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physics
particle physics

Questions and Answers of Particle Physics

(a) Is the collision in Figure 4.23 elastic, inelastic, or totally inelastic? How can you tell? (b) Verify your answer by comparing the initial kinetic energy of the two-cart system with the final
A \(0.2-\mathrm{kg}\) cart 1 initially at rest is struck by an identical cart 2 traveling at \(v_{2 x, i}=+0.5 \mathrm{~m} / \mathrm{s}\) along a low-friction track. After the collision, the velocity
Choose an appropriate closed system and make a bar diagram representing the energy conversions and transfers that occur when (a) a pan of water is heated on a propane burner, (b) a cyclist
Two carts, one of inertia \(m_{1}=0.25 \mathrm{~kg}\) and the other of inertia \(m_{2}=0.40 \mathrm{~kg}\), travel along a straight horizontal track with velocities \(v_{1 x, \mathrm{i}}=+0.20
A rubber ball of inertia \(m_{\mathrm{b}}=0.050 \mathrm{~kg}\) is fired along a track toward a stationary cart of inertia \(m_{\mathrm{c}}=0.25 \mathrm{~kg}\). The kinetic energy of the system after
A white car of inertia \(1200 \mathrm{~kg}\) that is moving at a speed of \(7.2 \mathrm{~m} / \mathrm{s}\) rear-ends a blue car of inertia \(1000 \mathrm{~kg}\) that is initially at rest. Immediately
A \(0.20-\mathrm{kg}\) steel ball is dropped into a ball of dough, striking the dough at a speed of \(2.3 \mathrm{~m} / \mathrm{s}\) and coming to rest inside the dough. If it were possible to turn
A \(0.25-\mathrm{kg}\) cart is held at rest against a compressed spring as in Figure \(5.8 a\) and then released. The cart's speed after it separates from the spring is \(2.5 \mathrm{~m} /
Consider an isolated object at rest in space. The object contains internal energy in some form or another. Is it-in principle-possible to convert the internal energy to kinetic energy so that the
Imagine squeezing a piece of foam with your hands. Choose an appropriate closed system and make a bar diagram representing the energy conversions and transfers that occur during the squeezing.
When you heat a pot of water on a gas stove, the water temperature increases until the water begins to boil. This change in thermal state from cool water to hot water is due to chemical energy from
An electric fan turns electrical energy into wind energy (a form of kinetic energy because it involves moving air). Suppose a blowing fan is suddenly unplugged. Even though the fan no longer receives
Moving sidewalks are commonplace at large airports, but you must use caution getting on and off them. What should you do to make the transition easy when stepping onto one of these sidewalks? When
A flying bug hits the helmet of a coasting bicyclist. (What kind of collision do you expect this to be?) Draw the momentum vectors for the bug and the bicyclist before and after the collision \((a)\)
The data in the table were recorded for two race cars, A and \(B\), driving down a straight stretch of track. Determine the average velocity of car B as measured by an observer in car A. Time (s) Car
An observer in the Earth reference frame observes cart A and cart B moving toward each other with the same speed until they collide and come to rest. Consider this event as seen by observer A moving
You are sitting, facing rearward, in the bed of a pickup truck and hop off while the truck is moving forward. When you land, do you move toward or away from the truck \((a)\) from the point of view
Two objects, A and B, of equal inertia approach each other with relative velocity \(\vec{v}_{\mathrm{AB}}\) and collide elastically. For each object, draw a velocity-versus-time graph for the
A woman standing beside a road sees a car accelerate from rest to \(30 \mathrm{~m} / \mathrm{s}\). Describe the car's motion as seen by the driver of a truck traveling in the same direction as the
On a long bus ride, you walk from your seat to the back of the bus to use the restroom. If the bus is driving at \(100 \mathrm{~km} / \mathrm{h}\), and you walk at \(2.0 \mathrm{~m} / \mathrm{s}\)
A pickup truck has several empty soda cans loose in the bed. Why do the cans roll forward in the bed when the truck slows down?
