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physics
college physics 2nd
College Physics 2nd Edition OpenStax - Solutions
A powerful motorcycle can produce an acceleration of 3.50 m/s2 while traveling at 90.0 km/h. At that speed the forces resisting motion, including friction and air resistance, total 400 N. (Air resistance is analogous to air friction. It always opposes the motion of an object.) What is the magnitude
A rock is thrown straight up. What is the net external force acting on the rock when it is at the top of its trajectory?
A soccer player starts from rest and accelerates forward, reaching a velocity of 8.00 m/s in 2.50 s. (a) What was his average acceleration?(b) What average force did he exert backward on the ground to achieve this acceleration? The player’s mass is 70.0 kg, and air resistance is
The rocket sled shown in Figure 4.32 accelerates at a rate of 49.0 m/s2. Its passenger has a mass of 75.0 kg.(a) Calculate the horizontal component of the force the seat exerts against his body. Compare this with his weight by using a ratio.(b) Calculate the direction and magnitude of the total
(a) Give an example of different net external forces acting on the same system to produce different accelerations. (b) Give an example of the same net external force acting on systems of different masses, producing different accelerations.(c) What law accurately describes both effects? State it in
Repeat the previous problem for the situation in which the rocket sled decelerates at a rate of 201 m/s2. In this problem, the forces are exerted by the seat and restraining belts.
If a constant, nonzero force is applied to an object, what can you say about the velocity and acceleration of the object?
Suppose the mass of a fully loaded module in which astronauts take off from the Moon is 10,000 kg. The thrust of its engines is 30,000 N.(a) Calculate its the magnitude of acceleration in a vertical takeoff from the Moon.(b) Could it lift off from Earth? If not, why not? If it could, calculate the
The gravitational force on the basketball in Figure 4.6 is ignored. When gravity is taken into account, what is the direction of the net external force on the basketball—above horizontal, below horizontal, or still horizontal? m₂ (a) (b) The free-body diagrams for both objects are the
What net external force is exerted on a 1100-kg artillery shell fired from a battleship if the shell is accelerated at 2.40 x 104 m/s2? What is the magnitude of the force exerted on the ship by the artillery shell?
When you take off in a jet aircraft, there is a sensation of being pushed back into the seat. Explain why you move backward in the seat—is there really a force backward on you? (The same reasoning explains whiplash injuries, in which the head is apparently thrown backward.)
A rugby player is being pushed backward by an opposing player who is exerting a force of 800 N on him. The mass of the losing player plus equipment is 90.0 kg, and he is accelerating at 1.20 m/s2 backward.(a) What is the force of friction between the losing player's feet and the grass?(b) What
A device used since the 1940s to measure the kick or recoil of the body due to heart beats is the “ballistocardiograph.” What physics principle(s) are involved here to measure the force of cardiac contraction? How might we construct such a device?
Describe a situation in which one system exerts a force on another and, as a consequence, experiences a force that is equal in magnitude and opposite in direction. Which of Newton’s laws of motion apply?
What force does a trampoline have to apply to a 45.0-kg gymnast to accelerate her straight up at 7.50 m/s2? Note that the answer is independent of the velocity of the gymnast-she can be moving either up or down, or be stationary.
Why does an ordinary rifle recoil (kick backward) when fired? The barrel of a recoilless rifle is open at both ends. Describe how Newton’s third law applies when one is fired. Can you safely stand close behind one when it is fired?
Newton’s third law of motion tells us that forces always occur in pairs of equal and opposite magnitude. Explain how the choice of the “system of interest” affects whether one such pair of forces cancels.
Suppose a 60.0-kg gymnast climbs a rope.(a) What is the tension in the rope if they climb at a constant speed?(b) What is the tension in the rope if they accelerate upward at a rate of 1.50 m/s2?
