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college physics reasoning

College Physics Reasoning and Relationships 2nd edition Nicholas Giordano - Solutions

Your friend is an environmentalist who is living in a tree for the summer. You are helping provide her with food, and you do so by throwing small packages up to her tree house. If her tree house is 30 m above the ground, what is the minimum (initial) speed you must use when throwing packages up to
You are standing at the top of a deep, vertical cave and want to determine the depth of the cave. Unfortunately, all you have is a rock and a stopwatch. You drop the rock into the cave and measure the time that passes until you hear the rock hitting the floor of the cave far below. If the elapsed
A roofing tile falls from rest off the roof of a building. An observer from across the street notices that it takes 0.43 s for the tile to pass between two windowsills that are 2.5 m apart. How far is the sill of the upper window from the roof of the building?
A rock is dropped from a tall bridge into the water below. If the rock begins with a speed of zero and has a speed of 12 m/s just before it hits the water, what is the height of the bridge as measured from the surface of the water?
Two children are playing on a 150-m-tall bridge. One child drops a rock (initial velocity zero) at t - 0. The other waits 1.0 s and then throws a rock downward with an initial speed v0. If the two rocks hit the ground at the same time, what is v0?
A ball is thrown directly upward with an initial velocity of 15 m/s. If the ball starts at an initial height of 3.5 m, how long is the ball in the air? Ignore air drag.
An apple falls from a branch near the top of a tall tree. If the branch is 12 m above the ground, what is the apple’s speed just before it hits the ground?
Basketball on the Moon. If LeBron James can jump 1.5 m high on Earth, how high could he jump on the Moon (assume an indoor court), where g - 1.6 m/s2?
A squirrel is resting in a tall tree when it slips from a branch that is 50 m above the ground. It is a very agile squirrel and manages to land safely on another branch after only 0.50 s. What is the height of the branch it lands on?
A baseball is hit directly upward with an initial speed of 45 m/s. Find the velocity of the ball when it is at a height of 40 m. Is there one correct answer for v or two? Explain why.
A rock is dropped from a very tall tower. If it takes 4.5 s for the rock to reach the ground, what is the height of the tower?
A hockey puck slides along a rough, icy surface. It has an initial velocity of 35 m/s and slides to a stop after traveling a distance of 95 m. Find the coefficient of kinetic friction between the puck and the ice.
Anti lock brakes. A car travels at 65 mi/h when the brakes are suddenly applied. Consider how the tires of a moving car come in contact with the road. When the car goes into a skid (with wheels locked up), the rubber of the tire is moving with respect to the road; otherwise, when the tires roll,
Jeff Gordon (a race car driver) discovers that he can accelerate at 4.0 m/s2 without spinning his tires, but if he tries to accelerate more rapidly, he always “burns rubber.” (a) Find the coefficient of friction between his tires and the road. Assume the force from the engine is applied to
A ball is thrown upward with a speed of 35 m/s from the edge of a cliff of height h - 15 m (similar to Fig. P3.22). (a) What is the speed of the ball when it passes by the cliff on its way down to the ground? (b) What is the speed of the ball when it hits the ground? Ignore air drag.
A bullet is fired upward with a speed v0from the edge of a cliff of height h (Fig. P3.22).(a) What is the speed of the bullet when it passes by the cliff on its way down? (b) What is the speed of the bullet just before it strikes the ground? (c) If the bullet is instead fired downward
A car is traveling at 25 m/s when the driver spots a large pothole in the road a distance 30 m ahead. She immediately applies her brakes. If her acceleration is -27 m/s2, does she manage to stop before reaching the pothole?
Your car is initially traveling at a speed of 25 m/s. As you approach an intersection, you spot a dog in the road 30 m ahead and immediately apply your brakes. (a) If you stop the instant before you reach the dog, what was the magnitude of your acceleration? (b) If your velocity is
To measure the height of a tree, you throw a rock directly upward, with a speed just fast enough that the rock brushes against the uppermost leaves and then falls back to the ground. If the rock is in the air for 3.6 s, how tall is the tree?
