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physics
mechanics

Questions and Answers of Mechanics

Find the order of magnitude of your age in seconds.
What level of precision is implied in an order-of-magnitude calculation?
Estimate the mass of this textbook in kilograms. If a scale is available, check your estimate.
In reply to a student’s question, a guard in a natural history museum says of the fossils near his station, “When I started work here twenty-four years ago, they were eighty million years old, so
The speed of sound in air is 331 m/s. During the next thunderstorm, try to estimate your distance from a lightning bolt by measuring the time lag between the flash and the thunderclap. You can ignore
The average velocity of a particle moving in one dimension has a positive value. Is it possible for the instantaneous velocity to have been negative at any time in the interval? Suppose the particle
If the average velocity of an object is zero in some time interval, what can you say about the displacement of the object for that interval?
Can the instantaneous velocity of an object at an instant of time ever be greater in magnitude than the average velocity over a time interval containing the instant? Can it ever be less?
If an object’s average velocity is nonzero over some time interval, does this mean that its instantaneous velocity is never zero during the interval? Explain your answer.
If an object’s average velocity is zero over some time interval, show that its instantaneous velocity must be zero at some time during the interval. It may be useful in your proof to sketch a graph
If the velocity of a particle is nonzero, can its acceleration be zero? Explain.
If the velocity of a particle is zero, can its acceleration be nonzero? Explain.
Two cars are moving in the same direction in parallel lanes along a highway. At some instant, the velocity of car A exceeds the velocity of car B. Does this mean that the acceleration of A is greater
Is it possible for the velocity and the acceleration of an object to have opposite signs? If not, state a proof. If so, give an example of such a situation and sketch a velocity–time graph to prove
Consider the following combinations of signs and values for velocity and acceleration of a particle with respect to a one-dimensional x axis:Describe what a particle is doing in each case, and give a
Can the equations of kinematics (Eqs. 2.9–2.13) be used in0 a situation where the acceleration varies in time? Can they be used when the acceleration is zero?
A stone is thrown vertically upward from the roof of a building. Does the position of the stone depend on the location chosen for the origin of the coordinate system? Does the stone’s velocity
A child throws a marble into the air with an initial speed vi. Another child drops a ball at the same instant. Compare the accelerations of the two objects while they are in flight.
A student at the top of a building of height h throws one ball upward with a speed of vi and then throws a second ball downward with the same initial speed, vi. How do the final velocities of the
An object falls freely from height h. It is released at time zero and strikes the ground at time t. (a) When the object is at height 0.5h, is the time earlier than 0.5t, equal to 0.5t, or later than
You drop a ball from a window on an upper floor of a building. It strikes the ground with speed v. You now repeat the drop, but you have a friend down on the street who throws another ball upward at
What is the angular speed of the second hand of a clock? What is the direction of w as you view a clock hanging on a vertical wall? What is the magnitude of the angular acceleration vector a of the
One blade of a pair of scissors rotates counterclockwise in the xy plane. What is the direction of w? What is the direction of a if the magnitude of the angular velocity is decreasing in time?
Are the kinematic expressions for a, &, and (valid when the angular position is measured in degrees instead of in radians?
If a car’s standard tires are replaced with tires of larger outside diameter, will the reading of the speedometer change? Explain.
Suppose a = b and M > m for the system of particles described in Figure 10.8. About which axis (x, y, or z) does the moment of inertia have the smallest value? the largest value?
Suppose that the rod in Figure 10.10 has a non-uniform mass distribution. In general, would the moment of inertia about the y axis still be equal to ML2/12? If not, could the moment of inertia be
Suppose that just two external forces act on a stationary rigid object and the two forces are equal in magnitude and opposite in direction. Under what condition does the object start to rotate?
Suppose a pencil is balanced on a perfectly frictionless table. If it falls over, what is the path followed by the center of mass of the pencil?
Explain how you might use the apparatus described in Example 10.12 to determine the moment of inertia of the wheel. (If the wheel does not have a uniform mass density, the moment of inertia is not
Using the results from Example 10.12, how would you calculate the angular speed of the wheel and the linear speed of the suspended counterweight at t = 2 s, if the system is released from rest at t =
If a small sphere of mass M were placed at the end of the rod in Figure 10.24, would the result for & be greater than, less than, or equal to the value obtained in Example 10.14?
Explain why changing the axis of rotation of an object changes its moment of inertia.
