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college physics reasoning

Questions and Answers of College Physics Reasoning

Two crates of mass m1= 35 kg and m2= 15 kg are stacked on the back of a truck (Fig. P4.54). The frictional forces are strong enough that the crates do not slide off the truck. Assume the truck is
Estimate the terminal velocity for a golf ball.
Two forces are acting on an object. One force has a magnitude of 45 N and is directed along the +x axis. The other force has a magnitude of 30 N and is directed along the +y axis. What is the
A car is traveling down a hill that makes an angle of 20° with the horizontal. The driver applies her brakes, and the wheels lock so that the car begins to skid. The coefficient of kinetic friction
A skier is traveling at a speed of 40 m/s when she reaches the base of a friction less ski hill. This hill makes an angle of 10° with the horizontal. She then coasts up the hill as far as possible.
An airplane of mass 25,000 kg (approximately the size of a Boeing 737) is coming in for a landing at a speed of 70 m/s. Estimate the normal force on the landing gear when the airplane lands.
Consider the rock-on-a-string accelerometer in Figure 4.30. What is the accelerometer angle if the airplane has a horizontal acceleration of 1.5 m/s2?Figure 4.30 mg mg T cos 8 -T sin0 mg
Consider the accelerometer design shown in Figure P4.57, in which a small sphere sits in a hemispherical dish. Suppose the dish has an acceleration of axalong the horizontal and a small amount of
Consider a commercial passenger jet as it accelerates on the runway during takeoff. This jet has a rock-on-a-string accelerometer installed (as in Fig. 4.30). Estimate the angle of the string during
A soccer ball has a diameter of about 22 cm and a mass of about 430 g. What is its terminal velocity?
A skier travels down a steep, friction less slope of angle 20° with the horizontal. Assuming she has reached her terminal velocity, estimate her speed.
Consider the motion of a bicycle with air drag included. We saw how to deal with the motion on a hill in connection with Figure 4.33. Now assume the bicycle is coasting on level ground and is being
What is the approximate magnitude of the drag force on an airplane (such as a commercial jet) traveling at 250 m/s? Consider only the drag force on the fuselage of the airplane (and not on the wings).
Consider the system of blocks in Figure P4.64, with m2= 5.0 kg and Î¸ = 35Â°. If the coefficient of static friction between block 1 and the inclined plane is ÂµS= 0.25, what is the largest mass
A water skier (Fig. P4.65) of mass m = 65 kg is pulled behind a boat at a constant speed of 25 mi/h. If the tension in the horizontal rope is 1000 N (approximately 225 lb), what are the magnitude and
An abstract sculpture is constructed by suspending a sphere of polished rock along the vertical with four cables connected to a square wooden frame 1.2 m on a side as shown in Figure P4.66. If the
An airplane pulls a 25-kg banner on a cable as depicted in Figure P4.67. When the airplane has a constant cruising velocity, the cable makes an angle Î¸ = 20Â° with the horizontal. (a) What
A piece of wood with mass m = 2.4 kg is held in a vise sandwiched between two wooden jaws as shown in Figure P4.68. A blow from a hammer drives a nail that exerts a force of 450 N on the wood. If the
Stomp rocket. A â€œstomp rocketâ€ is a toy projectile launcher illustrated in Figure P4.69 (left), which uses a blast of air to propel a dart made of plastic. The air blast is produced by
You are a serious basketball player and want to use physics to improve your free-throw shooting. Do an approximate calculation of the minimum speed the ball must have to travel from your hand to the
Consider once again the swimmer in Example 4.7. Assume she can swim at a velocity of 0.30 m/s and the river is 15 m wide. She needs to get across the river as quickly as possible. (a) What
A bartender slides a mug of root beer with mass m = 2.6 kg down a bar top of length L = 2.0 m to an inattentive patron who lets the mug fall a height h = 1.1 m to the floor. The bar top (Fig. P4.72)
Two workers must slide a crate designed to be pushed with a rigid rod (on the left in Fig. P4.73) and at the same time pulled with a rope (on the right). The crate has mass m = 45 kg, the angle Î¸
Inner ear. A student constructs a model of the utricle of the ear by attaching wooden balls (m = 0.080 kg) by strings to the bottom of a fish tank and then submerging them in water so that they float