A barge on a still lake is moving toward a bridge at 10.0 m/s. When the bridge is 40.0 m away, the pilot slows the boat with a constant acceleration of -0.73 m/s2. (a) Use Equation 3.3 to find the time it takes the barge to reach the bridge. Note that you will obtain two answers! Do both
A hockey puck has an initial velocity of 50 m/s and a final velocity of 35 m/s. (a) If it travels 35 m during this time, what is the acceleration? (b) If the mass of the puck is 0.11 kg, what is the horizontal force on the puck?
An object with an initial velocity of 12 m/s accelerates uniformly for 25 s. (a) If the final velocity is 45 m/s, what is the acceleration? (b) How far does the object travel during this time?
An elevator is moving at 1.2 m/s as it approaches its destination floor from below. When the elevator is a distance h from its destination, it accelerates with a - -0.50 m/s2, where the negative sign indicates a downward vertical direction. (“Up” is positive.) Find h.
Explain why the air bags in a car reduce the forces on a passenger in the event of an accident.
An airplane must reach a speed of 200 mi/h to take off. If the runway is 500 m long, what is the minimum value of the acceleration that will allow the airplane to take off successfully?
For the books in Figure Q3.14, there is a force F from the table supporting the book on the bottom. Identify two action€“reaction force pairs for each of the following objects: (a) The table, (b) The book on top, (c) The book on the bottom, and (d) The Earth.Figure
A drag racer is able to complete the 0.40-km course (0.25 mi)in 6.1 s. (a) If her acceleration is constant, what is a? (b) What is her speed when she is halfway to the finish line?
The bacterium in Figure 3.30 experiences a force due to drag from the surrounding fluid. Does the reaction force to Fdrag act on (a) The flagellum, (b) The body of the bacterium, or (c) The fluid?Figure 3.30
Consider a sprinter who starts at rest, accelerates to a maximum speed vmax, and then slows to a stop after crossing the finish line. Draw qualitative plots of the acceleration, velocity, and position as functions of time. Indicate the location of the finish line on the x–t plot.
Two balls of the same diameter are dropped simultaneously from a very tall bridge. One ball is solid lead, and the other is hollow plastic and has a much smaller mass than the solid lead ball. Use a free-body diagram to explain why the solid lead ball reaches the ground first.
Draw a qualitative plot of the total force acting on the ball in Figure 3.15 (page 68) as a function of time. Begin your plot while the ball is still in the thrower€™s hand and end it after the ball comes to rest back on the ground.Figure 3.15 Free-body diagram Ball Уo- 'É. grav gгav
Consider a string with one end tied to a tall ceiling and the other end hanging freely. Explain why the tension at the bottom of the string is smaller than the tension at the top.
Pulling g’s. Suppose again you are the astronaut in Problem 9. When most people are subjected to an acceleration greater than about 5 × g, they will usually become unconscious (“black out”). Will you be in danger of blacking out?Data From Problem 9You are a newly graduated astronaut
The lower piece of silk in Figure 3.20 is acted on by two forces, +T2at the upper end and -T2at the lower end. These two forces are equal in magnitude and opposite in direction. Are they an action€“reaction force pair? Explain why or why not.Figure 3.20 -Silk T1 Free-body T1 diagrams For
You are a newly graduated astronaut preparing for your first trip into space. Plans call for your spacecraft to reach a velocity of 500 m/s after 2.4 min. If your mass is 75 kg, what force will be exerted on your body? Assume the acceleration is constant.
(a) Suppose a tire rolls without slipping on a horizontal road. Explain the role friction plays in this motion. What two surfaces are involved in this frictional force? Is it static friction or kinetic friction?(b) Suppose a race car driver wants to get his car started very quickly and “burns
Your car has a dead battery. It is initially at rest, and you push it along a level road with a force of 120 N, finding that it reaches a velocity of 2.0 m/s in 50 s. What is the mass of the car? Ignore friction.
Two balls are thrown from a tall bridge. One is thrown upward with an initial velocity +v0, while the other is thrown downward with an initial velocity -v0. Which one has the greater speed just before it hits the ground?
