Engineering Mechanics Dynamics 8th Edition James L. Meriam, L. G. Kraige, J. N. Bolton - Solutions

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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 you can add it up.” What should the student conclude about the age of the fossils?
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 time it takes for the light flash to reach you. Why?
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 started at the origin x = 0. If its average velocity is positive, could the particle ever have been
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 of x versus t and to note that vx(t) is a continuous function.
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 than that of B? Explain.
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 your point.
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 real life example for an automobile on an east-west one-dimensional axis, with east considered the
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 depend on the choice of origin? Explain your answers.
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 balls compare when they reach the ground?
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 0.5t? (b) When the time is 0.5t, is the height of the object greater than 0.5h, equal to 0.5h, or
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 speed v. Your friend throws the ball upward at exactly the same time that you drop yours from the
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 second hand?
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 calculated without knowledge of the manner in which the mass is distributed?
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 necessarily equal to.)
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 = 0? Is the expression v =" Rw valid in this situation
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 axis with the smallest moment of inertia.
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 the two eggs on the floor and comparing the rotational motions. Which egg spins faster? Which rotates
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 center and perpendicular to its plane? Of a uniform door turning on its hinges of a coin turning
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 radius of the roll of remaining tape decreases how does the torque on the reel change with time? How
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 removed and transferred to the polar regions to make the Earth a perfect sphere?
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 basketball rolling with the same initial speed. It keeps rolling from one end of the gym to the other. Why
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 the same elevation and roll without slipping. Which object reaches the bottom first? Which reaches it
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 small wheels? Do you want to use solid disk-like wheels or hoop-like wheels? Should the wheels be heavy
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 the Universe?
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 the magnitude of your resultant displacement from mile marker 260?
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 pairs of vectors that will satisfy this condition; we choose that pair with one vector parallel to the
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 velocity? Its average velocity? Explain.
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 an angle ' with the horizontal.
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 resistance.
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 trajectory, (a) Its position, (b) Its velocity, and (c) Its acceleration. How would these results change
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 orientation of the spacecraft does not change, so that the acceleration remains perpendicular to 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 balls be closest to each other? Will the first ball always be traveling faster than the second ball?
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 with its engines thrusting the plane forward. (c) A rocket leaves the launch pad. (d) A rocket moving
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 the same distance from the projection point. Will both projectiles be in the air for the same time
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 vertical direction? What is its acceleration in the horizontal direction?
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 component of velocity.
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 in both cases? Neglect air resistance.
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 greater or less than 45.0°? Explain.
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 greater range? Which reaches the greater altitude? (Note that the free-fall acceleration on the Moon is
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 released from the same height and falls to the floor. Explain why the two objects hit the floor
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 constant speed. Draw a motion diagram showing her velocity and acceleration vectors at several points
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 the right of the central vertical line to a final position 45° to the left of the central vertical
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.) Discuss.
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 observer standing by the tracks outside the train. (b) How would these observations change if the train
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? Identify the reaction force in this case. (Neglect air resistance.)
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 forward and Clark falls into Claudette’s lap. Why did this happen?
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 in this case, what disposition would you make? Why?
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 gently or kick it toward the storage compartment? Why?
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 you give on behalf of the employees? Who do you think would win the case in court?
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 upward? How does the reading on the scale vary now?
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 rate through a hole in its bottom?
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 constant.

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Engineering Mechanics Dynamics 8th Edition James L. Meriam, L. G. Kraige, J. N. Bolton - Solutions

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