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physics
mechanics
Questions and Answers of
Mechanics
1. A small solid sphere and a small thin hoop are rolling along a horizontal surface with the same translational speed when they encounter a 20° rising slope. If these two objects roll up the slope
Express the following angles in radians: (a) 45.0°, (b) 60.0°, (c) 90.0°, (d) 360.0°, (e) 445°. Give as numerical values and as fractions of π.
What is the linear speed, due to the Earth's rotation, of a point(a) On the equator,(b) On the Arctic Circle (latitude 66.5° N),(c) At a latitude of 42.0° N?
How fast (in rpm) must a centrifuge rotate if a particle 8.0 cm from the axis of rotation is to experience an acceleration of 100,000 g's?
A 61-cm-diameter wheel accelerates uniformly about its center from 120 rpm to 280 rpm in 4.0 s. Determine(a) Its angular acceleration,(b) The radial and tangential components of the linear
An automobile engine slows down from 3500 rpm to 1200 rpm in 2.5 s. Calculate (a) Its angular acceleration, assumed constant, (b) The total number of revolutions the engine makes in this time.
Pilots can be tested for the stresses of flying high-speed jets in a whirling "human centrifuge," which takes 1.0 min to turn through 23 complete revolutions before reaching its final speed.(a) What
The Sun subtends an angle of about 0.5° to us on Earth, 150 million km away. Estimate the radius of the Sun.
A cooling fan is turned off when it is running at 850 rev min. It turns 1250 revolutions before it comes to a stop.(a) What was the fan's angular acceleration, assumed constant?(b) How long did it
The tires of a car make 75 revolutions as the car reduces its speed uniformly from to 55 km/s. The tires have a diameter of 0.80 m.(a) What was the angular acceleration of the tires? If the car
A 52-kg person riding a bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 cm. (a) What is the maximum torque she exerts? (b) How could she
A person exerts a horizontal force of 42 N on the end of a door 96 cm wide. What is the magnitude of the torque if the force is exerted?(a) Perpendicular to the door and(b) At a 60.0° angle to the
The bolts on the cylinder head of an engine require tightening to a torque of 95 m · N. If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end? If the
Determine the net torque on the 2.0-m-long uniform beam shown in Fig. 8-45. All forces are shown.Calculate about(a) point C, the CM,(b) point P at one end.
Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its center.
Estimate the moment of inertia of a bicycle wheel 67 cm in diameter. The rim and tire have a combined mass of 1.1 kg. The mass of the hub (at the center) can be ignored (why?).
A merry-go-round accelerates from rest to 0.68 rad/s in 34 s. Assuming the merry-go-round is a uniform disk of radius 7.0 m and mass 31,000 kg, calculate the net torque required to accelerate it.
A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of 0.380 kg.Calculate(a) Its moment of inertia about its center, and(b) The applied torque needed to accelerate it from rest
Assume that a 1.00-kg ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8-46. The ball is accelerated uniformly from
A softball player swings a bat, accelerating it from rest to 2.6 rev/s in a time of 0.20 s. Approximate the bat as a 0.90-kg uniform rod of length 0.95 m, and compute the torque the player applies to
A small 350-gram ball on the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculate (a) The moment of inertia of the ball about the center of the circle, and (b) The
Calculate the moment of inertia of the array of point objects shown in Fig. 8-47 about(a) The y axis, a (b) The x axis. Assume m = 2.2 kg, M = 3.4 kg, and the objects are wired together by very
The blades in a blender rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 4.0 s. What is the angular acceleration as the blades slow down?
