group work concepts
A cyclist goes around a level, circular track at constant speed. Do you agree or disagree with the following statement? "Since the cyclist's speed is constant, her acceleration is zero." Explain.
: I disagree! First of all, speed is a scalar while acceleration is a vector, so relating the two doesn't make much sense. Secondly, even with constant speed, if the cyclist is traveling in a circle, the direction of her velocity constantly changes. If velocity changes, there must be a nonzero acceleration
The following Figure shows the velocity-versus-time graphs for two objects A and B. Two students are asked to tell stories that correspond to the motion of the objects. Student 1 says, "The graph represents two cars traveling in opposite directions that definitely pass each other." Student 2 says, "No, I think they could be two rocks thrown vertically from a bridge; rock A is thrown upward and rock B is thrown downward." Is Student 1 correct, Student 2 correct, are both correct, or are neither correct? Explain.
According to the graph, Object A starts with a negative velocity (it is moving in the negative direction) but switches to a positive velocity within a short amount of time. In contrast, Object B starts with a positive velocity (it is moving in the positive direction) but switches to a negative velocity a fair bit of time later. Student 2 is not correct because Rock A starts out with a negative velocity; therefore it starts out moving down, not up as the student says. (Similarly, Rock B starts with a positive velocity, so it must be traveling upward to start, contradicting the student's statement.) Student 2 is thus not correct. (Moreover, the graph specifically shows the x-component of the velocity versus time, which should be 0 if the rock is thrown straight up or straight down.) Student 1 is closer, but still incorrect. Firstly, the velocities of A and B are not perfectly opposite. (Sometimes they are, as when one is positive and the other is negative, and sometimes they aren't, as when both are positive.) Diving in a bit deeper, though: For horizontal motion, Object A could be a car traveling to the left (in the negative direction), slowing until it stops, turns around, and starts speeding up in the positive direction. Object B could be a car traveling to the right (in the positive direction), slowing until it stops, turns around, and starts speeding up in the negative direction. The cars could pass each other, but we don't know that they actually do because we are not given any information about their positions (They could be on the opposite side of the world from each other.) The crossing point in the graph merely says that at that point in time, A and B have the same positive velocity. Since Student 1 says that the cars "definitely" pass each other, Student 1 is also incorrect.
Anna is running to the right, as shown in the Figure. Balls 1 and 2 are thrown toward her by friends standing on the ground. According to Anna, both balls are approaching her at the same speed. Which ball was thrown with the faster speed? Or were they thrown with the same speed? Explain.
Anna is running to the right, towards Ball 2, which is headed towards her. This means that Anna will perceive the ball as moving faster than it actually is, because they are moving towards each other. In contrast, Anna is running away from Ball 1, which is moving towards her, so she will perceive the ball as moving slower than it actually is. Since Anna sees the speed of the two balls as identical, Ball 1 is in reality faster than her observation while Ball 2 is moving slower than her observation. Thus Ball 1 was thrown with a faster speed than Ball 2.
On a roller coaster loop-the-loop the riders are upside-down at the top of the loop, while on a Ferris wheel the riders are upright at the top. Suppose a Ferris wheel and the loop of a roller coaster have the same diameter. If riders on each have the same magnitude of apparent weight at the top, which rider is moving faster? Explain. (Assume that the mass of the rider in the loop is the same as the mass of the rider in the Ferris wheel.)
First, note that the apparent weight is the normal force between the rider and their support, so I will use "normal force" going forward, noting that if the apparent weights are the same in the two cases, then the normal forces must also be the same. For the loop-theloop, the rider is upside-down at the top of the loop, so the forces acting on the rider are the force of gravity downwards and the normal force of the seat on the rider, also downwards. The radial acceleration also points down at this precise point, towards the center of the loop. By Newton's 2nd Law, the acceleration will depend on the addition of the force of gravity and the normal force. Since the radial acceleration is proportional to the speed squared, the speed will then depend on the addition of the force of gravity and the normal force. In contrast, for the Ferris wheel, the normal force on the person will point up, while the force of gravity will still point down. The radial acceleration is still down, towards the center of the Ferris wheel. This means that the acceleration, and therefore the Ferris wheel speed squared, is proportional to the force of gravity minus the normal force. Since in the loop case we're adding in the normal force and in the Ferris wheel case we're subtracting it, the speed of the rider in the loop-the-loop must be the greater speed.
A person trying to throw a ball as far as possible will run forward during the throw. Explain why this increases the distance of the throw.
