same as the tension on the other end of the rope. Due to Newton's 3rd law, the tension of the rope is equal to the strength either person is pulling on the rope, and so the each person is pulling just as hard as the other person.
An airplane flies north and travels with a speed of 100 miles per hour with respect to the air. If the wind blows towards the east with a speed of 100 miles per hour, in which direction is the airplane traveling with respect to the ground? A) To the east. B) To the north. C) To the northeast.
C) To the northeast. the final velocity is due to the addition of the velocity of the airplane with respect to the air and the wind velocity to the East.
Which has the greater mass? A) a king-size pillow B) neither - both have the same C) an automobile battery
C) an automobile battery
A person pushes a large crate across the room to the right. Friction acts on the crate as well as on the person's feet. If the crate accelerates to the right, the net force on the system made up of the person and the crate is A) directed to the left. B) zero. C) directed to the right.
C) directed to the right. The net force on this system is due to the force of friction acting on the person (to the right) and on the crate (to the left). Since the person is pushing harder than the force of friction on the crate, and since the crate must be pushing on the person with the same force as the person is pushing on the crate, the force of friction exerted on the person due to friction must be greater than the force of friction exerted on the crate.
Whenever the net force on an object is zero, its acceleration A) may be more than zero B) may be less than zero. C) is zero.
C) is zero.
An object's weight may properly be expressed in units of A) cubic centimeters. B) kilograms. C) newtons. D) meters.
C) newtons.
As a ball falls, the action force is the pull of Earth on the ball. The reaction force is the A) acceleration of the ball. B) none of these C) pull of the ball's mass on the Earth D) air resistance acting against the ball.
C) pull of the ball's mass on the Earth
An object is propelled along a straight-line path by a force. If the net force were doubled, the object's acceleration would be A) half as much. B) none of these C) the same. D) twice as much. E) four times as much
D) twice as much.
If one object has twice as much mass as another object, it also has twice as much A) velocity. B) all of these C) acceleration due to gravity. D) volume. E) inertia.
E) inertia.
If the forces that act on a cannonball and the recoiling cannon from which it is fired are equal in magnitude, why do the cannonball and cannon have very different accelerations?
Equal forces on unequal masses produce unequal accelerations, in accord with Newton's second law.
Consider an airplane that normally has an airspeed of 100 km/h in a 100-km/h crosswind blowing from west to east. Calculate its ground velocity when its nose is pointed north in the crosswind.
Ground velocity V = square root of [(100 km/h)squared + (100 km/h)squared] = 141 km/ h, 45° northeast (45° from the direction of the wind). The velocity relative to the ground makes the diagonal of a 45°-45°-90° triangle.
If a Mack truck and Honda Civic have a head-on collision, upon which vehicle is the impact force greater? Which vehicle experiences the greater deceleration? Explain your answers.
In accord with Newton's 3rd law, the force on each will be of the same magnitude. But the effect of the force (acceleration) will be different for each because of the different mass. The more massive truck undergoes less change in motion than the Civic.
Fill in the blanks, Newton's first law is often called the law of ________. Newton's second law is the law of ________ and Newton's third law is the law of ________ and ________.
Inertia; acceleration; action; reaction
Which of the three laws deals with interactions?
Newton's third law, the law of action-reaction
When you rub your hands together, can you push harder on one hand than the other?
No, for each hand pushes equally on the other in accord with Newton's third law- you cannot push harder on one hand than the other.
Can you physically touch a person without that person touching you with the same amount of force?
No, touching requires a two-ness; the toucher and the touchee
When, if ever, can a vector quantity be added to a scalar quantity?
No. A vector quantity and scalar quantity can never be added.
Resultant of two vectors at right angles to each other
R = square root of x2 + y2 a2+b2=c2, square root of c2
When you push against a wall with your fingers, they bend because they experience a force. Identify this force.
Reaction force - wall pushes back on your fingers.
Why is speed considered a scalar and velocity a vector?
Speed has no direction just a quantity (magnitude). Velocity has both a quantity (magnitude) and a direction.
A heavy bird sits on a clothesline. Will the tension in the clothesline be greater if the line sags a lot or if it sags a little?
Tension will be greater for a small sag. That's because large vectors in each side of the rope supporting the bird are needed for a resultant that is equal and opposite to the bird's weight.
A rocket becomes progressively easier to accelerate as it travels through space. Why is this so? (Hint: About 90% of the mass of a newly launched rocket is fuel.)