You drop your keys in a high-speed elevator going up at a constant speed. Do the keys accelerate faster toward the elevator floor than they would \((a)\) if the elevator were not moving?(b) if the
Train A, \(m_{\mathrm{A}}=150,000 \mathrm{~kg}\), is traveling west at \(60 \mathrm{~km} / \mathrm{h}\). Train B, \(m_{\mathrm{B}}=100,000 \mathrm{~kg}\), behind train A on the same track, is
A \(1000-\mathrm{kg}\) car traveling east at \(50 \mathrm{~km} / \mathrm{h}\) passes over the top of a hill and hits a \(3000-\mathrm{kg}\) truck stalled in the middle of the lane. The impact causes
You are riding a \(450-\mathrm{kg}\) horse at \(14.4 \mathrm{~km} / \mathrm{h}\) cast along a desert road. You have inertia equal to \(60.0 \mathrm{~kg}\). A police officer driving past (whom you
Two cars collide head-on on a busy street. An observer standing on the street witnesses the accident and calculates how much of the cars' initial kinetic energy went into deforming the cars upon
At an airport, two business partners both walk at \(1.5 \mathrm{~m} / \mathrm{s}\) from the gate to the main terminal, one on a moving sidewalk and the other on the floor next to it. The partner on
Do the laws of the universe change if the clocks in two inertial reference frames, \(A\) and \(B\), are not synchronized (in other words, if \(t_{\mathrm{A}}=t_{\mathrm{B}}+\Delta \tau\), where
You place a \(0.10-\mathrm{kg}\) sonic ranger on a low-friction track in front of a \(0.50-\mathrm{kg}\) cart to measure the cart's velocity in the Earth reference frame, which turns out to be
At the roller rink, two \(20-\mathrm{kg}\) girls accelerate toward each other until they are each moving at \(2.0 \mathrm{~m} / \mathrm{s}\) in the Earth reference frame. They then collide
Carts \(A\) and \(B\) are identical and are moving toward each other on a track. The speed of cart A is \(v\), while the speed of cart B is \(2 v\). In the Earth reference frame, the system of the
Two identical cars approach each other head-on while traveling at the same speed. What does an observer in the Earth reference frame measure for the speed of the zeromomentum reference frame of this
Is the kinetic energy of a system zero when measured from the zero-momentum reference frame for the system?
Two identical particles, A and B, collide elastically. In the zero-momentum reference frame, what can you say about the ratios of the final and initial speeds, \(v_{\mathrm{A}, \mathrm{f}} /
Figure P6.23 shows three identical carts placed on rails (so that they can slide easily left and right) and connected to one another by springs. There are two simple, symmetrical ways for this system
Consider two objects, A and B, of inertias \(m_{\mathrm{A}}\) and \(m_{\mathrm{B}} \gg m_{\mathrm{A}}\). If the two are moving at constant velocities with \(\vec{v}_{\mathrm{A}} eq
A \(4000-\mathrm{kg}\) dump truck is parked on a hill. The parking brake fails, and the truck rolls down the hill. It then coasts briefly along a horizontal stretch of road at \(36 \mathrm{~km} /
Object A has ten times the inertia of object B. They approach each other with relative velocity \(\vec{v}_{A B}\) and collide elastically. For each object, draw a velocity-versustime graph for the
In an elastic collision between a lightweight object and a heavy object, which one carries away more of the kinetic energy? Does the answer depend on the initial speeds? (Begin with the zero-momentum
When two identical objects traveling at the same speed collide head-on, an observer standing in the Earth reference frame sees both objects changing direction. Do observers in every inertial
You toss a ball into the air and note the time interval between the ball leaving your hand and reaching its greatest height above you. While you are doing this, a construction worker being lifted on
A student runs an experiment with two carts on a low-friction track. As measured in the Earth reference frame, cart 1 ( \(m=0.36 \mathrm{~kg}\) ) moves from left to right at \(1.0 \mathrm{~m} /
Notice that in Figure 6.12 the time intervals of the interaction are all the same, regardless of the reference frame shown. Is this true in all reference frames? Why or why not?Data from Figure 6.12
In a three-car crash, car A bumps into the back end of car \(B\), which then goes forward and bumps into the back end of car C. Is the distance that car B moves between the collisions the same in all
Riding up an escalator while staying on the same step for the whole ride takes \(30 \mathrm{~s}\). Walking up the same escalator takes \(20 \mathrm{~s}\). How long does it take to walk down the up
A woman is on a train leaving the station at \(4.0 \mathrm{~m} / \mathrm{s}\), while a friend waving goodbye runs alongside the car she's in. (a) If the friend is running at \(6.0 \mathrm{~m} /
Airline pilots who fly round trips know that their round-trip travel time increases if there is any wind. To see this, suppose that an airliner cruises at speed \(v\) relative to the air. (a) For a
The inertia of an object is \(m\) measured when the object is at rest in the Earth reference frame. According to Galilean relativity, what is its inertia measured by an observer moving past the
At what distance from the center of Earth is the center of mass of the Earth-Moon system?
