Use the orders of magnitude you found in the previous problem to answer the following questions to within an order of magnitude. (a) How many electrons would it take to equal the mass of a proton? (b) How many Earths would it take to equal the mass of the Sun? (c) How many Earth-Moon distances would it take to cover the distance from Earth to the Sun? (d) How many Moon atmospheres would it take to equal the mass of Earth's atmosphere? (e) How many moons would it take to equal the mass of Earth? (f) How many protons would it take to equal the mass of the Sun?
The following times are given in seconds. Use metric prefixes to rewrite them so the numerical value is greater than one but less than 1000. For example, 7.9×10−2 s could be written as either 7.9 cs or 79 ms. (a) 9.57×105 s; (b) 0.045 s; (c) 5.5×10−7 s; (d) 3.16×107 s.
The speed limit on some interstate highways is roughly 100 km/h. (a) What is this in meters per second? (b) How many miles per hour is this?
Consider the physical quantities s, v, a, and t with dimensions [s] = L, [v] = LT−1, [a] = LT−2, and [t] = T. Determine whether each of the following equations is dimensionally consistent. (a) v2 = 2as; (b) s = vt2 + 0.5at2; (c) v = s/t; (d) a = v/t.
Assuming the human body is primarily made of water, estimate the number of molecules in it. (Note that water has a molecular mass of 18 g/mol and there are roughly 1024 atoms in a mole. )
Suppose your bathroom scale reads your mass as 65 kg with a 3% uncertainty. What is the uncertainty your mass (in kilograms)?
A car is 2.0 km west of a traffic light at t = 0 and 5.0 km east of the light at t = 6.0 min. Assume the origin of the coordinate system is the light and the positive x direction is eastward. (a) What are the car's position vectors at these two times? (b) What is the car's displacement between 0 min and 6.0 min ?
Sketch the velocity-versus-time graph from the following position-versus-time graph. Position vs. Time
A cheetah can accelerate from rest to a speed of 30.0 m/s in 7.00 s. What is its acceleration?
A particle moves in a straight line at a constant velocity of 30 m/s. What is its displacement between t = 0 and t = 5.0 s ?
Calculate the displacement and velocity at times of (a) 0.500 s, (b) 1.00 s, (c) 1.50 s, (d) 2.00 s, and (e) 2.50 s for a rock thrown straight down with an initial velocity of 14.0 m/s from the Verrazano Narrows Bridge in New York City. The roadway of this bridge is 70.0 m above the water.
Between t = 0 and t = t0, a rocket moves straight upward with an acceleration given by a(t) = A − Bt1/2, where A and B are constants. (a) If x is in meters and t is in seconds, what are the units of A and B ? (b) If the rocket starts from rest, how does the velocity vary between t = 0 and t = t0 ? (c) If its initial position is zero, what is the rocket's position as a function of time during this same time interval?
Two ropes are attached to a tree, and forces of F→1 = 2.0 i^+4.0 j^N and F→2 = 3.0 i^+6.0 j^N are applied. The forces are coplanar (in the same plane). (a) What is the resultant (net force) of these two force vectors? (b) Find the magnitude and direction of this net force.
While sliding a couch across a floor, Andrea and Jennifer exert forces F→A and F→J on the couch. Andrea's force is due north with a magnitude of 130.0 N and Jennifer's force is 32∘ east of north with a magnitude of 180.0 N. (a) Find the net force in component form. (b) Find the magnitude and direction of the net force. (c) If Andrea and Jennifer's housemates, David and Stephanie, disagree with the move and want to prevent its relocation, with what combined force F→DS should they push so that the couch does not move?
If the sprinter from the previous problem accelerates at that rate for 20.00 m and then maintains that velocity for the remainder of a 100.00−m dash, what will her time be for the race?
The weight of an astronaut plus his space suit on the Moon is only 250 N. (a) How much does the suited astronaut weigh on Earth? (b) What is the mass on the Moon? On Earth?
(a) What net external force is exerted on a 1100.0-kg artillery shell fired from a battleship if the shell is accelerated at 2.40×104 m/s2 ? (b) What is the magnitude of the force exerted on the ship by the artillery shell, and why?
A leg is suspended in a traction system, as shown below. (a) Which pulley in the figure is used to calculate the force exerted on the foot? (b) What is the tension in the rope? Here T→ is the tension, w→leg is the weight of the leg, and w→ is the weight of the load that provides the tension.
A car moves along a horizontal road. Draw a free-body diagram; be sure to include the friction of the road that opposes the forward motion of the car.
Using values from Table 8.1 , 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 before they escaped and exposed viewers. )
A force F(x) = (−5.0x2 + 7.0x) N acts on a particle. How much work does the force do on the particle as it moves from x = 2.0 m to x = 5.0 m ?
A boy throws a ball of mass 0.25 kg straight upward with an initial speed of 20 m/s When the ball returns to the boy, its speed is 17 m/s How much much work does air resistance do on the ball during its flight?