If a person stands still to throw a ball, the x-component of the velocity will only be equal to what the person is physically capable of throwing. However, if the person runs forward while throwing the ball, the ball starts out with some positive velocity which is added to the x-component of the velocity of the throw itself, increasing the initial speed of the ball as it leaves the person's hand and increasing the distance of the throw.
You are standing on a straight stretch of road and watching the motion of a bicycle; you choose your position as the origin. At one instant, the position of the bicycle is negative and its velocity is positive. Is the bicycle getting closer to you or farther away? Explain.
The bicycle is getting closer to me. If I choose the area to my right as the positive axis, and the area to my left as the negative axis (with me at the origin), then the bike starts to my left. The bike has a positive velocity; this means it is moving in the positive direction, which is to the right, towards me.
Suppose you are holding a box in front of you and away from your body by squeezing its sides. What is the force that is holding the box up (the force that is opposite to the force of gravity on the box)? Would you still be able to hold up the box if instead it was a slightly melted block of ice (i.e. had a very slippery surface)? Explain.
The force of static friction between your hands and the box holds the box up. (The squeezing force provides the normal force on which the friction force is based.) If there were no friction between your hands and the box, no matter how hard you squeezed, it would fall due to the force of gravity acting on it unopposed. Trying to hold a slippery block of ice is a great example of this situation: the coefficient of friction between your hands and the ice is too low to counteract the force of gravity, so the block of ice will fall out of your grasp.
Janelle stands on a balcony, two stories above Michael. She throws Ball 1 straight up and Ball 2 straight down, but both with the same initial speed of 3 m/s. Which ball, if either, is moving faster when it passes Michael? Explain. (Hint: What is the speed of Ball 1 when it passes Janelle on the way down, and why?)
The speed of Ball 1 when it passes Janelle on the way down is 3 m/s because she threw it upward at 3 m/s, it reached a maximum height at which the velocity was zero, and then it started accelerating downward. The trip up and down is symmetrical because the acceleration is the same -9.8 m/s2 for the entire trip. This means that when Ball 1 passes Janelle on the way down, it is effectively in the same situation as Ball 2 when it was thrown straight down at 3 m/s. Since the acceleration is the same in both cases (-9.80 m/s2 ), and the distance traveled to Michael is the same, the balls must increase in speed by the same amount. Therefore both balls pass Michael at the same speed. (Though they do not pass him at the same point in time!)
When your car accelerates away from a stop sign, you feel like you're being pushed back into your seat. Can you identify the force that is pushing you back? If not, why do you feel like you're being pushed back?
There is no force "pushing you back". What's happening is that the car is running into you. You and the car are both at rest at the stop sign. Then the car starts to move forward. Though you are in the car, you are not the car itself, so there is a slight delay between the car starting forward and the car catching you to move you forward. Since your experience is from your point of view (you are the origin of your universe), you perceive the act of the car catching you from behind as being pushed back into the seat.
A ball is dropped from the roof of a tall building and students in a physics class are asked to sketch a motion diagram for this situation. A student submits the diagram shown in the Figure. (The dots indicate the location of the ball, and the numbers indicate the time in seconds since the ball was dropped.) Is the diagram correct? Explain your answer.
This diagram is not correct. In this diagram, the ball falls quickly at first and then falls more and more slowly because the distance between the time points is getting smaller. The correct motion diagram should show the opposite behavior: the ball should fall slowly at first (a shorter distance between subsequent time points) and then fall faster and faster (an increasing distance between subsequent time points).
A mountain climber's weight is slightly less on the top of a tall mountain than at the base, though his mass is the same. Why?
While the mountain climber's mass remains constant, the distance of the mountain climber from the center of the Earth increases by a non-negligible amount when he is on a tall enough mountain. By Newton's Law of Universal Gravitation, the farther apart the centers of the two objects being considered (the mountain climber and the Earth), the less the force of gravity acting between those two objects. Since the force of gravity acting on an object is its weight, the mountain climber weighs less on top of the mountain than he does at the base.
Can the normal force on an object be directed downward? If not, why not? If so, provide an example.
Yes! By Newton's 3rd Law, all forces come in pairs. Consider a box sitting on a table. With the box as the object of interest, there is a normal force upward on the box from the table. By Newton's 3rd Law, there is a force of equal magnitude but opposite direction acting on the table from the box. Thus, the normal force of the box on the table is directed downwards.