A rocket-powered sled of mass 3500 kg travels on a level snow-covered surface with an acceleration of +3.5 m/s2(Fig. P3.7). What are the magnitude and direction of the force on the sled?Figure P3.7 X-
You are riding in a car that starts from rest, accelerates for a short distance, and then moves with constant velocity. Explain why you feel a force from the back of your seat only while the car is accelerating and not while you are moving with a constant velocity.
A constant force of 400 N acts on a spacecraft of mass 8000 kg that has an initial velocity of 30 m/s. How far has the spacecraft traveled when it reaches a velocity of 5000 m/s?
Two mountain climbers are suspended by a rope as shown in Figure Q3.5. Which rope is most in danger of breaking? That is, which rope has the greatest tension?Figure Q3.5
A car has a velocity of 10 m/s at t - 7.0 s. It then accelerates uniformly and reaches a velocity of 42 m/s at t - 12.0 s. What is its acceleration during this period?
Two objects are released simultaneously from the same height. The objects are both spherical with the same radius, but their masses differ by a factor of two. (a) Ignoring air drag, which object strikes the ground first? Or do they strike at the same time? Explain. (b) Including air drag,
An object moves with a constant acceleration of 4.0 m/s2. If it starts with an initial speed of 30 m/s, how long does it take to reach a velocity of 250 m/s?
Give an example of motion in one dimension for an object that starts at the origin at t = 0. At some time later, the displacement from the origin is zero but the velocity is not zero. Draw the corresponding position–time and velocity–time graphs.
An ice skater moves without friction on a frozen pond. While traveling at 8.0 m/s, she finds that it takes 17 s to travel the length of the pond. How long is the pond?
A hockey puck moves on an icy surface that is friction less, with a constant speed of 30 m/s. How long does it take the puck to travel the length of the hockey rink (60 m)?
A spacecraft that is initially at rest turns on its engine at t - 0. If its mass is m - 3000 kg and the force from the engine is 45 N, what is the acceleration of the spacecraft?
An object is found to move with an acceleration of magnitude 12 m/s2 when it is subjected to a force of magnitude 200 N. Find the mass of the object.
Make a hypothetical sketch of a velocity–time graph in which the velocity is always positive, but the acceleration is always negative. Give a physical example of such motion.
A ball is thrown into the air with an upward velocity of 10 m/s. A short time later, it is caught on its way down, also with a speed of 10 m/s.(a) Draw the velocity–time graph for this situation.(b) Draw the acceleration–time graph for this situation.(c) Many people would describe the ball’s
When a car collides with a wall, a force on the car causes it to stop. Identify an action–reaction pair of forces involving the car.
You push on a refrigerator, as in Figure 2.1, but the refrigerator does not move. Hence, even though you are applying a nonzero force, the acceleration is still zero. Explain why this does not contradict Newton€™s second law.Figure 2.1
A falling baseball has an acceleration of magnitude 9.8 m/s2. What is its acceleration in feet per second squared?
A car is traveling on an icy road that is extremely slippery. The driver finds that she is not able to stop or turn the car. Explain this situation in terms of the principle of inertia (Newton’s first law).
An elite runner can run 1500 m in 3 minutes and 35 s. What is his average speed? Give your answer to two significant figures.
A car is initially at rest on an icy road that is extremely slippery. The driver finds that he is unable to get the car to drive away because the wheels simply spin when he tries to accelerate. Explain this situation in terms of the principle of inertia (Newton’s first law).
Consider the motion of a sprinter running a 100-m dash. When it is run outdoors, this race is run along a straight-line portion of a track, so it is an example of motion in one dimension. Draw qualitative plots of the position, velocity, and acceleration as functions of time for the sprinter. Start
In SI units, acceleration is measured in units of meters per second squared (m/s2). Which of the following combinations of units can also be used to measure acceleration?(a) Cm/s(b) Cm/s2(c) m3/(mm2 • s2)(d) Km/s2(e) Miles per hour
A jogger maintains a speed of 3.0 m/s for 200 m until he encounters a stoplight, and he abruptly stops and waits 30 s for the light to change. He then resumes his exercise and maintains a speed of 3.5 m/s for the remaining 50 m to his home. (a) What was his average velocity for this entire
Give an example of motion for which the average velocity is zero, but the speed is never zero.