A mysterious constant force of 10 N acts horizontally on everything. The direction of the force is found to be always pointed toward a wall in a big hall. Find the potential energy of a particle due to this force when it is at a distance x from the wall, assuming the potential energy at the wall to be zero.
In the reality television show "Amazing Race", a contestant is firing 12-kg watermelons from a slingshot to hit targets down the field. The slingshot is pulled back 1.5 m and the watermelon is considered to be at ground level. The launch point is 0.3 m from the ground and the targets are 10 m horizontally away. Calculate the spring constant of the slingshot.
A skater of mass 40 kg is carrying a box of mass 5 kg. The skater has a speed of 5 m/s with respect to the floor and is gliding without any friction on a smooth surface. a. Find the momentum of the box with respect to the floor. b. Find the momentum of the box with respect to the floor after she puts the box down on the frictionless skating surface.
A 75.0-kg person is riding in a car moving at 20.0 m/s when the car runs into a bridge abutment (see the following figure). a. Calculate the average force on the person if he is stopped by a padded dashboard that compresses an average of 1.00 cm. b. Calculate the average force on the person if he is stopped by an air bag that compresses an average of 15.0 cm.
Train cars are coupled together by being bumped into one another. Suppose two loaded train cars are moving toward one another, the first having a mass of 1.50×105 kg and a velocity of (0.30 m/s)i^, and the second having a mass of 1.10×105 kg and a velocity of −(0.12 m/s)i^. What is their final velocity?
A 5.50−kg bowling ball moving at 9.00 m/s collides with a 0.850−kg bowling pin, which is scattered at an angle of 15.8∘ to the initial direction of the bowling ball and with a speed of 15.0 m/s. a. Calculate the final velocity (magnitude and direction) of the bowling ball. b. Is the collision elastic?
Three point masses are placed at the corners of a triangle as shown in the figure below. Find the center of mass of the three-mass system.
(a) A 5.00−kg squid initially at rest ejects 0.250 kg of fluid with a velocity of 10.0 m/s. What is the recoil velocity of the squid if the ejection is done in 0.100 s and there is a 5.00−N frictional force opposing the squid's movement? (b) How much energy is lost to work done against friction?
A 0.90−kg falcon is diving at 28.0 m/s at a downward angle of 35∘. It catches a 0.325−kg pigeon from behind in midair. What is their combined velocity after impact if the pigeor's initial velocity was 7.00 m/s directed horizontally? Note that v^1,i is a unit vector pointing in the direction in which the falcon is initially flying.
A track star runs a 400-m race on a 400-m circular track in 45 s. What is his angular velocity assuming a constant speed?
A wheel has a constant angular acceleration of 5.0 rad/s2. Starting from rest, it turns through 300 rad. (a) What is its final angular velocity? (b) How much time elapses while it turns through the 300 radians?
A man stands on a merry-go-round that is rotating at 2.5 rad/s. If the coefficient of static friction between the man's shoes and the merry-go-round is μS = 0.5, how far from the axis of rotation can he stand without sliding?
(a) Calculate the rotational kinetic energy of Earth on its axis. (b) What is the rotational kinetic energy of Earth in its orbit around the Sun?
Using the parallel axis theorem, what is the moment of inertia of the rod of mass m about the axis shown below?
Two flywheels of negligible mass and different radii are bonded together and rotate about a common axis (see below). The smaller flywheel of radius 30 cm has a cord that has a pulling force of 50 N on it. What pulling force needs to be applied to the cord connecting the larger flywheel of radius 50 cm such that the combination does not rotate? F = ?
Suppose you exert a force of 180 N tangential to a 0.280−m-radius, 75.0−kg grindstone (a solid disk). (a)What torque is exerted? (b) What is the angular acceleration assuming negligible opposing friction? (c) What is the angular acceleration if there is an opposing frictional force of 20.0 N exerted 1.50 cm from the axis?
A wind turbine rotates at 20 rev/min. If its power output is 2.0 MW, what is the torque produced on the turbine from the wind?
What is the angular velocity of a 75.0−cm-diameter tire on an automobile traveling at 90.0 km/h ? A boy rides his bicycle 2.00 km. The wheels have radius 30.0 cm. What is the total angle the tires rotate through during his trip?
A bird flies overhead from where you stand at an altitude of 300.0 m and at a speed horizontal to the ground of 20.0 m/s. The bird has a mass of 2.0 kg. The radius vector to the bird makes an angle θ with respect to the ground. The radius vector to the bird and its momentum vector lie in the xy-plane. What is the bird's angular momentum about the point where you are standing?
The Sun's mass is 2.0×1030 kg, its radius is 7.0×105 km, and it has a rotational period of approximately 28 days. If the Sun should collapse into a white dwarf of radius 3.5×103 km, what would its period be if no mass were ejected and a sphere of uniform density can model the Sun both before and after?