An American football lineman reasons that it is senseless to try to out-push the opposing player, since no matter how hard he pushes he will experience an equal and opposite force from the other player. Use Newton’s laws and draw a free body diagram of an appropriate system to explain how he can
(a) Calculate the tension in a vertical strand of spider web if a spider of mass 8.00 x 10-5 kg hangs motionless on it.(b) Calculate the tension in a horizontal strand of spider web if the same spider sits motionless in the middle of it much like the tightrope walker in Figure 4.16. The strand sags
Is there a real force that throws water from clothes during the spin cycle of a washing machine? Explain how the water is removed.
An ordinary workshop grindstone has a radius of 7.50 cm and rotates at 6500 rev/min.(a) Calculate the magnitude of the centripetal acceleration at its edge in meters per second squared and convert it to multiples of g.(b) What is the linear speed of a point on its edge?
This problem returns to the tightrope walker studied in Example 4.6, who created a tension of 3.94 x 103 N in a wire making an angle 5.0° below the horizontal with each supporting pole. Calculate how much this tension stretches the steel wire if it was originally 15 m long and 0.50 cm in
Calculate the angular velocity of a 0.300 m radius car tire when the car travels at 15.0 m/s (about 54 km/h). See Figure 6.5.Strategy 3 V v=rw
There is an analogy between rotational and linear physical quantities. What rotational quantities are analogous to distance and velocity?
What is the magnitude of the centripetal acceleration of a car following a curve of radius 500 m at a speed of 25.0 m/s (about 90 km/h)? Compare the acceleration with that due to gravity for this fairly gentle curve taken at highway speed. See Figure 6.8(a).StrategyBecause and are given, the first
Calculate the centripetal acceleration of a point 7.50 cm from the axis of an ultracentrifuge spinning at 7.5 x 104 rev/min. Determine the ratio of this acceleration to that due to gravity. See Figure 6.8(b).StrategyThe term rev/min stands for revolutions per minute. By converting this to radians
Microwave ovens rotate at a rate of about 6 rev/min. What is this in revolutions per second? What is the angular velocity in radians per second?
If you wish to reduce the stress (which is related to centripetal force) on high-speed tires, would you use large- or small-diameter tires? Explain.
An automobile with 0.260 m radius tires travels 80,000 km before wearing them out. How many revolutions do the tires make, neglecting any backing up and any change in radius due to wear?
(a) Calculate the centripetal force exerted on a 900 kg car that negotiates a 500 m radius curve at 25.0 m/s.(b) Assuming an unbanked curve, find the minimum static coefficient of friction, between the tires and the road, static friction being the reason that keeps the car from slipping (see Figure
Define centripetal force. Can any type of force (for example, tension, gravitational force, friction, and so on) be a centripetal force? Can any combination of forces be a centripetal force?
(a) What is the period of rotation of Earth in seconds?(b) What is the angular velocity of Earth?(c) Given that Earth has a radius of 6.4 x 106 mat its equator, what is the linear velocity at Earth's surface?
Curves on some test tracks and race courses, such as the Daytona International Speedway in Florida, are very steeply banked. This banking, with the aid of tire friction and very stable car configurations, allows the curves to be taken at very high speed. To illustrate, calculate the speed at which
If centripetal force is directed toward the center, why do you feel that you are ‘thrown’ away from the center as a car goes around a curve? Explain.
A baseball pitcher brings his arm forward during a pitch, rotating the forearm about the elbow. If the velocity of the ball in the pitcher’s hand is 35.0 m/s and the ball is 0.300 m from the elbow joint, what is the angular velocity of the forearm?
Race car drivers routinely cut corners as shown in Figure 6.29. Explain how this allows the curve to be taken at the greatest speed. I Tite Path 2 Path 1
In lacrosse, a ball is thrown from a net on the end of a stick by rotating the stick and forearm about the elbow. If the angular velocity of the ball about the elbow joint is 30.0 rad/s and the ball is 1.30 m from the elbow joint, what is the velocity of the ball?