A 0.72-m-diameter solid sphere can be rotated about an axis through its center by a torque of 10.8 m · N which accelerates it uniformly from rest through a total of 160 revolutions in 15.0 s. What
Let us treat a helicopter rotor blade as a long thin rod, as shown in Fig. 8-49.(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 135 kg, calculate the moment of
To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8-50. Suppose that the satellite has a mass of 3600 kg and a radius
Two blocks are connected by a light string passing over a pulley of radius 0.15 m and moment of inertia I.The blocks move (towards the right) with an acceleration of 1.00 m/s2 along their
An Atwood machine consists of two masses, mA = 65kg and mB = 75kg, connected by a massless inelastic cord that passes over a pulley free to rotate, Fig. 8-52. The pulley is a solid cylinder of radius
An automobile engine develops a torque of 265 m · N at 3350 rpm. What is the horsepower of the engine?
The platter of the hard drive of a computer rotates at 7200 rpm (rpm revolutions per minute = rev/min). (a) What is the angular velocity (rad/s) of the platter? (b) If the reading head of the drive
A centrifuge rotor has a moment of inertia of 3.25 × 10-2 kg·m2. How much energy is required to bring it from rest to 8750 rpm?
Calculate the translational speed of a cylinder when it reaches the foot of an incline 7.20 m high. Assume it starts from rest and rolls without slipping.
A bowling ball of mass 7.25 kg and radius 10.8 cm rolls without slipping down a lane at 3.10 m/s. Calculate its total kinetic energy.
A rotating uniform cylindrical platform of mass 220 kg and radius 5.5 m slows down from 3.8 rev/s to rest in 16 s when the driving motor is disconnected. Estimate the power output of the motor (hp)
A merry-go-round has a mass of 1440 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 7.00 s? Assume it is a solid cylinder.
A ball of radius r rolls on the inside of a track of radius R (see Fig. 8-53). If the ball starts from rest at the vertical edge of the track, what will be its speed when it reaches the lowest point
Two masses, mA = 32.0kg and mB = 38.0 kg, are connected by a rope that hangs over a pulley (as in Fig. 8-54). The pulley is a uniform cylinder of radius R = 0.311 m and mass 3.1 kg. Initially mA is
A 1.80-m-long pole is balanced vertically with its tip on the ground. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the
What is the angular momentum of a 0.270-kg ball revolving on the end of a thin string in a circle of radius 1.35 m at an angular speed of 10.4 rad/s?
(a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 28 cm when rotating at 1300 rpm? (b) How much torque is required to stop it in 6.0 s?
A person stands, hands at his side, on a platform that is rotating at a rate of 0.90 rev/s. If he raises his arms to a horizontal position, Fig. 8-55, the speed of rotation decreases to 0.60rev/s.(a)
A figure skater can increase her spin rotation rate from an initial rate of 1.0 rev every 1.5 s to a final rate of 2.5rev/s. If her initial moment of inertia was 4.6kg· m2, what is her final moment
(a) What is the angular momentum of a figure skater spinning 3.0rev/s at with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of
A person of mass 75 kg stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia 820 kg· m2. The platform rotates without friction with angular velocity 0.95
A potter's wheel is rotating around a vertical axis through its center at a frequency of 1.5rev/s. The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then
A 4.2-m-diameter merry-go-round is rotating freely with an angular velocity of 0.80 rad/s. Its total moment of inertia is 1360 kg·m2. Four people standing on the ground, each of mass 65 kg, suddenly
A uniform disk turns at 3.3 rev/s around a frictionless central axis. A nonrotating rod, of the same mass as the disk and length equal to the disk's diameter, is dropped onto the freely spinning
An asteroid of mass 1.0 × 105 kg, traveling at a speed of 35km/s relative to the Earth hits the Earth at the equator tangentially, in the direction of Earth's rotation, and is embedded there. Use
Suppose a 65-kg person stands at the edge of a 5.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 1850 kg· m2. The turntable is at rest
A merry-go-round with a moment of inertia equal to 1260 kg·m2 and a radius of 2.5 m rotates with negligible friction at 1.70 rad/s. A child initially standing still next to the merry-go-round jumps
A 1.6-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of 24 rev/s from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque
On a 12.0-cm-diameter audio compact disc (CD), digital bits of information are encoded sequentially along an outward spiraling path. The spiral starts at radius R1 = 2.5 cm and winds its way out to
A cyclist accelerates from rest at a rate of 1.00 m/s2. How fast will a point at the top of the rim of the tire (diameter = 68.0 cm) be moving after 2.25 s?