Give an example of motion for which the average velocity is equal to the instantaneous velocity.
Abracadabra! A magician pulls a tablecloth off of a set table with one swift, graceful motion. Amazingly, the fine china, glassware, and silverware are practically undisturbed. Although amazing, this feat is not an illusion. Describe the behavior of the plates and glasses in terms of the principle
A hockey puck that is sliding on an icy surface will eventually come to rest. The (horizontal) force that makes it stop is due to friction between the puck and the ice. Draw qualitative plots of the position, velocity, and acceleration as functions of time for the puck. Pay special attention to the
Consider a marble falling through a very thick fluid, such as molasses. Draw qualitative plots of the position, velocity, and acceleration as functions of time for the marble, assuming it is released from rest just above the molasses.
Give examples of motion matching the following descriptions. (a) The velocity is positive and the acceleration is positive. (b) The velocity is negative and the acceleration is negative. (c) The velocity is positive and the acceleration is negative.
A person riding on a skateboard is initially coasting on level ground. He then uses his feet to push on the ground so that he speeds up for a few seconds, and then he coasts again. Draw qualitative plots of his position, velocity, and acceleration as functions of time.
A car starts from the origin at t = 0. At some later time, is it possible for the car’s velocity to be positive but its displacement from the origin to be zero? Explain and give an example.
In the drop zone. Consider a skydiver who jumps from an airplane. Suppose she waits for 1 min before opening her parachute and she lands 4 min after leaving the airplane. Draw qualitative plots of the position, velocity, and acceleration as functions of time for the skydiver, starting from the time
The acceleration of an object that falls freely under the action of gravity near the Earth’s surface is negative and constant. (a) Does the object’s instantaneous acceleration equal its average acceleration? (b) Draw the corresponding velocity–time graph. (c) Does the
Consider a skier who coasts up to the top of a hill and then continues down the other side. Draw a qualitative plot of what the skier’s speed might look like.
Consider again Example 2.8. Draw plots of the position, velocity, and acceleration as functions of time, starting from when the ball is released and ending after the ball hits the ground. Indicate the time at which the ball hits the ground.
Figure P2.13 shows three motion diagrams, where the dots indicate the positions of an object after equal time intervals. Assume left-to-right motion. For each motion diagram, sketch the appropriate position€“time, velocity€“time, and acceleration€“time graphs.Figure
A typical airplane can fly at a speed of 400 miles per hour. What is its speed in meters per second?
In SI units, velocity is measured in units of meters per second (m/s). Which of the following combinations of units can also be used to measure velocity?(a) Cm/s(b) Cm/s2(c) m3/(mm2 • s2)(d) Km/s(e) Miles per hour (f) Km/hour (g) Miles/cm
Make a qualitative sketch of the position y as a function of time for the center of a yo-yo (the point at the middle of the axle). Also make sketches of the velocity and acceleration as functions of time. Is the total force on the yo-yo zero or nonzero? Explain how you can tell from your graphs.
A bicycle is moving initially with a constant velocity along a level road. The bicyclist then decides to slow down, so she applies her brakes over a period of several seconds. Thereafter, she again travels with a constant velocity. Draw qualitative sketches of her position, velocity, and
Figure Q2.15 shows a motion diagram for a rocket powered car. The photos are taken at 1.0-s intervals. Make qualitative plots of the position, velocity, acceleration, and force on the car as functions of time.Figure Q2.15 -t = 0.0 s- -t = 7.0 s- х (m)- 500 400 |200 l100| 300
Figure P2.15 shows several hypothetical position€“time graphs. For each graph, sketch qualitatively the corresponding velocity€“ time graph.Figure P2.15 Case 1 Case 2 Case 3
A person stands on level ground and throws a baseball straight upward, into the air. (a) Does the person exert a force on the ball while it is in his hand? After it leaves his hand? (b) Does the ball ever exert a force on the person? If so, what is the direction of this force? (c) If
The position€“time graphs in Figure P2.15 each describe the possible motion of a particular object. Give at least one example of what the object and motion might be in each case.Figure P2.15 Case 1 Case 2 Case 3
Consider the motion of the Moon as it orbits the Earth. (a) Is the Moon’s acceleration zero or nonzero? Explain. (b) If the Moon has a nonzero acceleration, what force is responsible?