The moment of inertia of an object depends on the choice of rotation axis, as suggested by the parallel-axis theorem. Argue that an axis passing through the center of mass of an object must be the
Suppose you remove two eggs from the refrigerator, one hard-boiled and the other uncooked. You wish to determine which is the hard-boiled egg without breaking the eggs. This can be done by spinning
Which of the entries in Table 10.2 applies to finding the moment of inertia of a long straight sewer pipe rotating about its axis of symmetry? Of an embroidery hoop rotating about an axis through its
Is it possible to change the translational kinetic energy of an object without changing its rotational energy?
Must an object be rotating to have a nonzero moment of inertia?
If you see an object rotating, is there necessarily a net torque acting on it?
Can a (momentarily) stationary object have a nonzero angular acceleration?
In a tape recorder, the tape is pulled past the read-and writes heads at a constant speed by the drive mechanism. Consider the reel from which the tape is pulled. As the tape is pulled from it, the
The polar diameter of the Earth is slightly less than the equatorial diameter. How would the moment of inertia of the Earth about its axis of rotation change if some mass from near the equator were
Suppose you set your textbook sliding across a gymnasium floor with a certain initial speed. It quickly stops moving because of a friction force exerted on it by the floor. Next, you start a
When a cylinder rolls on a horizontal surface as in Figure 10.28, do any points on the cylinder have only a vertical component of velocity at some instant? If so, where are they?
Three objects of uniform density€”a solid sphere, a solid cylinder, and a hollow cylinder€”are placed at the top of an incline (Fig. Q10.24). They are all released from rest at
In a soap-box derby race, the cars have no engines; they simply coast down a hill to race with one another. Suppose you are designing a car for a coasting race. Do you want to use large wheels or
Two vectors have unequal magnitudes. Can their sum be zero? Explain.
Can the magnitude of a particle’s displacement be greater than the distance traveled? Explain.
The magnitudes of two vectors A and B are A = 5 units and B = 2 units. Find the largest and smallest values possible for the magnitude of the resultant vector R = A % B.
Which of the following are vectors and which are not: force, temperature, the volume of water in a can, the ratings of a TV show, the height of a building, the velocity of a sports car, the age of
A vector A lies in the xy plane. For what orientations of A will both of its components be negative? For what orientations will its components have opposite signs?
A book is moved once around the perimeter of a tabletop with the dimensions 1.0 m x 2.0 m. If the book ends up at its initial position, what is its displacement? What is the distance traveled?
While traveling along a straight interstate highway you notice that the mile marker reads 260. You travel until you reach mile marker 150 and then retrace your path to the mile marker 175. What is
If the component of vector A along the direction of vector B is zero, what can you conclude about the two vectors?
Can the magnitude of a vector have a negative value? Explain.
Under what circumstances would a nonzero vector lying in the xy plane have components that are equal in magnitude?
If A = B, what can you conclude about the components of A and B?
Is it possible to add a vector quantity to a scalar quantity? Explain.
The resolution of vectors into components is equivalent to replacing the original vector with the sum of two vectors, whose sum is the same as the original vector. There are an infinite number of
In what circumstance is the x component of a vector given by the magnitude of the vector times the sine of its direction angle?
Can an object accelerate if its speed is constant? Can an object accelerate if its velocity is constant?
If you know the position vectors of a particle at two points along its path and also know the time it took to move from one point to the other, can you determine the particle’s instantaneous
Construct motion diagrams showing the velocity and acceleration of a projectile at several points along its path if (a) The projectile is launched horizontally and (b) The projectile is launched at
A baseball is thrown with an initial velocity of (10i & 15j) m/s. When it reaches the top of its trajectory, what are? (a) Its velocity and (b) Its acceleration? Neglect the effect of air
A baseball is thrown such that its initial x and y components of velocity are known. Neglecting air resistance, describe how you would calculate, at the instant the ball reaches the top of its
A spacecraft drifts through space at a constant velocity. Suddenly a gas leak in the side of the spacecraft gives it a constant acceleration in a direction perpendicular to the initial velocity. The
A ball is projected horizontally from the top of a building. One second later another ball is projected horizontally from the same point with the same velocity. At what point in the motion will the
A rock is dropped at the same instant that a ball, at the same initial elevation, is thrown horizontally. Which will have the greater speed when it reaches ground level?