(a) Determine the location of the center of mass of the system shown in Figure P6.38. All three disks are made of sheet metal of the same material, and the diameters are \(1.0 \mathrm{~m}, 2. 0
A boy and a girl are resting on separate rafts \(10 \mathrm{~m}\) apart in calm water when the girl notices a small beach toy floating midway between the rafts. The girl and her raft have twice the
The two cubes in Figure P6.40 have different inertias. The cubes are connected to each other by a spring, and a hammer strikes them in the two ways, \((a)\) and \((b)\), shown in the figure. Assuming
Determine the position of the center of mass of the baton shown in Figure P6.41, taking the origin of your coordinate axis to be \((a)\) the center of the larger ball, \((b)\) the center of the
The empty cubical box shown in Figure \(\mathrm{P} 6. 42\) has no top face; that is, the box is made up of only five square faces. If all five faces have the same inertia, at what height above the
How can you tell from the motion of the center of mass of an isolated system whether the reference frame from which the motion is measured is inertial?
Determine the center of mass of a pool cue whose diameter decreases smoothly from \(40 \mathrm{~mm}\) to \(10 \mathrm{~mm}\) over its \(1.40-\mathrm{m}\) length (Figure P6.44). Assume that the cue is
An object of inertia \(m_{1}\) collides totally inelastically with a stationary object of inertia \(m_{2}\). Plot the fraction of the kinetic energy lost as a function of \(m_{2} / m_{1}\) in the
A 3. 0-g particle is moving toward a stationary 7. 0-g particle at \(3.0 \mathrm{~m} / \mathrm{s}\). What percentage of the original kinetic energy is convertible to internal energy?
Think of a system of two objects of different inertias \(m_{1}
(a) Is there a reference frame in which the kinetic energy of a system is a minimum? If so, what is this reference frame? (b) Is there a reference frame in which the kinetic energy of a system is a
You hit a pitched baseball with a bat. In which reference frame is the translational (nonconvertible) kinetic energy greater: the reference frame in which the bat is at rest immediately before the
What is the ratio \(K_{1} / K_{2}\) when \(K_{1}\) is the kinetic energy converted to internal energy when two cars each initially traveling ar \(88 \mathrm{~km} / \mathrm{h}\) collide head-on and
A \(0.075-\mathrm{kg}\) disk initially at rest in the Earth reference frame is free to move parallel to a horizontal bar through a hole at the disk's center. The disk is struck face-on by a
Take the common case where a moving object of inertia \(m_{\text {moving }}\) collides with a stationary object of inertia \(m_{\text {rest }}\). (a) Show that the fraction of kinetic energy not
Ball 1 is moving toward you at \(10 \mathrm{~m} / \mathrm{s}\), and you decide to throw ball 2 at it to make it reverse its velocity. The balls collide head-on, and the coefficient of restitution for
Ball 1 from Problem 53 is moving away from you at \(5.0 \mathrm{~m} / \mathrm{s}\), and you decide to throw ball 2 at it to make it go faster. Onee again the balls collide head-on, and the
If the relative velocities are the same in both cases, which has more convertible kinetic energy: a collision between two objects each of inertia \(m\) or a collision between an object of inertia
After coming down a slope, a 60-kg skier is coasting northward on a level, snowy surface at a constant \(15 \mathrm{~m} / \mathrm{s}\). Her \(5.0-\mathrm{kg}\) cat, initially running southward at
You toss a \(0.40-\mathrm{kg}\) ball at \(9.0 \mathrm{~m} / \mathrm{s}\) to a \(14-\mathrm{kg}\) dog standing on an iced-over pond. The dog catches the ball and begins to slide on the ice. (a)
Instead of defining a reduced inertia \(\mu\) to characterize the convertible kinetic energy of a system, we could define a reduced velocity \(v_{\text {red }}\) as follows: For a system of two
You learned about the zero-momentum reference frame. You may be curious whether there is such a thing as a zero-energy reference frame. Does a zero-kinetic energy reference frame always exist, never
After a totally inelastic collision, the kinetic energy of an isolated system composed of two objects is zero. What was the momentum of the system in the same reference frame before the collision?
