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You drop a rock off a bridge. When the rock has fallen 4m, you drop a second rock. As the two rocks continue to call, what happens to their velocities?
Both increase at the same rate

You are pushing a heavy box on a rough floor. When you are initially pushing the box an it is accelerating?
The force you exert on the box is equal to the force pushing back on you.

The normal force on an extreme skier descending a steep slope (inclined plane) can be zero if?
 He leaves the slope
 The slope vertical is 90 degrees

Is weight a force or a mass?
Force

What are the SI units for acceleration?
m/s^2

What are the SI units for velocity?
m/s

what are the SI units for radius?
m

What is the equation for acceleration with radius and velocity?
a=v^2/r

You are driving down the highway and another car moving in the same direction passes you. At the instant the car passes you, which quantity is the is the same for both?
Position

What is the equation for force?
F=ma

Is an astroid massless in space?
no

Is an astroid weightless in space?
Yes

What does the slope on the position vs. time graph represent?
Velocity

What is the correct equation for constant velocity?
v=Delta x/Delta t

If a baseball is thrown strait up, does it accelerate on the way up? On the way down?

Does a person riding a Ferris wheel accelerate?
 yes
 The velocity and acceleration is directed to the middle of the circle

What is the equation for constant acceleration?
a=delta v/delta t

The acceleration was positive for the “push.” What was the direction (sign) of the push from the force of your hand causing acceleration?
+

The acceleration was negative between the “push” and the “stop,” including at the top. What is the direction (sign) of the component of the gravitational force causing the acceleration?


The acceleration was positive for the “stop.” What was the direction (sign) of the push from the force of the catch causing the acceleration.
+

Is distance a vector?
Yes

Is Displacement a vector?
Yes


Is Velocity a vector?
Yes

Is acceleration a vector?
Yes

Is the resultant seem to be the same no matter which order you add the vectors?
Yes

What is sin theta
sin theta = opp/hyp

What is Newtons first law?
 The law of inertia
 An object in motion will stay in motion unless acted on by an outside force

What is Newtons second law?
F=ma

What is Newtons third law?
Every action causes an equal and opposite reaction.

Does a car speedometer measure speed, velocity or both?
Speed, velocity is a vector which needs direction, the car doesn’t care what direction.

When an object move with constant velocity, does its average velocity during any time interval differ from its instantaneous velocity at any instant?
When an object moves with constant velocity, the average velocity and the instantaneous velocity are the same at all times.

If one object has greater speed than a second object does the first object necessarily have a greater acceleration? Explain and use examples.
No, if one object has a greater speed than a second object, it does not necessarily have a greater acceleration. For example, consider a speeding car, traveling at constant velocity, which passes a stopped police car. The police car will accelerate from rest to try to catch the speeder. The speeding car has a greater speed than the police car (at least initially!), but has zero acceleration. The police car will have an initial speed of zero, but a large acceleration

Can an object have a northward velocity and a southward acceleration? Explain
Yes, for example, a car that is traveling northward and slowing down has a northward velocity and a southward acceleration.

Can an object be increasing in speed as its acceleration decreases? If so give an example. If not explain.
Yes. Remember that acceleration is a change in velocity per unit time, or a rate of change in velocity. So, velocity can be increasing while the rate of increase goes down. For example, suppose a car is traveling at 40 km/h and a second later is going 50 km/h. One second after that, the car's speed is 55 km/h. The car's speed was increasing the entire time, but its acceleration in the second time interval was lower than in the first time interval.

Give an example where both the velocity and acceleration are negative.
Both velocity and acceleration are negative in the case of a car traveling in the negative xdirection and speeding up. If the upward direction is chosen as +y, a falling object has negative velocity and negative acceleration.

As a freely falling object speeds up, what is happening to its acceleration due to gravitydoes it increase decrease or stay the same? (a)
If air resistance is negligible, the acceleration of a freely falling object stays the same as the object falls toward the ground. (Note that the object's speed increases, but since it increases at a constant rate, the acceleration is constant.)

