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physics
college physics 2nd

College Physics 2nd Edition OpenStax - Solutions

How does a pulley enable a person to lift a load as heavy as a piano with little effort?
Suppose a 900-kg car is on the bridge in Figure 9.32 with its center of mass halfway between the hinges and the cable attachments. (The bridge is supported by the cables and hinges only.) (a) Find the force in the cables.(b) Find the direction and magnitude of the force exerted by the hinges on
Why are the forces exerted on the outside world by the limbs of our bodies usually much smaller than the forces exerted by muscles inside the body?
A sandwich board advertising sign is constructed as shown in Figure 9.33. The sign’s mass is 8.00 kg.(a) Calculate the tension in the chain assuming no friction between the legs and the sidewalk. (b) What force is exerted by each side on the hinge? Hinge Chain 02001 Brooks/Cole-Thomson
Explain why the forces in our joints are several times larger than the forces we exert on the outside world with our limbs. Can these forces be even greater than muscle forces?
(a) What minimum coefficient of friction is needed between the legs and the ground to keep the sign in Figure 9.33 in the position shown if the chain breaks?(b) What force is exerted by each side on the hinge?Data given in figure 9.33 Hinge Chain 02001 Brooks/Cole-Thomson Learning CG CG 0.50
Certain types of dinosaurs were bipedal (walked on two legs). What is a good reason that these creatures invariably had long tails if they had long necks?
An athlete is attempting to perform splits. From the information given in Figure 9.34, calculate the magnitude and direction of the force exerted on each foot by the floor. Hip pivot CG 1.8 m w = 700N 0.90 m 0.30 m
Swimmers and athletes during competition need to go through certain postures at the beginning of the race. Consider the balance of the person and why start-offs are so important for races.
If the maximum force the biceps muscle can exert is 1000 N, can we pick up an object that weighs 1000 N? Explain your answer.
To get up on the roof, a person (mass 70.0 kg) places a 6.00-m aluminum ladder (mass 10.0 kg) against the house on a concrete pad with the base of the ladder 2.00 m from the house. The ladder rests against a plastic rain gutter, which we can assume to be frictionless. The center of mass of the
In Figure 9.20, the cg of the pole held by the pole vaulter is 2.00 m from the left hand, and the hands are 0.700 m apart. Calculate the force exerted by (a) His right hand and(b) His left hand. (c) If each hand supports half the weight of the pole in Figure 9.18, show that the second condition
Suppose the biceps muscle was attached through tendons to the upper arm close to the elbow and the forearm near the wrist. What would be the advantages and disadvantages of this type of construction for the motion of the arm?
What is the mechanical advantage of a nail puller-similar to the one shown in Figure 9.21 -where you exert a force 45 cm from the pivot and the nail is 1.8 cm on the other side? What minimum force must you exert to apply a force of 1250 N to the nail? F₁ Free-body diagram N FIF = ril 1₁ =
a) What is the mechanical advantage of a wheelbarrow, such as the one in Figure 9.22, if the center of gravity of the wheelbarrow and its load has a perpendicular lever arm of 5.50 cm, while the hands have a perpendicular lever arm of 1.02 m?(b) What upward force should you exert to support the
Suppose you needed to raise a 250-kg mower a distance of 6.0 cm above the ground to change a tire. If you had a 2.0-m long lever, where would you place the fulcrum if your force was limited to 300 N?