A vintage sports car accelerates down a slope of Î¸ = 17° as depicted in Figure P4.75. The driver notices that the strings of the fuzzy dice hanging from his rear view mirror are
A spacecraft is traveling through space parallel to the x direction with an initial velocity of magnitude v0 = 3500 m/s. At t = 0, the pilot turns on the engines, producing an acceleration of
Two blocks of mass m1and m2are sliding down an inclined plane (Fig. P4.79). (a) If the plane is friction less, what is the magnitude of the contact force between the two masses? (b) If the
A juvenile delinquent wants to break a window near the top of a tall building using a rock. The window is 30 m above ground level, and the base of the building is 20 m from his hiding spot behind a
A cannon shell is fired from a battleship with an initial speed of 700 m/s. (a) What is the maximum range of the shell? (b) For the firing angle that gives the maximum range, what is the
Daredevil stunt. Once upon a time, a stuntman named Evel Knievel boasted that he would jump across the Grand Canyon on a motorcycle. (This stunt was never attempted.) The width of the Grand Canyon
Although Evel Knievel never succeeded in jumping over the Grand Canyon (see Problem 80), he was famous for jumping (with the help of his motorcycle) over, among other things, 14 large trucks. This
A person travels on a ski lift (Fig. P4.82). (a) If the support strut on the ski lift makes an angle Î¸ = 15Â°, what is the horizontal acceleration of the person? (b) If the person plus
A block slides up a friction less, inclined plane with Î¸ = 25Â° (Fig. P4.83). (a) If the block reaches a maximum height h = 4.5 m, what was the initial speed of the lock? (b) Now
A golf ball is hit with an initial velocity of magnitude 60 m/s at an angle of 65° with respect to the horizontal (x) direction. At the same time, a second golf ball is hit with an initial speed v0
A car travels along a level road with speed v = 25 m/s (about 50 mi/h). The coefficient of kinetic friction between the tires and the pavement is µK = 0.55. (a) If the driver applies the brakes
A person riding a bicycle on level ground at a speed of 10 m/s throws a baseball forward at a speed of 15 m/s relative to the bicycle at an angle of 35° relative to the horizontal (x)
Two blocks of mass m1= 2.5 kg and m2= 3.5 kg rest on a double inclined plane with equal angles (Fig. P4.87). The blocks are connected by a string that passes over a pulley, and the blocks are in
A canoe travels across a 40-m-wide river that has a current of speed 5.0 m/s. The canoe has a speed of 0.80 m/s relative to the water (Fig. P4.88). The person paddles the canoe so as to cross the
Hanging out. (a) A block of mass m = 20 kg hangs from two cables attached to a ceiling as shown in Figure P4.89A. What is the approximate tension in each cable? (b) The two cables are now
A projectile is fired uphill as sketched in Figure P4.90. If v0= 150 m/s and Î¸ = 30°, what is L?Figure P4.90 0 = 30°
When airplanes land or take off, they always travel along a runway in the direction that is “into” the wind because the “lift force” on an airplane wing depends on the speed of the airplane
Soccer on a windy day. A professional soccer player can kick a ball with a speed of about 30 m/s (about 75 mi/h). Does air drag play a significant role in the trajectory of the ball? Give a reason
An archer lines up an arrow on the horizontal exactly dead center on a target as drawn in Figure P4.28. She releases the arrow, and it strikes the target a distance h = 7.6 cm below the center. If
Consider a baseball player who wants to catch the fly ball in Problem 26(b). Estimate the force exerted by the ball on the player’s glove as the ball is coming to rest.
A baseball is hit with an initial speed of 45 m/s at an angle of 358 relative to the x (horizontal) axis. (a) Find the speed of the ball at t = 3.2 s. (b) What angle does v(vector) make
The rock-on-a-string accelerometer in Figure 4.30 can be used to measure acceleration along a horizontal direction. Discuss how you could use it to also measure the vertical component of the
Two ropes are attached to a skater as sketched in Figure P4.1 and exert forces on her as shown. Find the magnitude and direction of the total force exerted by the ropes on the skater.Figure P4.1 Top
At what angle should a ball be thrown so that it has the maximum range? Ignore air drag.