You travel from point A to point B in a car moving at a constant speed of 70km/hr. Then you travel the same distance from point B to point C, moving at a constant speed of 90km/hr. Is your average speed for the entire trip from A to C 80km/hr? Explain why or why not.
Average speed is the displacement divided by the time. If the distances from A to B and from B to C are equal, then you spend more time traveling at 70 km/h than at 90 km/h, so your average speed should be less than 80 km/h. If the distance from A to B (or B to C) is x, then the total distance traveled is 2x. The total time required to travel this distance is x/70 plus x/90

Which on of these motions is not at constant acceleration; a rock falling from a cliff, an elevator moving from the second floor to the fifth floor making stops along the way, a dish resting on the table?
A rock falling from a cliff has a constant acceleration IF we neglect air resistance. An elevator moving from the second floor to the fifth floor making stops along the way does NOT have a constant acceleration. Its acceleration will change in magnitude and direction as the elevator starts and stops. The dish resting on a table has a constant acceleration (zero)

Can an object have zero velocity and nonzero acceleration the same time? give examples.
Yes. Anytime the velocity is constant, the acceleration is zero. For example, a car traveling at a constant 90 km/h in a straight line has nonzero velocity and zero acceleration.

Can an object have a varying speed if its velocity is constant? Can it have varying velocity if its speed is
constant? If yes, give examples in each case.
If the velocity of an object is constant, the speed must also be constant. (A constant velocity means that the speed and direction are both constant.) If the speed of an object is constant, the velocity CAN vary. For example, a car traveling around a curve at constant speed has a varying velocity, since the direction of the velocity vector is changing.

One car travels due east at 40 km/h, and a second car travels north at 40 km/h. Are their velocities equal? Explain.
No. Velocity is a vector quantity, with a magnitude and direction. If two vectors have different directions, they cannot be equal.

Can you conclude that a car is not accelerating if its speedometer indicates a steady 60 km/h?
No. The car may be traveling at a constant speed of 60 km/h and going around a curve, in which case it would be accelerating.

Can you give several examples of an object's motion in which a great distance is traveled but the displacement is zero?
Automobile races that begin and end at the same place; a roundtrip by car from New York to San Francisco and back; a balloon flight around the world.

Can the displacement vector for a particle moving in two dimensions ever be longer than the length of path traveled by the particle over the same time interval? Can it ever be less? Discuss.
The length of the displacement vector is the straightline distance between the beginning point and the ending point of the trip and therefore the shortest distance between the two points. If the path is a straight line, then the length of the displacement vector is the same as the length of the path. If the path is curved or consists of different straight line segments, then the distance from beginning to end will be less than the path length. Therefore, the displacement vector can never be longer than the length of the path traveled, but it can be shorter.

During baseball practice, a batter hits a very high fly ball and then runs in a straight line and catches it. Which had the greater displacement, the player or the ball?
The player and the ball have the same displacement.

If V = V1 + V2, is V necessarily greater than V1 and/or V2? Discuss.
V is the magnitude of the vector V ; it is not necessarily larger than the magnitudes V1 and V2. For
instance, if V1 and V2 have the same magnitude as each other and are in opposite directions, then V 12
is zero.

Two vectors have length V1 = 3.5 km and V2 = 4.0 km. What are the maximum and minimum magnitudes of their vector sum?
The maximum magnitude of the sum is 7.5 km, in the case where the vectors are parallel. The minimum magnitude of the sum is 0.5 km, in the case where the vectors are antiparallel.

Can two vectors, of unequal magnitude, add up to give the zero vector? Can three unequal vectors? Under what conditions?
No. The only way that two vectors can add up to give the zero vector is if they have the same magnitude and point in exactly opposite directions. However, three vectors of unequal magnitudes can add up to the zero vector. As a onedimensional example, a vector 10 units long in the positive x direction added to two vectors of 4 and 6 units each in the negative x direction will result in the zero vector. In two dimensions, consider any three vectors that when added form a triangle.

Can the magnitude of a vector ever (a) equal, or (b) be less than, one of its components?
(a) Yes. In three dimensions, the magnitude of a vector is the square root of the sum of the squares of the components. If two of the components are zero, the magnitude of the vector is equal to the magnitude of the remaining component.
(b) No.

Can a particle with constant speed be accelerating? What if it has constant velocity?
Yes. A particle traveling around a curve while maintaining a constant speed is accelerating because its direction is changing. A particle with a constant velocity cannot be accelerating, since the velocity is not changing in magnitude or direction.

Does the odometer of a car measure a scalar or a vector quantity? What about the speedometer?
The odometer and the speedometer of the car both measure scalar quantities (distance and speed, respectively).

A child wishes to determine the speed a slingshot imparts to a rock. How can this be done using only a meter stick, a rock, and the slingshot?
Launch the rock with a horizontal velocity from a known height over level ground. Use the equations for projectile motion in the ydirection to find the time the rock is in the air. (Note that the initial velocity has a zero ycomponent.) Use this time and the horizontal distance the rock travels in the equation for xdirection projectile motion to find the speed in the xdirection, which is the speed the slingshot imparts. The meter stick is used to measure the initial height and the horizontal distance the rock travels.