A typical car has an axle with 1.10 cm radius driving a tire with a radius of 27.5 cm. What is its mechanical advantage assuming the very simplified model in Figure 9.23(b)? (b) Fo ro= ro F - G₁ = ₁₁
What force does the nail puller in Exercise 9.19 exert on the supporting surface? The nail puller has a mass of 2.10 kg.Data given in Exercise 9.19What is the mechanical advantage of a nail puller-similar to the one shown in Figure 9.21 -where you exert a force 45 cm from the pivot and the nail is
If you used an ideal pulley of the type shown in Figure 9.24(a) to support a car engine of mass 115 kg,(a) What would be the tension in the rope? (b) What force must the ceiling supply, assuming you pull straight down on the rope? Neglect the pulley system's mass. (a) MA 2 W O (b) MA = 3 W (c) MA
Repeat Exercise 9.24 for the pulley shown in Figure 9.24(c), assuming you pull straight up on the rope. The pulley system's mass is 7.00 kg.Data given in Exercise 9.24If you used an ideal pulley of the type shown in Figure 9.24(a) to support a car engine of mass 115 kg,(a) What would be the tension
Verify that the force in the elbow joint in Example 9.4 is 407 N, as stated in the text.Data given in Example 9.4Calculate the force the biceps muscle must exert to hold the forearm and its load as shown in Figure 9.25, and compare this force with the weight of the forearm plus its load. You may
Two muscles in the back of the leg pull on the Achilles tendon as shown in Figure 9.35. What total force do they exert? F₂(200 N) Lateral gastrocnemius Achilles' tendon 20% 20° F₁(200 N) Medial gastrocnemius
The upper leg muscle (quadriceps) exerts a force of 1250 N, which is carried by a tendon over the kneecap (the patella) at the angles shown in Figure 9.36. Find the direction and magnitude of the force exerted by the kneecap on the upper leg bone (the femur). 55° F 1250 N 75° Fa
A device for exercising the upper leg muscle is shown in Figure 9.37, together with a schematic representation of an equivalent lever system. Calculate the force exerted by the upper leg muscle to lift the mass at a constant speed. Explicitly show how you follow the steps in the Problem-Solving
A person working at a drafting board may hold her head as shown in Figure 9.38, requiring muscle action to support the head. The three major acting forces are shown. Calculate the direction and magnitude of the force supplied by the upper vertebrae FVto hold the head stationary, assuming that this
We analyzed the biceps muscle example with the angle between forearm and upper arm set at 90°. Using the same numbers as in Example 9.4, find the force exerted by the biceps muscle when the angle is 120° and the forearm is in a downward position.Data given in Example 9.4Calculate the force the
A 75-kg man stands on his toes by exerting an upward force through the Achilles tendon, as in Figure 9.40.(a) What is the force in the Achilles tendon if he stands on one foot?(b) Calculate the force at the pivot of the simplified lever system shown—that force is representative of forces in the
A father lifts his child as shown in Figure 9.41. What force should the upper leg muscle exert to lift the child at a constant speed? Fa 2.0 cm =20.0 cm CG mg = 4.0 kg W109 W child = 38.0 cm = 10 kg
Unlike most of the other muscles in our bodies, the masseter muscle in the jaw, as illustrated in Figure 9.42, is attached relatively far from the joint, enabling large forces to be exerted by the back teeth.(a) Using the information in the figure, calculate the force exerted by the lower teeth on
Explain in terms of impulse how padding reduces forces in a collision. State this in terms of a real example, such as the advantages of a carpeted vs. tile floor for a day care center.
(a) Find the recoil velocity of a 70.0-kg ice hockey goalie, originally at rest, who catches a 0.150-kg hockey puck slapped at him at a velocity of 35.0 m/s.(b) How much kinetic energy is lost during the collision? Assume friction between the ice and the puck-goalie system is negligible. (See
In the collision pictured in Figure 8.9, two carts collide inelastically. Cart 1 (denoted m carries a spring which is initially compressed. During the collision, the spring releases its potential energy and converts it to internal kinetic energy. The mass of cart 1 and the spring is 0.350 kg, and
While jumping on a trampoline, sometimes you land on your back and other times on your feet. In which case can you reach a greater height and why?
Suppose the following experiment is performed. A 0.250-kg object (m1) is slid on a frictionless surface into a dark room, where it strikes an initially stationary object with mass of 0.400 kg (m2) . The 0.250-kg object emerges from the room at an angle of 45.0° with its incoming direction. The
The mass of Earth is 5.972 x 1024 kg and its orbital radius is an average of 1.496 x 1011 m. Calculate its linear momentum.
Tennis racquets have “sweet spots.” If the ball hits a sweet spot then the player's arm is not jarred as much as it would be otherwise. Explain why this is the case.
A bullet is accelerated down the barrel of a gun by hot gases produced in the combustion of gun powder. What is the average force exerted on a 0.0300-kg bullet to accelerate it to a speed of 600.0 m/s in a time of 2.00 ms (milliseconds)?
Which statement is correct? (a) Net force causes motion.(b) Net force causes change in motion. Explain your answer and give an example.