The three forces shown in Figure P4.2 act on a particle. If the particle is in transnational equilibrium, find F3(the magnitude of force 3) and the angle Î¸3.Figure P4.2 (50 N 60° х
Two children are having a snowball fight, and one is trying to land a snowball on a friend who is hiding behind a wall (Fig. Q4.2). The child on the left can only throw snowballs with one value of
Several forces act on a particle as shown in Figure P4.3. If the particle is in transnational equilibrium, what are the values of F3(the magnitude of force 3) and Î¸3(the angle that force
An object has an initial velocity v(vector)iand a final velocity v(vector)fas sketched in Figure Q4.3. Sketch the approximate direction of the acceleration a(vector) of the object during this time
A man is lazily floating on an air mattress in a swimming pool (Fig. P4.4). (a) Draw a free-body diagram for the man and for the mattress. (b) Identify the reaction forces for all the
During a particular time interval, an object has an acceleration a(vector) in the direction shown in Figure Q4.4. If v(vector)iis the initial velocity of the object, draw a vector v(vector)fthat
The arrangement in Example 4.2 (p. 95) makes it possible to amplify a force. (Compare this example to the block and tackle in Fig. 3.23.) Amplifying forces in this way comes at a price. To appreciate
A person leans against a wall (Fig. P4.5). Draw a free-body diagram for the person. Assume there is no frictional force between the wall and the person.Figure P4.5
Consider a wedge that rests on a horizontal table as shown in Figure Q4.6 and assume there is no friction between the wedge and the table. A force is now applied vertically as shown in the figure.
The sled in Figure 4.2 is stuck in the snow. A child pulls on the rope and finds that the sled just barely begins to move when he pulls with a force of 25 N, with the rope at an angle of 30° with
Consider again the wedge in Question 6, but now assume a block is placed onto it as shown in Figure Q4.7. There is again no friction between the wedge and the table, and there is also no friction
A system of cables is used to support a crate of mass m = 45 kg as shown in Figure P4.7. Find the tensions in all three cables.Figure P4.7 T3 T1 K60° х T2 т
Balancing act. The tightrope walker in Figure P4.8 gets tired and decides to stop for a rest. During this rest period, she is in transnational equilibrium. She stops at middle of the rope and finds
Time of flight. Equation 4.26 gives a relation for the time at which a batted baseball lands. Use the quadratic formula to find the solutions for tlands. (See Appendix B if you don€™t
A flag of mass 2.5 kg is supported by a single rope as shown in Figure P4.9. A strong horizontal wind exerts a force of 12 N on the flag. Find the tension in the rope and the angle u the rope makes
Explain why the string in Figure 4.30 hangs vertically if the velocity is constant. Consider both an airplane moving horizontally and one moving with a nonzero velocity component along y.Figure 4.30
A car of mass 1400 kg is parked on a very slippery hillside (Fig. P4.10). To keep it from sliding down the hill, the owner attaches a cable. (a) Sketch all the forces on the car. Include
Explain why you cannot run unless there is a frictional force between your feet and the ground.
A crate is placed on an inclined board as shown in Figure P4.11. One end of the board is hinged so that the angle Î¸ is adjustable. If the coefficient of static friction between the crate
Peel out! The author has a small pickup truck. He finds that it is much easier to “burn rubber” (i.e., spin the back wheels so that they slip relative to the road surface) when the truck is empty
Two blocks of mass m1= 45 kg and m2= 12 kg are connected by a mass less string that passes over a pulley as shown in Figure P4.12. The coefficient of static friction between m1and the table is
Give an example in which the magnitude of the instantaneous velocity is always larger than the average velocity.
For the system in Problem 12 and Figure P4.12, how large can m2be made without the system starting into motion?Data From Problem 12Two blocks of mass m1 = 45 kg and m2 = 12 kg are connected by a mass
Give an example in which the acceleration is perpendicular to the velocity.
Stemming a chimney. A rock climber of mass 60 kg wants to make her way up the crack between two rocks as shown in Figure P4.14. The coefficient of friction between her shoes and the rock surface is
Give an example of motion in which the instantaneous velocity is zero but the acceleration is not zero.
A rock is thrown up in the air in such a way that its speed is zero at the top of its trajectory. Where does the rock land?