In archery, should the arrow be aimed directly at the target? How should your angle of aim depend on the distance to the target?
No. The arrow will fall toward the ground as it travels toward the target, so it should be aimed above the target. Generally, the farther you are from the target, the higher above the target the arrow should be aimed, up to a maximum launch angle of 45o. (The maximum range of a projectile that starts and stops at the same height occurs when the launch angle is 45o.)

A projectile is launched at an upward angle of 30° to the horizontal with a speed of 30 m/s. How does the horizontal component of its velocity 1.0 s after launch compare with its horizontal component of velocity 2.0 s after launch, ignoring air resistance?
As long as air resistance is negligible, the horizontal component of the projectile's velocity remains constant until it hits the ground. It is in the air longer than 2.0 s, so the value of the horizontal component of its velocity at 1.0 s and 2.0 s is the same.

A projectile has the least speed at what point in its path?
A projectile has the least speed at the top of its path. At that point the vertical speed is zero. The horizontal speed remains constant throughout the flight, if we neglect the effects of air resistance.

It was reported in World War I that a pilot flying at an altitude of 2km caught in his bare hands a bullet fired at the plane! Using the fact that a bullet slows down considerably due to air resistance, explain how this incident
occurred.
If the bullet was fired from the ground, then the ycomponent of its velocity slowed considerably by the time it reached an altitude of 2.0 km, because of both acceleration due to gravity (downward) and air resistance. The xcomponent of its velocity would have slowed due to air resistance as well. Therefore, the bullet could have been traveling slowly enough to be caught!

Two cannonballs, A and B, are fired from the ground with
identical initial speeds, but with θA larger than θB. (a) Which cannonball reaches a higher elevation? (b) Which stays longer in the air? (c) Which travels farther?
(a) Cannonball A, because it has a larger initial vertical velocity component.(b) Cannonball A, same reason.
(c) It depends. If θA < 45o, cannonball A will travel farther. If θB > 45o, cannonball B will travel
farther. If θA > 45o and θB < 45o, the cannonball whose angle is closest to 45o will travel farther.

A person sitting in an enclosed train car, moving at constant velocity, throws a ball straight up into the air in her refer ence frame, (a) Where does the ball land? What is your answer if the car (b) accelerates, (c) decelerates, (d) rounds a curve, (e) moves with constant velocity but is open to the air?
(a) The ball lands back in her hand
(b) The ball lands behind her hand.
(c) The ball lands in front of her hand.
(d) The ball lands beside her hand, to the outside of the curve.
(e) The ball lands behind her hand, if air resistance is not negligible.

If you are riding on a train that speeds past another train moving in the same direction on an adjacent track, it appears that the other train is moving backward. Why?
This is a question of relative velocity. From the point of view of an observer on the ground, both trains are moving in the same direction (forward), but at different speeds. From your point of view on the faster train, the slower train (and the ground) will appear to be moving backward. (The ground will be moving backward faster than the slower train!)

Two rowers, who can row at the same speed in still water, set off across a river at the same time. One heads straight across and is pulled downstream somewhat by the current. The other one heads upstream at an angle so as to arrive at a point opposite the starting point. Which rower reaches the opposite side first?
The time it takes to cross the river depends on the component of velocity in the direction straight across the river. Imagine a river running to the east and rowers beginning on the south bank. Let the still water speed of both rowers be v. Then the rower who heads due north (straight across the river) has a northward velocity component v. The rower who heads upstream, though, has a northward velocity component of less than v. Therefore, the rower heading straight across reaches the opposite shore first. (However, she won't end up straight across from where she started!)

Why does a child in a wagon seem to fall backward when you give the wagon a sharp pull forward?
When you give the wagon a sharp pull forward, the force of friction between the wagon and the child acts on the child to move her forward. But the force of friction acts at the contact point between the child and the wagon  either the feet, if the child is standing, or her bottom, if sitting. In either case, the lower part of the child begins to move forward, while the upper part, following Newton's first law (the law of inertia), remains almost stationary, making it seem as if the child falls backward.

If you stand motionless under an umbrella in a rainstorm where the drops fall vertically you remain relatively dry. However, if you start running, the rain begins to hit your legs even if they remain under the umbrella. Why?
As you run forward, the umbrella also moves forward and stops raindrops that are at its height above the ground. Raindrops that have already passed the height of the umbrella continue to move toward the ground unimpeded. As you run, you move into the space where the raindrops are continuing to fall (below the umbrella). Some of them will hit your legs and you will get wet.