Calculate the force the professor exerts on the cart in Figure 4.10 using data from the previous example if needed. StrategyIf we now define the system of interest to be the cart plus equipment (System 2 in Figure 4.10), then the net external force on System 2 is the force the professor exerts on
Construct Your Own Problem Consider a ball tossed over a fence. Construct a problem in which you calculate the ball’s needed initial velocity to just clear the fence. Among the things to determine are; the height of the fence, the distance to the fence from the point of release of the ball, and
If the sprinter from the previous problem accelerates at that rate for 20 m, and then maintains that velocity for the remainder of the 100-m dash, what will be his time for the race?Data given in Previous ProblemA 63.0-kg sprinter starts a race with an acceleration of 4.20 m/s2. What is the net
A physics professor pushes a cart of demonstration equipment to a lecture hall, as seen in Figure 4.10. Her mass is 65.0 kg, the cart’s is 12.0 kg, and the equipment’s is 7.0 kg. Calculate the acceleration produced when the professor exerts a backward force of 150 N on the floor. All forces
How are inertia and mass related?
A cleaner pushes a 4.50-kg laundry cart in such a way that the net external force on it is 60.0 N. Calculate the magnitude of its acceleration.
Since astronauts in orbit are apparently weightless, a clever method of measuring their masses is needed to monitor their mass gains or losses to adjust diets. One way to do this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of 50.0 N
What is the relationship between weight and mass? Which is an intrinsic, unchanging property of a body?
Consider the skier on a slope shown in Figure 4.12. Her mass including equipment is 60.0 kg. (a) What is her acceleration if friction is negligible?(b) What is her acceleration if friction is known to be 45.0 N?StrategyThis is a two-dimensional problem, since the forces on the skier (the system of
In Figure 4.7, the net external force on the 24-kg mower is stated to be 51 N. If the force of friction opposing the motion is 24 N, what force (in newtons) is the person exerting on the mower? Suppose the mower is moving at 1.5 m/s when the force is removed. How far will the mower go before
Calculate the tension in the wire supporting the 70.0-kg tightrope walker shown in Figure 4.16.StrategyAs you can see in the figure, the wire is not perfectly horizontal (it cannot be!), but is bent under the person's weight. Thus, the tension on either side of the person has an upward component
The same rocket sled drawn in Figure 4.30 is decelerated at a rate of 196 m/s2. What force is necessary to produce this deceleration? Assume that the rockets are off. The mass of the system is 2100 kg. N W
Why can we neglect forces such as those holding a body together when we apply Newton’s second law of motion?
(a) If the rocket sled shown in Figure 4.31 starts with only one rocket burning, what is the magnitude of its acceleration? Assume that the mass of the system is 2100 kg, the thrust T is 2.4 x 104 N, and the force of friction opposing the motion is known to be 650 N.(b) Why is the acceleration not
Suppose two tugboats push on a barge at different angles, as shown in Figure 4.21. The first tugboat exerts a force of 2.7 x 105 N in the x-direction, and the second tugboat exerts a force of 3.6 x 105 N in the y-direction.If the mass of the barge is 5.0 x 106 kg and its acceleration is observed to
Explain how the choice of the “system of interest” affects which forces must be considered when applying Newton’s second law of motion.
Consider the traffic light (mass 15.0 kg) suspended from two wires as shown in Figure 4.22. Find the tension in each wire, neglecting the masses of the wires.StrategyThe system of interest is the traffic light, and its free-body diagram is shown in Figure 4.22(c). The three forces involved are not
Describe a situation in which the net external force on a system is not zero, yet its speed remains constant.
What is the deceleration of the rocket sled if it comes to rest in 1.1 s from a speed of 1000 km/h? (Such deceleration caused one test subject to black out and have temporary blindness.)
Figure 4.23 shows a 75.0-kg man (weight of about 165 lb) standing on a bathroom scale in an elevator. Calculate the scale reading:(a) If the elevator accelerates upward at a rate of 1.20 m/s2, and(b) If the elevator moves upward at a constant speed of 1 m/s.StrategyIf the scale is accurate, its
A system can have a nonzero velocity while the net external force on it is zero. Describe such a situation.
Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. The first child exerts a force of 75.0 N, the second a force of 90.0 N, friction is 12.0 N, and the mass of the third child plus wagon is 23.0 kg.a. What is the system of interest if the
Consider the baby being weighed in Figure 4.33.(a) What is the mass of the child and basket if a scale reading of 55 N is observed?(b) What is the tension T1 in the cord attaching the baby to the scale?(c) What is the tension T2 in the cord attaching the scale to the ceiling, if the scale has a
In a traction setup for a broken bone, with pulleys and rope available, how might we be able to increase the force along the tibia using the same weight? (See Figure 4.29.) (Note that the tibia is the shin bone shown in this image.) T W leg T 0 w = mg
A 5.00 x 105-kg rocket is accelerating straight up. Its engines produce 1.250 x 107 N of thrust, and air resistance is 4.50 x 106 N. What is the rocket's acceleration? Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton's laws of motion.