Given that the Moon orbits Earth each 27.3 d and that it is an average distance of 3.84 x 108 m from the center of Earth, calculate the period of an artificial satellite orbiting at an average altitude of 1500 km above Earth's surface.StrategyThe period, or time for one orbit, is related to the
A number of amusement parks have rides that make vertical loops like the one shown in Figure 6.30. For safety, the cars are attached to the rails in such a way that they cannot fall off. If the car goes over the top at just the right speed, gravity alone will supply the centripetal force. What
What is the direction of the force exerted by the car on the passenger as the car goes over the top of the amusement ride pictured in Figure 6.30 under the following circumstances:(a) The car goes over the top at such a speed that the gravitational force is the only force acting?(b) The car goes
Integrated Concepts When kicking a football, the kicker rotates his leg about the hip joint.(a) If the velocity of the tip of the kicker’s shoe is 35.0 m/s and the hip joint is 1.05 m from the tip of the shoe, what is the shoe tip’s angular velocity?(b) The shoe is in contact with the initially
As a skater forms a circle, what force is responsible for making her turn? Use a free body diagram in your answer.
Suppose a child is riding on a merry-go-round at a distance about halfway between its center and edge. She has a lunch box resting on wax paper, so that there is very little friction between it and the merry-go round. Which path shown in Figure 6.31 will the lunch box take when she lets go? The
Consider an amusement park ride in which participants are rotated about a vertical axis in a cylinder with vertical walls. Once the angular velocity reaches its full value, the floor drops away and friction between the walls and the riders prevents them from sliding down. Construct a problem in
A fairground ride spins its occupants inside a flying saucer-shaped container. If the horizontal circular path the riders follow has an 8.00 m radius, at how many revolutions per minute will the riders be subjected to a centripetal acceleration whose magnitude is 1.50 times that due to gravity?
Do you feel yourself thrown to either side when you negotiate a curve that is ideally banked for your car’s speed? What is the direction of the force exerted on you by the car seat?
A runner taking part in the 200 m dash must run around the end of a track that has a circular arc with a radius of curvature of 30 m. If the runner completes the 200 m dash in 23.2 s and runs at constant speed throughout the race, what is the magnitude of their centripetal acceleration as they run
Suppose a mass is moving in a circular path on a frictionless table as shown in figure. In the Earth’s frame of reference, there is no centrifugal force pulling the mass away from the centre of rotation, yet there is a very real force stretching the string attaching the mass to the nail. Using
Taking the age of Earth to be about 4 x 109 years and assuming its orbital radius of 1.5 x1011 m. has not changed and is circular, calculate the approximate total distance Earth has traveled since its birth (in a frame of reference stationary with respect to the Sun).
When a toilet is flushed or a sink is drained, the water (and other material) begins to rotate about the drain on the way down. Assuming no initial rotation and a flow initially directly straight toward the drain, explain what causes the rotation and which direction it has in the northern
The propeller of a World War II fighter plane is 2.30 m in diameter.(a) What is its angular velocity in radians per second if it spins at 1200 rev/min?(b) What is the linear speed of its tip at this angular velocity if the plane is stationary on the tarmac?(c) What is the centripetal acceleration
Newton’s laws of motion and gravity were among the first to convincingly demonstrate the underlying simplicity and unity in nature. Many other examples have since been discovered, and we now expect to find such underlying order in complex situations. Is there proof that such order will always be
A mother pushes her child on a swing so that his speed is 9.00 m/s at the lowest point of his path.The swing is suspended 2.00 m above the child’s center of mass.(a) What is the magnitude of the centripetal acceleration of the child at the low point?(b) What is the magnitude of the force the
(a) A 22.0 kg child is riding a playground merry-goround that is rotating at 40.0 rev/min. What centripetal force must she exert to stay on if she is 1.25 m from its center?(b) What centripetal force does she need to stay on an amusement park merry-go-round that rotates at 3.00 rev/min if she is
In what frame(s) of reference are Kepler’s laws valid? Are Kepler’s laws purely descriptive, or do they contain causal information?
Calculate the centripetal force on the end of a 100 m (radius) wind turbine blade that is rotating at 0.5 rev/s. Assume the mass is 4 kg.
What is the ideal banking angle for a gentle turn of 1.20 km radius on a highway with a 105 km/h speed limit (about 65 mi/h), assuming everyone travels at the limit?
Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen in Figure 6.33. To be stable, the force exerted by the ground must be on a line going through the center of gravity. The force on the bicycle wheel can be resolved into two perpendicular components—friction
What is the ideal speed to take a 100 m radius curve banked at a 20.0° angle?
(a) What is the radius of a bobsled turn banked at 75.0° and taken at 30.0 m/s, assuming it is ideally banked?(b) Calculate the centripetal acceleration.(c) Does this acceleration seem large to you?
A large centrifuge, like the one shown in Figure 6.34(a), is used to expose aspiring astronauts to accelerations similar to those experienced in rocket launches and atmospheric reentries.(a) At what angular velocity is the centripetal acceleration 10g if the rider is 15.0 m from the center of
If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads).(a) Calculate the ideal speed to take a 100 m radius curve banked at 15.0º.(b) What is the minimum coefficient of friction
Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 x 1011 solar masses. A star orbiting on the galaxy's periphery is about 6.0 x 104 light years from its center. (a) What should the orbital period of that star be?(b) If its period is 6.0 x 107 years instead,
How much work is done on the lawn mower by the person in Figure 7.2(a) if he exerts a constant force of 75.0 N at an angle 35° below the horizontal and pushes the mower 25.0 m on level ground? Convert the amount of work from joules to kilocalories and compare it with this person's average daily
(a) Based on Kepler’s laws and information on the orbital characteristics of the Moon, calculate the orbital radius for an Earth satellite having a period of 1.00 h. (b) What is unreasonable about this result?(c) What is unreasonable or inconsistent about the premise of a 1.00 h orbit?
On February 14, 2000, the NEAR spacecraft was successfully inserted into orbit around Eros, becoming the first artificial satellite of an asteroid. Construct a problem in which you determine the orbital speed for a satellite near Eros. You will need to find the mass of the asteroid and consider
Suppose a 30.0-kg package on the roller belt conveyor system in Figure 7.4 is moving at 0.500 m/s. What is its kinetic energy?StrategyBecause the mass and speed are given, the kinetic energy can be calculated from its definition as given in the equation Fa 120 N app = m = 30.0 kg w N W f = 5.00 N d
Give an example of something we think of as work in everyday circumstances that is not work in the scientific sense. Is energy transferred or changed in form in your example? If so, explain how this is accomplished without doing work.
A 75.0-kg person climbs stairs, gaining 2.50 meters in height. Find the work done to accomplish this task.
Give an example of a situation in which there is a force and a displacement, but the force does no work. Explain why it does no work.
Suppose that you push on the 30.0-kg package in Figure 7.4 with a constant force of 120 N through a distance of 0.800 m, and that the opposing friction force averages 5.00 N.(a) Calculate the net work done on the package.(b) Solve the same problem as in part (a), this time by finding the work done
(a) Calculate the work done on a 1500-kg elevator car by its cable to lift it 40.0 m at constant speed, assuming friction averages 100 N. (b) What is the work done on the elevator car by the gravitational force in this process?(c) What is the total work done on the elevator car?
Describe a situation in which a force is exerted for a long time but does no work. Explain.
A spark of static electricity, such as that you might receive from a doorknob on a cold dry day, may carry a few hundred watts of power. Explain why you are not injured by such a spark.
A 5.00 × 105-kg subway train is brought to a stop from a speed of 0.500 m/s in 0.400 m by a large spring bumper at the end of its track. What is the force constant k of the spring?
Shivering is an involuntary response to lowered body temperature. What is the efficiency of the body when shivering, and is this a desirable value?
A pogo stick has a spring with a force constant of 2.50 × 104 N/m, which can be compressed 12.0 cm. To what maximum height can a child jump on the stick using only the energy in the spring, if the child and stick have a total mass of 40.0 kg?
A 60.0-kg skier with an initial speed of 12.0 m/s coasts up a 2.50-m-high rise as shown in Figure 7.37. Find her final speed at the top, given that the coefficient of friction between her skis and the snow is 0.0800. KE₁ V₁ 35° V₁ = ? 2.5 m
Discuss the relative impact of dieting and exercise, noting that most athletic activities consume food energy at a rate of 400 to 500 W, while a single cup of yogurt can contain 1360 kJ (325 kcal).