A box rests on the (frictionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton's laws, as seen (a) by Andrea standing on the ground beside the truck, and (b) by Jim who is riding on the truck (Fig. 427).
(a) Andrea, standing on the ground beside the truck, will see the box remain motionless while the truck accelerates out from under it. Since there is no friction, there is no net force on the box and it will not speed up.
(b) Jim, riding on the truck, will see the box appear to accelerate backwards with respect to his frame of reference, which is not inertial. (Jim better hold on, though; if the truck bed is frictionless, he too will slide off if he is just standing!)

If the acceleration of an object is zero, are no forces acting
on it? Explain.
If the acceleration of an object is zero, the vector sum of the forces acting on the object is zero (Newton's second law), so there can be forces on an object that has no acceleration. For example, a book resting on a table is acted on by gravity and the normal force, but it has zero acceleration, because the forces are equal in magnitude and opposite in direction.

If an object is moving, is it possible for the net force acting on it to be zero?
Yes, the net force can be zero on a moving object. If the net force is zero, then the object's acceleration is zero, but its velocity is not necessarily zero. [Instead of classifying objects as "moving" and "not moving," Newtonian dynamics classifies them as "accelerating" and "not accelerating." Both zero velocity and constant velocity fall in the "not accelerating" category.]

Only one force acts on an object. Can the object have zero acceleration? Can it have zero velocity? Explain.
If only one force acts on an object, the object cannot have zero acceleration (Newton's second law). It is possible for the object to have zero velocity, but only for an instant. For example (if we neglect air resistance), a ball thrown up into the air has only the force of gravity acting on it. Its speed will decrease while it travels upward, stop, then begin to fall back to the ground. At the instant the ball is at its highest point, its velocity is zero.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b)If so, what exerts the force?
(a) Yes, there must be a force on the golf ball (Newton's second law) to make it accelerate upward. (b) The pavement exerts the force (just like a "normal force").

If you walk along a log floating on a lake, why does the log move in the opposite direction?
As you take a step on the log, your foot exerts a force on the log in the direction opposite to the direction in which you want to move, which pushes the log "backwards." (The log exerts an equal and opposite force forward on you, by Newton's third law.) If the log had been on the ground, friction between the ground and the log would have kept the log from moving. However, the log is floating in water, which offers little resistance to the movement of the log as you push it backwards.

Why might your foot hurt if you kick a heavy desk or a wall?
When you kick a heavy desk or a wall, your foot exerts a force on the desk or wall. The desk or wall exerts a force equal in magnitude on your foot (Newton's third law). Ouch!

When you are running and want to stop quickly, you must decelerate quickly, (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experi ence) the maximum rate of deceleration of a person running at top speed to come to rest.
(a)
The force that causes you to stop quickly is the force of friction between your shoes and the ground (plus the forces your muscles exert in moving your legs more slowly and bracing yourself).
(b) If we assume the top speed of a person to be around 6 m/s (equivalent to about 12 mi/h, or a 5 minute mile), and if we assume that it take 2 s to stop, then the maximum rate of deceleration is about 3 m/s2.

a) Why do you push down harder on the pedals of a bicycle when first starting out than when moving at constant speed? (b) Why do you need to pedal at all when cycling at constant speed?
(a) When you first start riding a bicycle you need to exert a strong force to accelerate the bike and yourself. Once you are moving at a constant speed, you only need to exert a force to equal the opposite force of friction and air resistance.
(b) When the bike is moving at a constant speed, the net force on it is zero. Since friction and air resistance are present, you would slow down if you didn't pedal to keep the net force on the bike (and you) equal to zero.

A father and his young daughter are ice skating. They face each other at rest and push each other, moving in opposite directions. Which one has the greater final speed?
The father and daughter will each have the same magnitude force acting on them as they push each other away (Newton's third law). If we assume the young daughter has less mass than the father, her acceleration should be greater (a = F/m). Both forces, and therefore both accelerations, act over the same time interval (while the father and daughter are in contact), so the daughter's final speed will be greater than her dad's.

Suppose that you are standing on a cardboard carton that just barely supports you. What would happen to it if you jumped up into the air? It would (a) collapse; (b) be unaf fected; (c) spring upward a bit; (d) move sideways.
The carton would collapse (a). When you jump, you accelerate upward, so there must be a net upward force on you. This net upward force can only come from the normal force exerted by the carton on you and must be greater than your weight. How can you increase the normal force of a surface on you? According to Newton's third law, the carton pushes up on you just as hard as you push down on it. That means you push down with a force greater than your weight in order to accelerate upwards. If the carton can just barely support you, it will collapse when you exert this extra force.

