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physics
mechanics

Questions and Answers of Mechanics

A loaded grocery cart is rolling across a parking lot in a strong wind. You apply a constant force F = (30N)i - (40N)j to the cart as it undergoes a displacement 1 = (-9.0m)i - (3.0m)j. How much work
A 800-kg ball is tied to the end of a string 1.60 m long and swung in a vertical circle. (a) During one complete circle, starting anywhere, calculate the total work done on the ball by (i) the
(a) How many joules of kinetic energy does a 750-kg auto-mobile traveling at a typical highway speed of 65 m/h have? (b) By what factor would its kinetic energy decrease if the car traveled half as
Meteor Crater About 50,000 years ago, a meteor crashed into the earth near present-day Flagstaff, Arizona. Recent (2005) measurements estimate that this meteor had a mass of about 1.4 X 108 kg
Some Typical Kinetic Energies (a) How many joules of kinetic energy does a 75-kg person have when walking and when running? (b) In the Bohr model of the atom, the ground-state electron in
The mass of a proton is 1836 times the mass of an electron. (a) A proton is traveling at speed V. At what speed (in terms of V) would an electron have the same kinetic energy as the proton? (b)
A 4.80-kg watermelon is dropped from rest from the m of a 25.0.m-tall building and feels no appreciable air resistance. (a) Calculate the work done by gra on the watermelon during its displacement
Use the work-energy' theorem to solve each of these problems. You can use Newton's laws to check your answers. Neglect air resistance in sell cases. (a) A branch falls from the top of a 95.0.m-tall
You throw a 20-N rock vertically into the air from ground level. You observe that when it is 15.0 m above the ground, it is traveling at 25.0 m/s upward. Use the work-energy theorem to find (a) The
You are a member of an Alpine Rescue Team. You must project a box of supplies up an incline of constant slope angle a so that it reaches a stranded skier who is a vertical distance h above the bottom
A mass m slides down a smooth inclined plane from an initial vertical height h, making an angle a with the horizontal. (a) The work done by a force is the sum of the work done by the components of
A car is stopped in a distance D by a constant friction force that is independent of the car's speed. What is the stopping distance (in terms of D) (a) If the car's initial speed is tripled, and
A moving electron has kinetic energy K,. After a net amount of work W has been done on it, the electron is moving one-quarter as fast in the opposite direction. (a) Find W in terms of K. (b) Does
A sled with mass 8.00 kg moves in a straight line on a frictionless horizontal surface. At one point in its path, its speed is 4.00 m/s; after it has traveled 250 m beyond this point, its speed is
A soccer ball with mass 0.420 kg is initially moving with speed 2.00 m/s. A soccer player kicks the ball, exerting a constant force of magnitude 40.0 N in the same direction as the ball's motion.
A 12-pack of Omni-Cola (mass 4.30 kg) is initially at rest on a horizontal floor. It is then pushed in a straight line for 1.20 m by a trained dog that exerts a horizontal force with magnitude 36.0
A batter hits a baseball with mass 0.145 kg straight upward with an initial speed of 25.0 m/s. (a) How much work has gravity done on the baseball when it reaches a height of 20.0 m above the bat?
A little red wagon with mass 7.00 kg moves in a straight line on a frictionless horizontal surface. It has an initial speed of 4.00 m/s and then is pushed 3.0 m in the direction of the initial
A block of ice with mass 2.00 kg slides 0.750 m down an inclined plane that slopes downward at an angle of 36.9° below the horizontal. If the block of ice starts from rest, what is its final speed?
Stopping Distance a car is traveling on a level road with speed Vo at the instant when the brakes lock, so that the tires slide rather than roll. (a) Use the work-energy theorem to calculate the
To stretch a spring 3.00 cm from its unscratched length, 12.0 I of work must be done. (a) What is the force constant of this spring? (b) What magnitude force is needed to stretch the spring 3.00
A force of 160 N stretches a spring 0.050 m beyond its unscratched length (a) What magnitude of force is required to stretch the spring 0.015 m beyond its unscratched length? To compress the spring
A child applies a force F parallel to the x-axis to a l0.0-kg sled moving on the frozen surface of a small pond. As the child controls the speed of the sled, the x-component of the force she applies
Suppose the sled in Exercise 6.30 is initially at rest at x = O. Use the work-energy theorem to find the speed of the sled at (a) x = 8.0 m and (b) x = 12.0 m. You can ignore friction between the
A balky cow is leaving the barn as you try harder and harder to push her back in. In coordinates with the origin at the barn door, the cow walks from x = 0 to x = 6.9 m as you apply a force with
A 6.0-kg box moving at 3.0 m/s on a horizontal, frictionless surface runs into a light spring of force constant 75 N/cm. Use the work-energy theorem to find the maximum compression of the spring.