Suppose David puts a 0.60-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle, accelerating it from rest to a rate of 75 rpm after 5.0 s. What is the
Figure 8-59 illustrates an H2O molecule. The O - H bond length is 0.096 nm and the H - O - H bonds make an angle of 104°. Calculate the moment of inertia of the H20 molecule (assume the atoms are
A hollow cylinder (hoop) is rolling on a horizontal surface V = 3.0 m/s at speed when it reaches a 15° incline.(a) How far up the incline will it go?(b) How long will it be on the incline before it
If the coefficient of static friction between a car's tires and the pavement is 0.65, calculate the minimum torque that must be applied to the 66-cm-diameter tire of a 1080-kg automobile in order to
A 4.00-kg mass and a 3.00-kg mass are attached to opposite ends of a very light 42.0-cm-long horizontal rod (Fig. 8–61). The system is rotating at angular speed ω = 5.60 rad/s about a
A small mass m attached to the end of a string revolves in a circle on a frictionless tabletop. The other end of the string passes through a hole in the table (Fig. 8-62). Initially, the mass
Suppose a star the size of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 9.0 days. If it were to undergo gravitational collapse to a neutron star of
Water drives a waterwheel (or turbine) of radius R = 3.0m as shown in Fig. 8-66. The water enters at a speed v1 = 7.0 m/s and exits from the waterwheel at a speed v2 = 3.8 m/s.(a) If 85 kg of water
Total solar eclipses can happen on Earth because of amazing coincidences: for one, the sometimes near-perfect alignment of Earth, Moon, and Sun. Secondly, using the information inside the front
Will a clock using a pendulum supported on a long thin brass rod that is accurate at 20°C run fast or slow on a hot day (30°C)? Explain.
What exactly does it mean when we say that oxygen boils at - 183°C?
(a) Why does food cook faster in a pressure cooker? (b) Why does pasta or rice need to boil longer at high altitudes? (c) Is it harder to boil water at high altitudes?
Explain why it is advisable to add water to an overheated automobile engine only slowly, and only with the engine running.
1. Rod A has twice the diameter of rod B, but both are made of iron and have the same initial length. Both rods are now subjected to the same change in temperature (but remain solid). How would the
Which of the following is not true about an ideal gas? (a) The average kinetic energy of the gas molecules increases as the temperature increases. (b) The volume of an ideal gas increases with
When using the ideal gas law, which of the following rules must be obeyed? (a) Always use temperature in kelvins and absolute pressure. (b) Always use volume in m3 and temperature in kelvins. (c)
The rms speed of the molecules of an ideal gas (a) Is the same as the most probable speed of the molecules. (b) Is always equal to √2 times the maximum molecular speed. (c) Will increase as the
1. One mole of an ideal gas in a sealed rigid container is initially at a temperature of 100°C. The temperature is then increased to 200°C. The pressure in the gas (a) Remains constant. (b)
1. Two identical bottles at the same temperature contain the same gas. If bottle B has twice the volume and contains half the number of moles of gas as bottle A, how does the pressure in B compare
1. Two ideal gases, A and B, are at the same temperature. If the molecular mass of the molecules in gas A is twice that of the molecules in gas B, the molecules' root-mean-square speed is (a) The
How does the number of atoms in a 27.5-gram gold ring compare to the number in a silver ring of the same mass?
A concrete highway is built of slabs 12 m long (15°C). How wide should the expansion cracks between the slabs be (at 15°C) to prevent buckling if the range of temperature is - 30◦C to + 50◦C?