The answer is given in the equation a = F/m. As fuel is burned, the mass of the rocket becomes less. As m decreases as F remains the same, a increases! There is less mass to be accelerated as fuel is consumed.
Identify the force that propels a rocket.
The force that propels a rocket is the reaction to the force the rocket exerts on the exhaust gases.
A farmer urges his horse to pull a wagon. The horse refuses, saying that to try would be futile, for it would flout Newton's third law. The horse concludes that she can't exert a greater force on the wagon than the wagon exerts on her and therefore, that she won't be able to accelerate the wagon. What is your explanation to convince the horse to pull?
The forces do not cancel because they act on different things—one acts on the horse, and the other acts on the wagon. It's true that the wagon pulls back on the horse, and this prevents the horse from running as fast as it could without the attached wagon. But the force acting on the wagon (the pull by the horse minus friction) divided by the mass of the wagon, produces the acceleration of the wagon. To accelerate, the horse must push against the ground with more force than it exerts on the wagon and the wagon exerts on it. So tell the horse to push backward on the ground.
Two people of equal mass attempt a tug-of-war with a 12-m rope while standing on frictionless ice. When they pull on the rope, each of them slides toward the other. How do their accelerations compare, and how far does each person slide before they meet?
The forces on each are the same in magnitude, and their masses are the same, so their accelerations will be the same. They will slide equal distances of 6 meters to meet at the midpoint.
If you exert a horizontal force of 200 N to slide a crate across a factory floor at constant velocity, how much friction is exerted by the floor on the crate? Is the force of friction equal and oppositely directed to your 200-N push? If the force of friction isn't the reaction force to your push, what is?
The friction on the crate is 200 N, which cancels your 200-N push on the crate to yield the zero net force that accounts for the constant velocity (zero acceleration). Although the friction force is equal and oppositely directed to the applied force, the two do not make an action-reaction pair of forces. That's because both forces do act on the same object—the crate. The reaction to your push on the crate is the crate's push back on you. The reaction to the frictional force of the floor on the crate is the opposite friction force of the crate on the floor.
How does a helicopter get its lifting force?
The helicopter blades force air downward, and in doing so the air forces the blades upward. The upward force provides lift.
A boxer can hit a heavy bag with great force. Why can't he hit a piece of tissue paper in midair with the same amount of force?
The mass of the tissue paper is not equal to the mass of the boxer. He can't exert any more force on the tissue paper than the tissue paper can exert on him. The tissue paper has insufficient inertia for a great force.
Consider hitting a baseball with a bat. If we call the force on the bat against the ball the action force, identify the reaction force.
The reaction force is the ball hitting the bat.
What aspect of physics was not known by the writer of this newspaper editorial that ridiculed early experiments by Robert H. Goddard on rocket propulsion above Earth's atmosphere? "Professor Goddard . . . does not know the relation of action to reaction, and of the need to have something better than a vacuum against which to react . . . he seems to lack the knowledge ladled out daily in high schools."
The relation of action to reaction. The law of action and reaction is precisely how a rocket works in a vacuum. It pushes out gas in one direction, and gets an equal and opposite momentum in the other direction.
According to the parallelogram rule, what quantity is represented by the diagonal of a constructed parallelogram?
The resultant of the vectors that make up the sides of the parallelogram.
Two 100-N weights are attached to a spring scale as shown. Does the scale read 0, 100, or 200 N, or does it give some other reading? (Hint: Would it read any differently if one of the ropes were tied to the wall instead of to the hanging 100-N weight?)
The scale will read 100 N, it would read the same if one of the ends were tied to a wall instead of tied to the 100-N hanging weight. Although the net force on the system is zero, the tension in the rope within the system is 100 N, as shown on the scale reading.
In a tug-of-war between Sam and Maddy, each pulls on the rope with a force of 250 N. What is the tension in the rope? If both remain motionless, what horizontal force does each exert against the ground?
The tension in the rope is 250 N. Since they aren't accelerating, each must experience a 250-N force of friction via the ground. This is provided by pushing against the ground with 250 N.
Consider Nellie hanging at rest. If the ropes were vertical, with no angle involved, what would be the tension in each rope?
The tension on each rope would be half of Nellie's weight. Nellie has a mass of m (units: kilograms). Nellie is hanging from two vertical ropes on earth (thus g = 9.8 m/s^2) The downward force of Nellie is mg. The tension in the two ropes equals mg. Each rope holds half the tension. The tension in a roe is mg / 2.