Leg Presses. As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each
(a) In Example 6.7 (Section 6.3) it was calculated that with the air track turned off, the glider travels 8.6 cm before it stops instantaneously. How large would the coefficient of static friction
A 4.00-kg block of ice is placed against a horizontal spring that has force constant k = 200 N/m and is compressed 0.025 m. The spring is released and accelerates the block along a horizontal
A force F is applied to a 2.O-kg m dio-controlled model car parallel to the x-axis as it moves along a straight track. The x-component of the force varies with the x-coordinate of the car as shown in
Suppose the 2.0-kg model car in Exercise 6.37 is initially at rest at x = 0 and F is the net force acting on it. Use the work-energy theorem to find the speed of the car at (a) x = 3.0 m; (b) x =
At a water park, sleds with riders are sent along a slippery, horizontal surface by the release of a large compressed spring. The spring with force constant k = 40.0 N learn and negligible mass rests
Half of a spring (a) Suppose you cut a mass less ideal spring in half. If the full spring had a force constant k, what is the force constant of each half, in terms of k? (Hint: Think of the
A small glider is placed against a compressed spring at the bottom of an air track that slopes upward at an angle of 40.0o above the horizontal. The glider has mass 0.0900 kg. The spring has k = 640
An ingenious bricklayer builds a device for shooting bricks up to the top of the wall where he is working. He places a brick on a vertical compressed spring with force constant k = 450 N/m and
How many joules of energy does a 100-watt light bulb use per hour? How fast would a 70-kg person have to run to have that amount of kinetic energy?
The total consumption of electrical energy in the United States is about 1.0 X IOt9 J per year. (a) What is the average rate of electrical energy consumption in watts? (b) The population of the
Magnetar on December 27, 2004, astronomers observed the greatest lash of light ever recorded from outside the solar system. It came from the highly magnetic neutron star SGR 1806-20 (a magnetar).
A 20.0-kg rock is sliding on a rough, horizontal surface at 8.00 m/s and eventually stops due to friction. The coefficient of kinetic friction between the rock and the surface is 0.200. What average
A tandem (two-person) bicycle team must overcome a force of 165 N to maintain a speed of 9.00 m/s. Find the power required per rider, assuming that each contributes equally. Express your answer in
When its 75-kW (100-hp) engine is generating full power, a small single-engine airplane with mass 700 kg gains altitude at a rate of 2.5 m/s (150 m/min, or 500 ft/min) What fraction of the engine
Working like a Horse. Your job is to lift 30-kg crates a vertical distance of 0.90 m from the ground onto the bed of a truck. (a) How many crates would you have to load onto the truck in 1 minute
An elevator has mass 600 kg, not including passengers. The elevator is designed to ascend, at constant speed, a vertical distance of 20.0 m (five floors) in 16.0 s, and it is driven by a motor that
Automotive Power It is not unusual for a 1000-kg car to get 30 mil gal when traveling at 60 mi/h on a level road. If this car makes a 200-km trip, (a) How many joules of energy does it consume, and
The aircraft carrier John F. Kennedy has mass 7.4 X 107 kg. When its engines are developing their full power of 280,000 hp, the John F. Kennedy travels at its top speed of 35 knots (65 km/h). If 70%
A ski tow operates on a 15.0" slope of length 300 m. The rope moves at 12.0 km/h and provides power for 50 riders at one time, with an average mass per rider of 70.0 kg. Estimate the power required
A typical flying insect applies an average force equal to twice its weight during each downward stroke while hovering. Take the mass of the insect to be 10 g, and assume the wings move an average
Rotating Bar A thin, uniform 12.O-kg bar that is 2.00 m long rotates uniformly about a pivot at one end, making 5.00 complete revolutions every 3.00 seconds. What is the kinetic energy of this bar?