A mother penguin and her chick are on a flat, icy surface. The mother is lying at rest \(0.50 \mathrm{~m}\) from the edge of the water. The chick, which has one-fourth of its mother's inertia, is
A \(50-\mathrm{kg}\) ice skater moves across the ice at a constant speed of \(2.0 \mathrm{~m} / \mathrm{s}\). She is caught by her \(70-\mathrm{kg}\) partner, and then the pair continues to glide
In an inertial reference frame F, an orange of inertia \(m_{\text {orange }}\) and velocity \(\vec{v}_{\text {orange }}\) collides totally inelastically with an apple of inertia \(m_{\text {apple
A \(50-\mathrm{kg}\) meteorite moving at \(1000 \mathrm{~m} / \mathrm{s}\) strikes Earth. Assume the velocity is along the line joining Earth's center of mass and the meteor's center of mass. (a)
A \(0.20-\mathrm{kg}\) softball is traveling at a velocity of \(20 \mathrm{~m} / \mathrm{s}\) to the east relative to Earth. It collides head-on with a 0. 40 \(\mathrm{kg}\) rubber ball traveling at
Derive an expression showing that when an elastic collision between two objects is viewed from the zero momentum reference frame, the direction of the momentum of each object is reversed and the
Just as a car passes a school crossing guard, a child throws a toy from the back seat of the car toward his sister in the front seat. The toy is thrown at a speed of \(2.0 \mathrm{~m} / \mathrm{s}\)
A \(20-\mathrm{kg}\) child is sliding on an icy surface toward her mother at \(3.0 \mathrm{~m} / \mathrm{s}\). Her \(68-\mathrm{kg}\) mother starts toward her at \(2.0 \mathrm{~m} / \mathrm{s}\),
An \(80-\mathrm{kg}\) man is walking ar \(2.0 \mathrm{~m} / \mathrm{s}\). A \(10-\mathrm{kg}\) dog is running at five times that speed in the same direction. At what speed and in what direction
One rider is in a descending clevator that is accelerating to a stop. Another is in an elevator that is accelerating upward from rest. With their eyes closed, can the riders tell which of the two
You are in a noninertial reference frame observing two isolated objects of inertias \(m_{1}\) and \(m_{2}\) that move at constant speed relative to each other. What can you say about each
A bug of inertia \(m_{\mathrm{B}}\) collides with the windshield of a Mack truck of inertia \(m_{\mathrm{T}} \gg m_{\mathrm{B}}\) at an instant when the relative speed of the two is
A \(0.045-\mathrm{kg}\) golf ball moving at \(50 \mathrm{~m} / \mathrm{s}\) (measured in the Earth reference frame) collides inelastically with a 1. 8 \(\mathrm{kg}\), heavy-duty plastic flowerpot
Asteroid \(\mathrm{A} 1, m_{\mathrm{A} 1}=3.60 \times 10^{6} \mathrm{~kg}\), and asteroid \(\mathrm{A} 2\), \(m_{\text {A2 }}=1.20 \times 10^{6} \mathrm{~kg}\), collide head-on in space. Approximate
A \(1500-\mathrm{kg}\) van is coasting to a stoplight at \(15 \mathrm{~m} / \mathrm{s}\). A \(1000-\mathrm{kg}\) car behind the van is doing the same thing at \(25 \mathrm{~m} / \mathrm{s}\) and
A \(0.30-\mathrm{kg}\) cart traveling along a low-friction track at \(2.0 \mathrm{~m} / \mathrm{s}\) relative to Earth collides with a \(0.50-\mathrm{kg}\) cart traveling in the same direction at
The transformation between position and time measurements in an inertial reference frame I and position and time measurements in a constantly accelerating (noninertial) reference frame \(\mathrm{N}\)
The medallion shown in Figure P6.79 has been made by cutting a small circular piece out of a larger circular disk. The diameter of the original disk is twice the diameter of the hole, and the
As an avid biker, you've come to realize that your top speed is really an air speed, not a ground speed, because air resistance is very noticeable when you ride fast. You like to ride at top speed
An uncoupled \(20,000-\mathrm{kg}\) railroad hopper car coasts along a track at \(2.0 \mathrm{~m} / \mathrm{s}\). As it passes a grain chute, the chute opens (Figure P6.81), grain fills the car at a
A skateboarder coasting at \(5.0 \mathrm{~m} / \mathrm{s}\) decides to coast into a friend going \(4.0 \mathrm{~m} / \mathrm{s}\) on rollerblades in the same direction. Unfortunately, the
Suppose that in the situation shown in Figure 6.2, a third ruler is affixed to some device (not shown) that moves to the right along the track at a speed of \(2.0 \mathrm{~mm} /\) frame. If in the
Which of these reference frames are inertial: one affixed to (a) a merry-go-round, (b) the space shuttle orbiting Earth, (c) an airplane taking off, (d) a train moving at constant speed along a
A \(0.12-\mathrm{kg}\) cart moving on a straight, low-friction track gets a shove so that its speed changes. Its initial and final speeds measured in the Earth reference frame are \(0.40 \mathrm{~m}
Consider a collision between the two carts of Table 6.1, starting from the same initial velocities, but with \(v_{\mathrm{EI} x, \mathrm{f}}=+0.30 \mathrm{~m} / \mathrm{s}\). Make a table like Table
For the colliding carts in Figure 6.8,(a) determine the velocity of the zero-momentum reference frame relative to Earth and \((b)\) show that the system momentum measured in the zero-momentum
You are driving at \(25 \mathrm{~m} / \mathrm{s}\) on a straight, horizontal road when a truck going \(30 \mathrm{~m} / \mathrm{s}\) in the same direction overtakes you. Let the positive \(x\)
The positions of two identical carts at rest on a low-friction track are measured relative to two axes oriented in the same direction along the track. On axis \(\mathrm{A}\), cart 1 is at

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