If you stand next to a wall on a frictionless skateboard and push the wall with a force of 30 N, how hard does the wall push on you? If your mass is 60 kg, show that your acceleration is 0.5 m/s2.
The wall pushes on you with 30 N. a = F/m = 30 N/60 kg = 0.5 m/s2.
Which team wins in a tug-of-war-the team that pulls harder on the rope, or the team that pushes harder against the ground? Explain.
The winning team pushes harder against the ground. The ground then pushes harder on them, producing a net force in their favor.
If raindrops fall vertically at a speed of 3 m/s and you are running at 4 m/s, how fast do they hit your face?
They hit your face with the resultant of the horizontal and vertical components: R = square root of [(3.0 m/s)squared + (4 .0 m/s)squared] = 5 m/s.
A balloon floats motionless in the air. A balloonist begins climbing the supporting cable. In which direction does the balloon move as the balloonist climbs?
To climb upward means pulling the rope downward, which moves the balloon downward as the person climbs.
What can you correctly say about two vectors that add together to equal zero?
Two vectors that add together to be equal to zero must have the same magnitude (length) and the opposite direction.
Which of the following are scalar quantities, which are vector quantities, and which are neither? (a) velocity (b) age (c) speed (d) acceleration (e) temperature.
Vector quantities are velocity and acceleration. All others are scalars.
If you drop a rubber ball on the floor, it bounces back up. What force acts on the ball to provide the bounce?
When the ball exerts a force on the floor, the floor exerts an equal and opposite force on the ball- hence bouncing. The force of the floor on the ball provides the bounce.
When the athlete holds the barbell overhead, the reaction force is the weight of the barbell on his hand. How does this force vary for the case in which the barbell is accelerated upward? Downward?
When the barbell is accelerated upward, the force exerted by the athlete is greater than the weight of the barbell (the barbell, simultaneously, pushes with greater force against the athlete). When acceleration is downward, the force supplied by the athlete is less.
Why does a rope climber pull downward on the rope to move upward?
When the climber pulls the rope downward, the rope simultaneously pulls the climber upward- the direction desired by the climber.
When can a nonzero vector have a zero horizontal component?
When the direction of the vector is vertical. Gravitational force has zero horizontal component.
Consider the system of a single football. If you kick it, is there a net force to accelerate the system? If a friend kicks it at the same time with an equal and opposite force, is there a net force to accelerate the system?
When there is one interaction between the foot and the football, the ball accelerates. If two kicks on the ball are simultaneous, equal, and opposite, then the net force on the ball is zero.
Why can you exert greater force on the pedals of a bicycle if you pull up on the handlebars?
When you pull up on the handlebars, the handlebars simultaneously pull down on you. This downward force is transmitted to the pedals.
You push a heavy car by hand. The car, in turn, pushes back with an opposite but equal force on you. Doesn't this mean that the forces cancel one another, making acceleration impossible? Why or why not?
When you push the car, you exert a force on the car. When the car simultaneously pushes back on you, that force is on you not the car. You don't cancel a force on the car with a force on you. For cancellation, the forces have to be equal and opposite and act on the same object.
Newton's third law of motion
Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.
To produce a net force on a system, must there be an externally applied net force?
Yes
Earth pulls down on you with a gravitational force that you call your weight. Do you pull up on Earth with the same amount of force?
Yes, You pull on the earth with exactly the same force that the earth pulls on you. Your effect on the earth is insignificant because acceleration = F/M.
Is it true that when you drop from a branch to the ground below, you pull upward on Earth? If so, then why is the acceleration of Earth not noticed?
Yes, it's true. The Earth can't pull you downward without you simultaneously pulling Earth upward. The acceleration of Earth is negligibly small, and not noticed, due to its enormous mass.
When a pair of vectors are at right angles, is the resultant always greater in magnitude than either of the vectors separately?
Yes. When a pair of vectors are at right angles, the resultant is always greater than either of the vectors separately.
parallelogram rule
a rule or regulation used to find the resultant of two vectors through construction of a parallelogram. The parallelogram has two adjacent sides or edges that represent the directions and magnitudes of the vectors.
A lead-filled tennis ball and a regular tennis ball are dropped from the top of a tall building at the same time. Air drag does affect motion. Which reaches the ground first? a) The lead-filled one. b) The regular one. c) They both reach the ground at the same time. d) No way to say.
a) The lead-filled one.
During each second of free fall, the speed of an object: a) increases by the same amount. b) changes by increasing amounts each second. c) remains constant. d) doubles each second.
a) increases by the same amount.