A hockey puck is given an initial velocity such that vx = 12 m/s and vy = 18 m/s, where the x–y plane is horizontal. (a) What is the initial speed of the puck? (b) What angle does the
Give three examples in which the force of friction on an object has the same direction as the velocity of the object.
A quarterback is asked to throw a football to a receiver who is 35 m away. What is the minimum speed the football must have when it leaves the quarterback’s hand? Assume the ball is caught at the
Ball 1 is thrown with an initial speed v0 at an angle θ relative to the horizontal (x) axis. Ball 2 is thrown at the same angle, but with an initial speed of 2v0. (a) If ball 1 is in the air
Which of the graphs in Figure P4.18 might be a plot of the vertical component of the velocity of a projectile that is thrown from the top of a building?Figure P4.18 A D
Ball 1 rolls off the edge of a table and falls to the floor below, while ball 2 is dropped from the same height (Fig. Q4.19). Which ball reaches the ground first? Explain why your answer does, or
A soccer ball is kicked with an initial speed of 30 m/s at an angle of 25° with respect to the horizontal. Find (a) The maximum height reached by the ball and (b) The speed of the ball
Two balls are thrown into the air with the same initial speed, directed at the same initial angle with respect to the horizontal. Ball 1 has a mass five times the mass of ball 2, and the force of air
Consider a rock thrown off a bridge of height 75 m at an angle Î¸ = 25° with respect to the horizontal as shown in Figure P4.20. The initial speed of the rock is 15 m/s. Find the
A football player wants to kick a ball through the uprights as shown in Figure P4.21. The ball is kicked from a distance of 30 m (he€™s playing metric football) with a velocity of magnitude
An airplane is flying horizontally with a constant velocity of 200 m/s at an altitude of 5000 m when it releases a package. (a) How long does it take the package to reach the ground? (b)
A horizontal rifle is fired at a target 50 m away. The bullet falls vertically a distance of 12 cm on the way to the target.(a) What is the speed of the bullet just after it leaves the rifle?(b) What
A bullet of mass 0.024 kg is fired horizontally with a speed of 75 m/s from a tall bridge. If the bullet is in the air for 2.3 s, how far from the base of the bridge does it land?
Consider the game of baseball. A pitcher throws a ball to the catcher at a speed of 100 mi/h (45 m/s). If the velocity of the ball is horizontal when it leaves the pitcher’s hand, how far
A batted baseball is hit with a speed of 45 m/s starting from an initial height of 1 m. Find how high the ball travels in two cases: (a) A ball hit directly upward and (b) A ball hit at an
Consider the problem of kicking a soccer ball past a goalkeeper into the goal (Fig. P4.29). You are 25 m away from the goal and kick the ball at an angle of 30° with respect to the horizontal,
A ball is thrown straight up and rises to a maximum height of 24 m. At what height is the speed of the ball equal to half its initial value? Assume the ball starts at a height of 2.0 m above the
Two rocks are thrown off a cliff. One rock (1) is thrown horizontally with a speed of 20 m/s. The other rock (2) is thrown at an angle θ relative to the horizontal with a speed of 30 m/s. While the
A bullet is fired from a rifle with speed v0at an angle Î¸ with respect to the horizontal axis (Fig. P4.32) from a cliff that is a height h above the ground below. (a) Calculate the
A high jumper can run horizontally with a top speed of 10.0 m/s. (a) If he can “convert” this velocity to the vertical direction when he leaves the ground, what is the theoretical limit on
A baseball is thrown with an initial velocity of magnitude v0 at an angle of 60° with respect to the horizontal (x) direction. At the same time, a second ball is thrown with the same initial speed
A swimmer is able to swim at a speed of 0.90 m/s in still water.(a) How long does it take the swimmer to go a distance of 1500 m in still water? Call this time t1. (b) The swimmer then decides
Consider a swimmer who wants to swim directly across a river as in Example 4.7. If the speed of the current is 0.30 m/s and the swimmer’s speed relative to the water is 0.60 m/s, how long will it
Suppose the swimmer in Figure 4.21 has a swimming speed relative to the water of 0.45 m/s and the current€™s speed is 2.5 m/s. If it takes the swimmer 200 s to cross the river, how wide is
An airplane has a velocity relative to the air of 200 m/s in a westerly direction. If the wind has a speed relative to the ground of 60 m/s directed to the north, what is the speed of the airplane

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