Super Invar™, an alloy of iron and nickel, is a strong material with a very low coefficient of thermal expansion (0.20 × 10-6 /C◦). A 1.8-m-long tabletop made of this alloy is used for sensitive
To what temperature would you have to heat a brass rod for it to be 1.5% longer than it is at 25°C?
To make a secure fit, rivets that are larger than the rivet hole are often used and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.872 cm in diameter is to
A brass plug is to be placed in a ring made of iron. At 15°C, the diameter of the plug is 8.755 cm and that of the inside of the ring is 8.741 cm. They must both be brought to what common
A certain car has 14.0 L of liquid coolant circulating at a temperature of 93°C through the engine's cooling system. Assume that, in this normal condition, the coolant completely fills the 3.5-L
An aluminum bar has the desired length when at 12°C. How much stress is required to keep it at this length if the temperature increases to 35°C?
If 3.50 m3 of a gas initially at STP is placed under a pressure of 3.20 atm, the temperature of the gas rises to 38.0°C. What is the volume?
If 16.00 mol of helium gas is at 10.0°C and a gauge pressure of 0.350 atm, calculate(a) The volume of the helium gas under these conditions,(b) The temperature if the gas is compressed to precisely
A storage tank at STP contains 28.5 kg of nitrogen (N2) (a) What is the volume of the tank? (b) What is the pressure if an additional 32.2 kg of nitrogen is added without changing the temperature?
A scuba tank is filled with air to a gauge pressure of 204 atm when the air temperature is 29°C.A diver then jumps into the ocean and, after a short time on the ocean surface, checks the tank's
What is the pressure inside a 38.0-L container holding 105.0 kg of argon gas at 21.6°C?
(a) "Room temperature" is often taken to be 68°F. What is this on the Celsius scale?(b) The temperature of the filament in a light-bulb is about 1900°C. What is this on the Fahrenheit scale?
A sealed metal container contains a gas at 20.0°C and 1.00 atm. To what temperature must the gas be heated for the pressure to double to 2.00 atm? (Ignore expansion of the container.)
A tire is filled with air at 15°C to a gauge pressure of 230 kPa. If the tire reaches a temperature of 38°C, what fraction of the original air must be removed if the original pressure of 230 kPa is
If 61.5 L of oxygen at 18.0°C and an absolute pressure of 2.45 atm are compressed to 38.8 L and at the same time the temperature is raised to 56.0°C, what will the new pressure be?
A helium-filled balloon escapes a child's hand at sea level and 20.0°C. When it reaches an altitude of 3600 m, where the temperature is 5.0°C and the pressure only 0.68 atm, how will its volume
Compare the value for the density of water vapor at exactly 100°C and 1 atm with the value predicted from the ideal gas law. Why would you expect a difference?
A sealed test tube traps 25.0 cm3 of air at a pressure of 1.00 atm and temperature of 18°C. The test tube's stopper has a diameter of 1.50 cm and will "pop off" the test tube if a net upward force
An air bubble at the bottom of a lake 41.0 m deep has a volume of 1.00 cm3. If the temperature at the bottom is 5.5°C and at the top 18.5°C, what is the radius of the bubble just before it reaches
(a) What is the average translational kinetic energy of a nitrogen molecule at STP?(b) What is the total translational kinetic energy of 1.0 mol of N2 molecules at 25°C?
Calculate(a) The rms speed of an oxygen molecule at 0°C(b) Determine how many times per second it would move back and forth across a 5.0-m-long room on average, assuming it made no collisions with
You have a sample of water and are able to control temperature and pressure arbitrarily.(a) Using Fig. 13-22, describe the phase changes you would see if you started at a temperature of 85°C, a
What is the partial pressure of water vapor at 30°C if the humidity is 75%?
(a) 18° below zero on the Celsius scale is what Fahrenheit temperature?(b) 18° below zero on the Fahrenheit scale is what Celsius temperature?
What is the air pressure at a place where water boils at 80°C?
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