Mass is most closely related to: a) inertia. b) weight. c) volume. d) location.
a) inertia
A lead-filled tennis ball and a regular tennis ball are dropped from the top of a tall building. Air drag does affect motion. The ball that experiences the greater amount of air drag is the: a) lead-filled one. b) regular one. c) Neither, for both experience the same amount of air resistance. d) No way to say.
a) lead-filled one Explanation: The faster ball of the same size experiences more air drag!
An object with a mass of 1 kilogram on Earth: a) weighs less on the Moon. b) weigh the same on the Moon. c) weighs more on the Moon. d) weighs the same everywhere.
a) weighs less on the Moon
Nellie Newton hangs motionless by one hand from a clothesline. Which side of the line, a or b, has the greater a. horizontal component of tension? b. vertical component of tension? c. tension?
a. horizontal component of tension - b. vertical component of tension - side a c. tension - side a
How many forces are required for an interaction?
at least two
Use Newton's second law to answer this question: The acceleration of a vertically thrown ball at the top of its path is: a) 0. b) 10 m/s2. c) between 0 and 10 m/s2. d) dependent on the initial speed of the ball.
b) 10 m/s2. Explanation: This question is a toughie for most people. At the top gravity still acts, so there's a force on it. It still has mass. So in accord with a = F/m, a cannot be 0 as is popularly and wrongly asserted.
A motorcycle undergoes acceleration when: a) ΣF = 0. b) a nonzero net force acts on it. c) it is in equilibrium. d) All of these.
b) a nonzero net force acts on it.
When your mass increases, your weight: a) may remain the same. b) also increases. c) decreases. d) transforms to greater volume.
b) also increases
As mass is added to a pushed object, its acceleration: a) increases. b) decreases. c) remains constant. d) quickly reaches zero.
b) decreases Explanation: Let the equation for Newton's second law guide your answers! More mass means less acceleration.
An object with a mass of 1 kilogram on Earth: a) has less mass on the Moon. b) has the same mass on the Moon. c) has more mass on the Moon. d) weighs the same everywhere.
b) has the same mass on the Moon
For a given force, acceleration and mass are: a) directly proportional to each other. b) inversely proportional to each other. c) not related. d) two words for the same concept.
b) inversely proportional to each other.
When we say that 1 kilogram weighs 10 N, we mean that: a) 1 kg is10N. b) it's true at Earth's surface. c) it's true everywhere. d) mass and weight are one and the same.
b) it's true at Earth's surface.
A cart is pushed and undergoes a certain acceleration. If the force is held constant and the mass of the cart doubles, its acceleration would be: a) one-quarter. b) one-half. c) the same. d) nearly but not quite twice.
b) one-half
The force of friction between two surfaces can act: a) only when the surfaces move relative to each other. b) whether or not the surfaces move relative to each other. c) even when the surfaces are far apart and not touching. d) only over microscopic distances.
b) whether or not the surfaces move relative to each other.
The force of gravity acting on a 2-kg melon is: a) 2kg. b) 10N. c) 20N. d) more than 20 N.
c) 20 N
The amount of air resistance that acts on a wingsuit flyer (and a flying squirrel) depends on the flyer's: a) area. b) speed. c) area and speed. d) acceleration.
c) area and speed
A cart is pushed and undergoes a certain acceleration. If it were pushed with twice the force while its mass doubles, its acceleration would be: a) one-quarter. b) one-half. c) the same. d) nearly but not quite double.
c) the same Explanation: Let the equation for Newton's second law, a = F/m, guide your answer. The ratios F/m and 2F/2m are the same. So acceleration is the same either way.
The force of air friction (air drag) against a falling sack of potatoes: a) acts upward. b) increases with increased area. c) increases with increased speed. d) All of the above.
d) All of the above
When a net force acts on an object, its acceleration depends on the object's: a) initial speed. b) volume. c) weight. d) mass.
d) mass.
The reason a 10-kg rock falls no faster than a 5-kg rock in free fall is that: a) the 10-kg rock has greater acceleration. b) the 5-kg rock has greater acceleration. c) the force of gravity is the same for both. d) the force/mass ratio is the same for both.
d) the force/mass ratio is the same for both.
Which is more likely to break - a hammock stretched tightly between a pair of trees or one that sags more when you sit on it?
the hammock that is stretched tightly
Does a baseball bat slow down when it hits a ball? Defend your answer.
yes The ball's momentum changes when it's hit. To impart this momentum change to the ball, the bat is going to lose momentum, and when it does so, it slows down.