Figure P2.17 shows several hypothetical velocity€“time graphs. For each case, sketch qualitatively the corresponding acceleration€“time graph.Figure P2.17 Case 2 Case 1 Case 3
Consider the motion of a marble as it falls to the bottom of a jar of honey. Experiments show (see also Chapter 3) that the marble moves with a constant velocity. Applying Newton’s first law, does that mean that no forces are acting on the marble?
Figure P2.17 shows several hypothetical velocity€“time graphs. For each case, sketch qualitatively a possible corresponding position€“time graph.Figure P2.17 Case 2 Case 1 Case 3
Give examples of objects whose motion might be described by the graphs in Figure P2.17.Figure P2.17 Case 2 Case 1 Case 3
According to Newton’s first law (the principle of inertia), if there is no force exerted on an object, the object will move with constant velocity. Consider the following examples of motion. Is the velocity of the object constant? What are the forces acting on each object? In cases in which the
Three blocks rest on a table as shown in Figure Q2.20. Identify three action€“reaction pairs of forces.Figure Q2.20 3 2.
Figure P2.20 shows several hypothetical acceleration€“time graphs. For each case, sketch qualitatively a possible corresponding velocity€“time graph.Figure P2.20 Л Case 2 Case 3 Case 1
Two football players start running at opposite ends of a football field (opposite goal lines), run toward each other, and then collide at the center of the field. They start from rest and are running at top speed when they collide. (a) Draw a graph showing the position as a function of time
Give examples of objects whose motion is described by the plots in Figure P2.20.Figure P2.20 Л Case 2 Case 3 Case 1
A person is riding in a car traveling on a straight level road.What is the direction of the net force on the person if the car is (a) Speeding up, (b) Slowing down, (c) Has a constant speed?
Match each of the following examples of motion to one of the position€“time graphs in Figure P2.22.(a) A person at the beginning of a race, starting from rest(b) A runner near the end of a race, just after crossing the finish line(c) A ball dropped from a window, hitting the ground below
Consider the position€“time graph shown in Figure P2.24. Make a careful graphical estimate of the velocity as a function of time by measuring the slopes of tangent lines. What is an approximate value of the maximum velocity of the object?Figure P2.24 -x (m) -3- -2- -1 Hi (s)
For the object described by Figure P2.24, estimate the average velocity (a) Over the interval from t - 2.0 s to t - 4.0 s and (b) Over the interval from t - 1.0 s to t - 5.0 s.Figure P2.24 -x (m) -4- -3- -2- -1 t (s) -0+i+2-3-4-5-6-7||
Repeat Problem 24 using the position€“time graph in Figure P2.26.Figure P2.26Data From Problem 24Consider the position€“time graph shown in Figure P2.24. Make a careful graphical estimate of the velocity as a function of time by measuring the slopes of tangent lines. What is an
Using a graphical approach (i.e., by estimating the slope at various points), find the qualitative behavior of the acceleration as a function of time for the object described by the velocity€“time graph in Figure P2.28.Figure P2.28 v (m/s)- Ht (s) 0- - 200–400–-600- -10-
For the object described by the velocity€“time graph in Figure P2.29, estimate the average acceleration over the interval from t - 0 s to t - 50 s and over the interval from t - 100 s to t - 200 s.Figure P2.29 v (m/s) 40- 30 20 10- t (s) -0- 200 100
Draw a possible position€“time graph for an object whose velocity as a function of time is described by (a) Figure P2.28 and (b) Figure P2.29.Figure P2.28Figure P2.29 v (m/s) HHt (s) 200-400–60- 0- -10 v (m/s) 40- 30- 20 10 100 t (s) 200- 0-

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