To simulate the apparent weightlessness of space orbit, astronauts are trained in the hold of a cargo aircraft that is accelerating downward at . Why will they appear to be weightless, as measured by standing on a bathroom scale, in this accelerated frame of reference? Is there any difference
The wheels of a midsize car exert a force of 2100 N backward on the road to accelerate the car in the forward direction. If the force of friction including air resistance is 250 N and the acceleration of the car is 1.80 m/s2, what is the mass of the car plus its occupants? Explicitly show how you
A cartoon shows the hat coming off the head of an elevator passenger when the elevator rapidly stops during an upward ride. Can this really happen without the person being tied to the floor of the elevator? Explain your answer.
Explain, in terms of the properties of the four basic forces, why people notice the gravitational force acting on their bodies if it is such a comparatively weak force.
When landing after a spectacular somersault, a 40.0-kg gymnast decelerates by pushing straight down on the mat. Calculate the force she must exert if her deceleration is 7.00 times the acceleration due to gravity. Explicitly show how you follow the steps in the Problem-Solving Strategy for
What is the dominant force between astronomical objects? Why are the other three basic forces less significant over these very large distances?
A freight train consists of two 8.00 x 104 -kg engines and 45 cars with average masses of 5.50 x 104 kg.(a) What force must each engine exert backward on the track to accelerate the train at a rate of 5.00 x 10-2 m/s2 if the force of friction is 7.50 x 105 N, assuming the engines exert identical
Give a detailed example of how the exchange of a particle can result in an attractive force. (For example, consider one child pulling a toy out of the hands of another.)
Commercial airplanes are sometimes pushed out of the passenger loading area by a tractor.(a) An 1800-kg tractor exerts a force of 1.75 x 104 N backward on the pavement, and the system experiences forces resisting motion that total 2400 N. If the acceleration is 0.150 m/s2, what is the mass of the
Two children pull a third child on a snow saucer sled exerting forces F1 and F2 as shown from above in Figure 4.35. Find the acceleration of the 49.00-kg sled and child system. Note that the direction of the frictional force is unspecified; it will be in the opposite direction of the sum of F1 and
A 1100-kg car pulls a boat on a trailer.(a) What total force resists the motion of the car, boat, and trailer, if the car exerts a 1900-N force on the road and produces an acceleration of 0.550 m/s2? The mass of the boat plus trailer is 700 kg.(b) What is the force in the hitch between the car and
Suppose your car was mired deeply in the mud and you wanted to use the method illustrated in Figure 4.36 to pull it out.(a) What force would you have to exert perpendicular to the center of the rope to produce a force of 12,000 N on the car if the angle is 2.00°? In this part, explicitly show how
Figure 4.38 shows Superhero and Trusty Sidekick hanging motionless from a rope. Superhero’s mass is 90.0 kg, while Trusty Sidekick’s is 55.0 kg, and the mass of the rope is negligible.(a) Draw a freebody diagram of the situation showing all forces acting on Superhero, Trusty Sidekick, and the
A nurse pushes a cart by exerting a force on the handle at a downward angle 35.0° below the horizontal. The loaded cart has a mass of 28.0 kg, and the force of friction is 60.0 N.(a) Draw a free- body diagram for the system of interest.(b) What force must the nurse exert to move at a constant
Consider the tension in an elevator cable during the time the elevator starts from rest and accelerates its load upward to some cruising velocity. Taking the elevator and its load to be the system of interest, draw a free-body diagram. Then calculate the tension in the cable. Among the things to
Construct Your Own Problem Consider two people pushing a toboggan with four children on it up a snow-covered slope. Construct a problem in which you calculate the acceleration of the toboggan and its load. Include a free-body diagram of the appropriate system of interest as the basis for your
Unreasonable Results(a) Repeat Exercise 4.29. but assume an acceleration of 1.20 m/s2 is produced.(b) What is unreasonable about the result?(c) Which premise is unreasonable, and why is it unreasonable?Data given in figure 4.29 T W leg T T Ө 0 w = mg
Unreasonable Results(a) What is the initial acceleration of a rocket that has a mass of 1.50 × 106 kg at takeoff, the engines of which produce a thrust of 2.00 x 106 N? Do not neglect gravity.(b) What is unreasonable about the result? (This result has been unintentionally achieved by several real
A flea jumps by exerting a force of 1.20 × 10-5 N straight down on the ground. A breeze blowing on the flea parallel to the ground exerts a force of 0.500 x 10-6 N on the flea. Find the direction and magnitude of the acceleration of the flea if its mass is 6.00 x 10-7 kg. Do not neglect the
Two muscles in the back of the leg pull upward on the Achilles tendon, as shown in Figure 4.39. (These muscles are called the medial and lateral heads of the gastrocnemius muscle.) Find the magnitude and direction of the total force on the Achilles tendon. What type of movement could be caused by
A 76.0-kg person is being pulled away from a burning building as shown in Figure 4.40. Calculate the tension in the two ropes if the person is momentarily motionless. Include a freebody diagram in your solution. 15° T₁ W T₂ J.10°
Integrated Concepts A 35.0-kg dolphin decelerates from 12.0 to 7.50 m/s in 2.30 s to join another dolphin in play. What average force was exerted to slow him if he was moving horizontally? (The gravitational force is balanced by the buoyant force of the water.)