A Near-Earth Asteroid On April 13, 2029 (Friday the 13th!), the asteroid 99942 Apophis will pass within 18,600 mi of the earth-about 1/13 the distance to the moon! It has a density of 2600 kg/m3, can
A luggage handler pulls a 20.O-kg suitcase up a ramp inclined at 25.0° above the horizontal by a force F of magnitude 140 N that acts parallel to the ramp. The coefficient of kinetic friction
Chin-Ups while doing a chin-up, a man lifts his body 0.40 m. (a) How much work must the man do per kilogram of body mass? (b) The muscles involved in doing a chin-up can generate about 70 I of
Simple Machines Ramps for the disabled are used because a large weight w can be raised by a relatively small force equal to w sin a plus the small friction force. Such inclined planes are an example
Consider the blocks in Exercise 6.7 as they move 75.0 cm. Find the total work done on each one (a) if there is no friction between the table and the 20.O-Nblock, and (b) if IL, = 0.500 and μk =
The space shuttle Endeavour, with mass 86,400 kg, is in a circular orbit of radius 6.66 X 106 m around the earth. It takes 90.1 min for the shuttle to complete each orbit. On a repair mission, the
A 5.00-kg package slides 1.50 m down a long ramp that is inclined at 12.0° below the horizontal. The coefficient of kinetic friction between the package and the ramp is μk = 0.310. Calculate
Two springs are in parallel if they are parallel to each other and are connected at their ends (Figure 6.33). We can think of this combination as being equivalent to a single spring. The force
Springs in Series two mass less springs are connected in series when they are attached one after the other, head to tail. (a) Show that the effective force constant (see Problem 6.63) of a series
An object is attracted toward the origin with a force given by Fx = k/x2. (Gravitational and electrical forces have this distance dependence.) (a) Calculate the work done by the force F. when the
The gravitational pull of the earth on an object is inversely proportional to the square of the distance of the object from the center of the earth. At the earth's surface this force is equal to the
Varying Coefficient of Friction A box is sliding with a speed of 4.50 m/s on a horizontal surface when, at point P. it encounters a rough section. On the rough section, the coefficient of friction is
Consider a spring that does not obey Hooke's law very faithfully. One end of the spring is fixed. To keep the spring stretched or compressed an amount x, a force along the x-axis with x-component F.
A small block with a mass of 0.120 kg is attached to a cord passing through a hole in a frictionless, horizontal surface (Fig. 6.34). The block is originally revolving at a distance of 0.40 m from
Proton Bombardment A proton with mass 1.67 X 10-27 kg is propelled at an initial speed of 3.00 X 105 m/s directly toward a uranium nucleus 5.00 m away. The proton is repelled by the uranium nucleus
A block of ice with mass 6.00 kg is initially at rest on a frictionless, horizontal surface. A worker then applies a horizontal force F to it. As a result the block moves along the x-axis such that
The Genesis Crash When the 210-kg Genesis Mission capsule crashed (see Exercise 5.17 in Chapter S) with a speed of 311 km/h, it buried itself 81.0 cm deep in the desert f1oor.Assuming constant
You and your bicycle have combined mass 80.0 kg. When you reach the base of a bridge, you are traveling along the road at 5.00 m/s (Fig. 6.35). At the top of the bridge, you have climbed a vertical
A force in the + x-direction has magnitude F = b/xn, where b and n are constants. (a) For n > 1, calculate the work done on a particle by this force when the particle moves along the x-axis from x =
You are asked to design spring bumpers for the walls of a parking garage. A freely rolling 1200-kg car moving at 0.65 m/s is to compress the spring no more than 0.070 m before stopping. What should
The spring of a spring gun has force constant k = 400 N/m and negligible mass. The spring is compressed 6.00 cm, and a ball with mass 0.0300 kg is placed in the horizontal barrel against the
A 2.50-kg textbook is forced against a horizontal spring of negligible mass and force constant 250 N/m, compressing the spring a distance of 0.250 m. When released, the textbook slides on a
Crash Barrier A student proposes a design for an automobile crash barrier in which a 1700-kg sport utility vehicle moving at 20.0 m/s crashes into a spring of negligible mass that slows it to a stop.