A stone hangs by a fine thread from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 428). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.
If a person gives a sharp pull on the dangling thread, the thread is likely to break below the stone. In the short time interval of a sharp pull, the stone barely begins to accelerate because of its great mass (inertia), and so does not transmit the force to the upper string quickly. The stone will not move much before the lower thread breaks. If a person gives a slow and steady pull on the thread, the thread is most likely to break above the stone because the tension in the upper thread is the applied force plus the weight of the stone. Since the tension in the upper thread is greater, it is likely to break first.

The force of gravity on a 2kg rock is twice as great as that on a 1kg rock. Why then doesn't the heavier rock fall faster?
The force of gravity on the 2kg rock is twice as great as the force on the 1kg rock, but the 2kg rock has twice the mass (and twice the inertia) of the 1kg rock. Acceleration is the ratio of force to mass (a = F/m, Newton's second law), so the two rocks have the same acceleration.

Would a spring scale carried to the Moon give accurate results if the scale had been calibrated on Earth, (a) in pounds, or (b) in kilograms?
A spring responds to force, and will correctly give the force or weight in pounds, even on the Moon. Objects weigh much less on the Moon, so a spring calibrated in kilograms will give incorrect results (by a factor of 6 or so).

You pull a box with a constant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the hori zontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.
The acceleration of the box will (c) decrease. Newton's second law is a vector equation. When you pull the box at an angle θ, only the horizontal component of the force, Fcosθ, will accelerate the box horizontally across the floor.

When an object falls freely under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton's third law the object exerts an equal and opposite force on the Earth. Does the Earth move?
The Earth actually does move as seen from an inertial reference frame. But the mass of the Earth is so great, the acceleration is undetectable (Newton's second law).

Compare the effort (or force) needed to lift a 10kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2kg object horizontally with a given speed on the Moon and on Earth.
Because the acceleration due to gravity on the Moon is less than it is on the Earth, an object with a mass of 10 kg will weigh less on the Moon than it does on the Earth. Therefore, it will be easier to lift on the Moon. (When you lift something, you exert a force to oppose its weight.) However, when throwing the object horizontally, the force needed to accelerate it to the desired horizontal speed is proportional to the object's mass, F = ma. Therefore, you would need to exert the same force to throw the 2kg object on the Moon as you would on Earth.

Which of the following objects weighs about 1 N: (a) an apple, (b) a mosquito, (c) this book, (d) you?
A weight of 1 N corresponds to 0.225 lb. That's about the weight of (a) an apple.

According to Newton's third law, each team in a tug of war (Fig. 429) pulls with equal force on the other team. What, then, determines which team will win?
Newton's third law involves forces on different objects, in this case, on the two different teams. Whether or not a team moves and in what direction is determined by Newton's second law and the net force on the team. The net force on one team is the vector sum of the pull of the other team and the friction force exerted by the ground on the team. The winning team is the one that pushes hardest against the ground (and so has a greater force on them exerted by the ground).

Whiplash sometimes results from an automobile accident when the victim's car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?
The victim's head is not really thrown backwards during the car crash. If the victim's car was initially at rest, or even moving forward, the impact from the rear suddenly pushes the car, the seat, and the person's body forward. The head, being attached by the somewhat flexible neck to the body, can momentarily remain where it was (inertia, Newton's first law), thus lagging behind the body.

When you stand still on the ground, how large a force does the ground exert on you? Why doesn't this force make you rise up into the air?
When you stand still on the ground, two forces act on you: your weight downward, and the normal force exerted upward by the ground. You are at rest, so Newton's second law tells you that the normal force must equal your weight, mg. You don't rise up off the ground because the force of gravity acts downward, opposing the normal force.

A bear sling, Fig. 430, is used in some national parks for placing backpackers' food out of the reach of bears. Explain why the force needed to pull the backpack up increases as the backpack gets higher and higher. Is it possible to pull the rope hard enough so that it doesn't sag at all?
No. In order to hold the backpack up, the rope must exert a vertical force equal to the backpack's weight, so that the net vertical force on the backpack is zero. The force, F, exerted by the rope on each side of the pack is always along the length of the rope. The vertical component of this force is Fsinθ, where θ is the angle the rope makes with the horizontal. The higher the pack goes, the smaller θ becomes and the larger F must be to hold the pack up there. No matter how hard you pull, the rope can never be horizontal because it must exert an upward (vertical) component of force to balance the pack's weight.

Mary exerts an upward force of 40N to hold a bag of groceries. Describe the "reaction" force (Newton's third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.
(a) The reaction force has a magnitude of 40 N.
(b) It points downward.
(c) It is exerted on Mary's hands and arms.
(d) It is exerted by the bag of groceries.