What is the difference between energy conservation and the law of conservation of energy? Give some examples of each.
(a) How high a hill can a car coast up (engine disengaged) if work done by friction is negligible and its initial speed is 110 km/h?(b) If, in actuality, a 750-kg car with an initial speed of 110 km/h is observed to coast up a hill to a height 22.0 m above its starting point, how much thermal
Using values from Table 7.1, how many DNA molecules could be broken by the energy carried by a single electron in the beam of an old-fashioned TV tube? (These electrons were not dangerous in themselves, but they did create dangerous x rays. Later model tube TVs had shielding that absorbed x rays
If the efficiency of a coal-fired electrical generating plant is 35%, then what do we mean when we say that energy is a conserved quantity?
If the energy in fusion bombs were used to supply the energy needs of the world, how many of the 9-megaton variety would be needed for a year’s supply of energy (using data from Table 7.1)? This is not as far-fetched as it may sound—there are thousands of nuclear bombs, and their energy can be
Using energy considerations and assuming negligible air resistance, show that a rock thrown from a bridge 20.0 m above water with an initial speed of 15.0 m/s strikes the water with a speed of 24.8 m/s independent of the direction thrown.
(a) Use of hydrogen fusion to supply energy is a dream that may be realized in the next century. Fusion would be a relatively clean and almost limitless supply of energy, as can be seen from Table 7.1. To illustrate this, calculate how many years the present energy needs of the world could be
Suppose a star 1000 times brighter than our Sun (that is, emitting 1000 times the power) suddenly goes supernova. Using data from Table 7.3:(a) By what factor does its power output increase? (b) How many times brighter than our entire Milky Way galaxy is the supernova?(c) Based on your answers,
A person in good physical condition can put out 100 W of useful power for several hours at a stretch, perhaps by pedaling a mechanism that drives an electric generator. Neglecting any problems of generator efficiency and practical considerations such as resting time:(a) How many people would it
What is the cost of operating a 3.00-W electric clock for a year if the cost of electricity is $0.0900 per kW.h?
(a) What is the average power consumption in watts of an appliance that uses 5.00 kW.h of energy per day? (b) How many joules of energy does this appliance consume in a year?
Very large forces are produced in joints when a person jumps from some height to the ground.(a) Calculate the magnitude of the force produced if an 80.0-kg person jumps from a 0.600–m-high ledge and lands stiffly, compressing joint material 1.50 cm as a result. (Be certain to include the weight
Action at a distance, such as is the case for gravity, was once thought to be illogical and therefore untrue. What is the ultimate determinant of the truth in physics, and why was this action ultimately accepted?
Olympic ice skaters are able to spin at about 5 rev/s.(a) What is their angular velocity in radians per second?(b) What is the centripetal acceleration of the skater’s nose if it is 0.120 m from the axis of rotation?(c) An exceptional skater named Dick Button was able to spin much faster in the
Two friends are having a conversation. Anna says a satellite in orbit is in freefall because the satellite keeps falling toward Earth. Tom says a satellite in orbit is not in freefall because the acceleration due to gravity is not 9.80m/s2 . Who do you agree with and why?
What percentage of the acceleration at Earth’s surface is the acceleration due to gravity at the position of a satellite located 300 km above Earth?
A non-rotating frame of reference placed at the center of the Sun is very nearly an inertial one. Why is it not exactly an inertial frame?
Action at a distance, such as is the case for gravity, was once thought to be illogical and therefore untrue. What is the ultimate determinant of the truth in physics, and why was this action ultimately accepted?
A rotating space station is said to create “artificial gravity”—a loosely-defined term used for an acceleration that would be crudely similar to gravity. The outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor
Two friends are having a conversation. Anna says a satellite in orbit is in freefall because the satellite keeps falling toward Earth. Tom says a satellite in orbit is not in freefall because the acceleration due to gravity is not 9.80m/s2. Who do you agree with and why?
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