A physics professor is pushed up a ramp inclined upward at 30.0° above the horizontal as he sits in his desk chair that slides 30 frictionless rollers. The combined mass of the professor and chair
A 5.00-kg block is moving at Vo = 6.00 m/s along a frictionless, horizontal surface toward a spring with force constant k = 500 N/m that is attached to a wall (Fig. 6.36). The spring has negligible
Consider the system shown in Fig. 6.37. The rope and pulley have negligible mass, and the pulley is frictionless. The coefficient of kinetic friction between the 8.00-kg block and the table-top is
Consider the system shown in Fig. 6.37. The rope and pulley have negligible mass, and the pulley is frictionless. Initially the 6.00-kg block is moving downward and the 8.00-kg block is moving to the
Bow and arrow Figure 6.38 shows how the force exerted by the string of a compound bow on an arrow varies as a function of how far back the arrow is polled (the draw length). Assume that the same
On an essentially frictionless, horizontal ice rink, a skater moving at 3.0 m/s encounters a rough patch that reduces her speed by 4S% due to a friction force that is 25% of her weight. Use the
Rescue your friend (mass 65.0 kg) is standing on the ice in the middle of a frozen pond. There is very little friction between her feet and the ice, so she is unable to walk. Fortunately, a light
A pump is required to lift 800 kg of water (about 210 gallons) per minute from a well 14.0 m deep and eject it with a speed of 18.0 m/s. (a) How much work is done per minute in lifting the water?
Find the power output of the worker in Problem 6.71 as a function of time. What is the numerical value of the power (in watts) alt = 4.00 s?
A physics student spends part of her day walking between classes or for recreation, during which time she expends energy at an average rate of 280 W. The remainder of the day she is sitting in class,
All birds, independent of their size, must maintain a power output of 10-25 watts per kilogram of body mass in order to fly by flapping their wings. (a) The Andean giant hummingbird (Patagona gigas)
The Grand Coulee Dam is 1270 m long and 170 m high. The electrical power output from generators at its base is approximately 2000 MW. How many cubic meters of water must flow from the top of the dam
The engine of a car with mass m supplies a constant power P to the wheels to accelerate the car. You can ignore rolling friction and air resistance. The car is initially at rest. (a) Show that the
Power of the Human Heart the human heart is a powerful and extremely reliable pump. Each day it takes in and discharges about 7S00 L of blood. Assume that the work done by the heart is equal to the
Six diesel units in series can provide 13.4 MW of power to the lead car of a freight train. The diesel units have total mass 1.10 X 106 kg. The average car in the train has mass 8.2 X 104 kg and
It takes a force of S3 kN on the lead car of a 16-car passenger train with mass 9.1 X 10' kg to poll it at a constant 45 m/s (WI mi/h) on level tracks. (a) What power must the locomotive provide to
An object has several forces acting on it. One of these forces is F = axyi, a force in the x-direction whose magnitude depends on the position of the object, with a = 2.S0 N/m2. Calculate the work
Cycling For a touring bicyclist the drag coefficient C(f air = 2 ) is 1.00, the frontal area A is 0.463 m2, and the coefficient of rolling friction is 0.0045. The rider has mass SO.O kg, and her bike
Automotive Power I A truck engine transmits 28.0 kW (37.S hp) to the driving wheels when the truck is traveling at a constant velocity of magnitude 60.0 km/h (37.3 mi/h) on a level road. (a) What
Automotive Power n (a) If 8.00 hp are required to drive a 1800-kg automobile at 60.0 km/h on a level road, what is the total retarding force due to friction, air resistance, and so on? (b) What
On a winter's day in Maine, a warehouse worker is shoving boxes up a rough plank inclined at an angle a above the horizontal. The plank is partially covered with ice, with more ice near the bottom of
A spring with Mass We usually ignores the kinetic energy of the moving coils of a spring, but let’s tries to get a reasonable approximation to this. Consider a spring of mass M, equilibrium length
An airplane in flight is subject to an air resistance force proportional to the square of its speed v. But there is an additional resistive force because the airplane has wings. Air flowing over the
Figure 6.40 shows the oxygen consumption rate of men walking and running at different speeds. The vertical axis shows the volume of oxygen (in cm3) that a man consumes per kilogram of body mass per
General Proof of the Work-Energy Theorem Consider a particle that moves along a curved path in space from (x1, y1, z1) to (X2, Y2,Z2) At the initial point, the particle bas velocity it = v,i + v,, +
In one day, a 75-kg mountain climber ascends from the1500-m level on a vertical cliff to the top at 2400 m. The next day, she descends from the top to the base of the cliff, which is at an elevation
A 5.00-kg sack of flour is lifted vertically at a constant speed of 3.50 m/s through a height of 15.0 m. (a) How great a force is required? (b) How much work is done on the sack by the lifting
A 120-kg mail bag hangs by a vertical rope 3.5 m long. A postal worker then displaces the bag to a position 2.0 m sideways from its original position, always keeping the rope taut. (a) What
A 72.0-kg swimmer jumps into the old swimming hole from a diving board 3.25 m above the water. Use energy conservation to find his speed just he hits the water (a) If he just holds his nose and

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