When starting a foot race, a 70.0-kg sprinter exerts an average force of 650 N backward on the ground for 0.800 s.(a) What is his final speed?(b) How far does he travel?
A large rocket has a mass of 2.00 × 106 kg at takeoff, and its engines produce a thrust of 3.50 x 107 N.(a) Find its initial acceleration if it takes off vertically.(b) How long does it take to reach a velocity of 120 km/h straight up, assuming constant mass and thrust?(c) In reality, the mass of
A 2.50-kg fireworks shell is fired straight up from a mortar and reaches a height of 110 m.(a) Neglecting air resistance (a poor assumption, but we will make it for this example), calculate the shell’s velocity when it leaves the mortar.(b) The mortar itself is a tube 0.450 m long. Calculate the
Integrated Concepts Repeat Exercise 4.47 for a shell fired at an angle 10.0° from the vertical.Data given in Exercise 4.47Integrated Concepts A 2.50-kg fireworks shell is fired straight up from a mortar and reaches a height of 110 m.(a) Neglecting air resistance (a poor assumption, but we will
Unreasonable Results(a) What is the final velocity of a car originally traveling at 50.0 km/h that decelerates at a rate of 0.400 m/s2 for 50.0 s?(b) What is unreasonable about the result?(c) Which premise is unreasonable, or which premises are inconsistent?
(a) What is the strength of the weak nuclear force relative to the strong nuclear force?(b) What is the strength of the weak nuclear force relative to the electromagnetic force? Since the weak nuclear force acts at only very short distances, such as inside nuclei, where the strong and
(a) What is the ratio of the strength of the gravitational force to that of the strong nuclear force?(b) What is the ratio of the strength of the gravitational force to that of the weak nuclear force?(c) What is the ratio of the strength of the gravitational force to that of the electromagnetic
What is the ratio of the strength of the strong nuclear force to that of the electromagnetic force? Based on this ratio, you might expect that the strong force dominates the nucleus, which is true for small nuclei. Large nuclei, however, have sizes greater than the range of the strong nuclear
A skier with a mass of 62 kg is sliding down a snowy slope. Find the coefficient of kinetic friction for the skier if friction is known to be 45.0 N.StrategyThe magnitude of kinetic friction was given in to be 45.0 N. Kinetic friction is related to the normal force N as fk = μk N; thus, the
Calculate the deceleration of a snow boarder going up a 5.0°, slope assuming the coefficient of friction for waxed wood on wet snow. The result of Exercise 5.9 may be useful, but be careful to consider the fact that the snow boarder is going uphill. Explicitly show how you follow the steps in
(a) Calculate the acceleration of a skier heading down a 10.0° slope, assuming the coefficient of friction for waxed wood on wet snow.(b) Find the angle of the slope down which this skier could coast at a constant velocity. You can neglect air resistance in both parts, and you will find the result
To maintain a constant speed, the force provided by a car's engine must equal the drag force plus the force of friction of the road (the rolling resistance).(a) What are the magnitudes of drag forces at 70 km/h and 100 km/h for a Toyota Camry? (Drag area is 0.70 m2)(b) What is the magnitude of drag
Stoke`s law describes sedimentation of particles in liquids and can be used to measure viscosity. Particles in liquids achieve terminal velocity quickly. One can measure the time it takes for a particle to fall a certain distance and then use Stoke`s law to calculate the viscosity of the liquid.
If a leg is suspended by a traction setup as shown in Figure 4.29, what is the tension in the rope? T W leg T w = mg
If the acceleration of a system is zero, are no external forces acting on it? What about internal forces? Explain your answers.

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