A gyroscope has a 0.5-kg disk that spins at 40 rev/s. The center of mass of the disk is 5 cm from a pivot with a radius of the disk of 10 cm. What is the precession angular velocity?
It is weigh-in time for the local under-85-kg rugby team. The bathroom scale used to assess eligibility can be described by Hooke's law and is depressed 0.75 cm by its maximum load of 120 kg. (a) What is the spring's effective force constant? (b) A player stands on the scales and depresses it by 0.48 cm. Is he eligible to play on this under-85-kg team?
Prove that using x(t) = Asin(ωt+ϕ) will produce the same results for the period for the oscillations of a mass and a spring. Why do you think the cosine function was chosen?
(a) A novelty clock has a 0.0100−kg-mass object bouncing on a spring that has a force constant of 1.25 N/m. What is the maximum velocity of the object if the object bounces 3.00 cm above and below its equilibrium position? (b) How many joules of kinetic energy does the object have at its maximum velocity?
The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle?
Some people think a pendulum with a period of 1.00 s can be driven with "mental energy" or psycho kinetically, because its period is the same as an average heartbeat. True or not, what is the length of such a pendulum?
Waves on a swimming pool propagate at 0.75 m/s. You splash the water at one end of the pool and observe the wave go to the opposite end, reflect, and return in 30.00 s. How far away is the other end of the pool?
A transverse wave on a string is modeled with the wave function y(x, t) = (0.20 cm)sin(2.00 m−1 x−3.00 s−1 t+π16). What is the height of the string with respect to the equilibrium position at a position x = 4.00 m and a time t = 10.00 s?
If a car has a suspension system with a force constant of 5.00×104 N/m, how much energy must the car's shocks remove to dampen an oscillation starting with a maximum displacement of 0.0750 m?
A copper wire has a density of ρ = 8920 kg/m3, a radius of 1.20 mm, and a length L. The wire is held under a tension of 10.00 N. Transverse waves are sent down the wire. (a) What is the linear mass density of the wire? (b) What is the speed of the waves through the wire?
Consider two sinusoidal sine waves traveling along a string, modeled as y1(x, t) = 0.3 msin(4 m−1 x+3 s−1 t+π3) and y2(x, t) = 0.6 msin(8 m−1 x−6 s−1 t). What is the height of the resultant wave formed by the interference of the two waves at the position x = 1.0 m at time t = 3.0 s?
A 2-m long string is stretched between two supports with a tension that produces a wave speed equal to vw = 50.00 m/s. What are the wavelength and frequency of the first three modes that resonate on the string?
Consider a sound wave modeled with the equations (x, t) = 4.00 nm cos(3.66 m−1 x−1256 s−1 t). What is the maximum displacement, the wavelength, the frequency, and the speed of the sound wave?
A string of length 5 m and a mass of 90 g is held under a tension of 100 N. A wave travels down the string that is modeled as y(x, t) = 0.01 m sin(15.7 m−1 x − 1170.12 s−1 t). What is the power over one wavelength?
The warning tag on a lawn mower states that it produces noise at a level of 91.0 dB. What is the intensity of this sound in watts per meter squared?
What is the length of a tube that has a fundamental frequency of 176 Hz and a first overtone of 352 Hz if the speed of sound is 343 m/s ?
What are the first three overtones of a bassoon that has a fundamental frequency of 90.0 Hz? It is open at both ends. (The overtones of a real bassoon are more complex than this example, because its double reed makes it act more like a tube closed at one end. )
What beat frequencies result if a piano hammer hits three strings that emit frequencies of 127.8, 128.1, and 128.3 Hz ?
(a) What frequency is received by a person watching an oncoming ambulance moving at 110 km/h and emitting a steady 800−Hz sound from its siren? The speed of sound on this day is 345 m/s. (b) What frequency does she receive after the ambulance has passed?
A jet flying at an altitude of 8.50 km has a speed of Mach 2.00, where the speed of sound is v = 340.00 m/s. How long after the jet is directly overhead, will a stationary observer hear a sonic boom?
A mole of ideal monatomic gas at 0∘C and 1.00 atm is warmed up to expand isobarically to triple its volume. How much heat is transferred during the process?
An engine is found to have an efficiency of 0.40 . If it does 200 J of work per cycle, what are the corresponding quantities of heat absorbed and discharged? In performing 100.0 J of work, an engine discharges 50.0 J of heat. What is the efficiency of the engine? An engine with an efficiency of 0.30 absorbs 500 J of heat per cycle. (a) How much work does it perform per cycle? (b) How much heat does it discharge per cycle?
A refrigerator has a coefficient of performance of 3.0 . (a) If it requires 200 J of work per cycle, how much heat per cycle does it remove the cold reservoir? (b) How much heat per cycle is discarded to the hot reservoir?
The temperature of the cold and hot reservoirs between which a Carnot refrigerator operates are −73∘C and 270∘C, respectively. Which is its coefficient of performance?