Determine which of the following moving objects obey the equations of projectile motion developed in this chapter.(a) A ball is thrown in an arbitrary direction. (b) A jet airplane crosses the sky
How can you throw a projectile so that it has zero speed at the top of its trajectory? So that it has nonzero speed at the top of its trajectory?
Two projectiles are thrown with the same magnitude of initial velocity, one at an angle ' with respect to the level ground and the other at angle 90°#'. Both projectiles will strike the ground at
A projectile is launched at some angle to the horizontal with some initial speed vi, and air resistance is negligible. Is the projectile a freely falling body? What is its acceleration in the
State which of the following quantities, if any, remain constant as a projectile moves through its parabolic trajectory:(a) Speed, (b) Acceleration, (c) Horizontal component of velocity, (d) Vertical
A projectile is fired at an angle of 30° from the horizontal with some initial speed. Firing the projectile at what other angle results in the same horizontal range if the initial speed is the same
The maximum range of a projectile occurs when it is launched at an angle of 45.0° with the horizontal, if air resistance is neglected. If air resistance is not neglected, will the optimum angle be
A projectile is launched on the Earth with some initial velocity. Another projectile is launched on the Moon with the same initial velocity. Neglecting air resistance, which projectile has the
A coin on a table is given an initial horizontal velocity such that it ultimately leaves the end of the table and hits the floor. At the instant the coin leaves the end of the table, a ball is
Explain whether or not the following particles have an acceleration: (a) A particle moving in a straight line with constant speed and (b) A particle moving around a curve with constant speed.
Correct the following statement: “The racing car rounds the turn at a constant velocity of 90 miles per hour.”
At the end of a pendulum’s arc, its velocity is zero. Is its acceleration also zero at that point?
An object moves in a circular path with constant speed v.(a) Is the velocity of the object constant? (b) Is its acceleration constant? Explain
Describe how a driver can steer a car traveling at constant speed so that (a) The acceleration is zero or (b) The magnitude of the acceleration remains constant.
An ice skater is executing a figure eight, consisting of two equal, tangent circular paths. Throughout the first loop she increases her speed uniformly, and during the second loop she moves at a
Based on your observation and experience, draw a motion diagram showing the position, velocity, and acceleration vectors for a pendulum that swings in an arc carrying from an initial position 45° to
What is the fundamental difference between the unit vectors r and the unit vectors i and j?
A sailor drops a wrench from the top of a sailboat’s mast while the boat is moving rapidly and steadily in a straight line. Where will the wrench hit the deck? (Galileo posed this question.)
A ball is thrown upward in the air by a passenger on a train that is moving with constant velocity. (a) Describe the path of the ball as seen by the passenger. Describe the path as seen by an
A passenger on a train that is moving with constant velocity drops a spoon. What is the acceleration of the spoon relative to? (a) The train and (b) The Earth?
A ball is held in a person’s hand. (a) Identify all the external forces acting on the ball and the reaction to each.(b) If the ball is dropped, what force is exerted on it while it is falling?
If a car is traveling westward with a constant speed of 20 m/s, what is the resultant force acting on it?
What is wrong with the statement “Because the car is at rest, there are no forces acting on it”? How would you correct this sentence?
In the motion picture It Happened One Night (Columbia Pictures, 1934), Clark Gable is standing inside a stationary bus in front of Claudette Colbert, who is seated. The bus suddenly starts moving
A passenger sitting in the rear of a bus claims that she was injured as the driver slammed on the brakes, causing a suitcase to come flying toward her from the front of the bus. If you were the judge
A space explorer is moving through space far from any planet or star. She notices a large rock, taken as a specimen from an alien planet, floating around the cabin of the ship. Should she push it
A rubber ball is dropped onto the floor. What force causes the ball to bounce?
While a football is in flight, what forces act on it? What are the action–reaction pairs while the football is being kicked and while it is in flight?
The mayor of a city decides to fire some city employees because they will not remove the obvious sags from the cables that support the city traffic lights. If you were a lawyer, what defense would
A weightlifter stands on a bathroom scale. He pumps a barbell up and down. What happens to the reading on the bathroom scale as this is done? What if he is strong enough to actually throw the barbell
Suppose a truck loaded with sand accelerates along a highway. If the driving force on the truck remains constant, what happens to the truck’s acceleration if its trailer leaks sand at a constant
As a rocket is fired from a launching pad, its speed and acceleration increase with time as its engines continue to operate. Explain why this occurs even though the thrust of the engines remains

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