A rock is thrown straight upward from the edge of a 30 m cliff, rising 10 m then falling all the way down to the base of the cliff. Find the rock’s displacement.
An infant crawls 5 m east, then 3 m north, then 1 m. What is the infant’s DISTANCE and DISPLACEMENT
An athlete runs exactly once around the track, a total distance of 500 m. Find the runner’s displacement for the race
An object with an initial velocity of 4 m/s moves along a straight axis under constant acceleration. Three seconds later, its velocity is 14 m/s. How far did it travel during this time? 27m
A car that’s initially traveling at 10 m/s accelerates uniformly for 4 seconds at a rate of 2 m/s 2 in a straight line. How far does the car travel during this time? 56m
A rock is dropped off a cliff that’s 80 m high. If it strikes the ground with an impact velocity of 40 m/s, what acceleration did it experience during its descent? 10 m/s 2
A rock is dropped from an 80 m cliff. How long does it take to reach the ground? 4s
A baseball is thrown straight upward with an initial speed of 20 m/s. How high will it go? 20m
One second after being thrown straight down, an object is falling with a speed of 20 m/s. How fast will it be falling 2 seconds later? -40 m/s
If an object is thrown straight upward with an initial speed of 8 m/s and takes 3 seconds to strike the ground, from what height was the object thrown? 21m
What net force is required to maintain a 5000 kg object moving at a constant velocity of magnitude 7500 m/s?
How much force is required to cause an object of mass 2 kg to have an acceleration of 4 m/s 2 ? 8 N
An object feels two forces; one of strength 8 N pulling to the left and one of strength 20 N pulling to the right. If the object’s mass is 4 kg, what is its acceleration? 3 m/s 2
A book whose mass is 2 kg rests on a table. Find the magnitude of the force exerted by the table on the book. 20 N
A can of paint with a mass of 6 kg hangs from a rope. If the can is to be pulled up to a rooftop with a constant velocity of 1 m/s , what must the tension in the rope be? 60 N
What force must be exerted to lift a 50 N object with an acceleration of 10 m/s 2 ? 100 N
Anything pointing towards the center of the circle is positive, anything pointing away is negative
An object of mass 5 kg moves at a constant speed of 6 m/s in a circular path of radius 2 m. Find the object’s acceleration and the net force responsible for its motion. 18 m/s 2 ; 90 N
An athlete who weighs 800 N is running around a curve at a speed of 5.0 m/s with a radius of 5.0 m. Find the centripetal force acting on him & what provides the centripetal force? 400 N & static friction
A roller-coaster car enters the circular loop portion of the ride. At the very top of the circle, the speed of the car is 15 m/s, and the acceleration points straight down. If the diameter of the loop is 40 m and the total mass of the car is 1200 kg, find the magnitude of the normal force exerted by the track on the car at this point. 1500 N
How would the normal force change if the car was at the bottom of the circle? 25,500 N
A crate is moved along a horizontal floor by a worker who’s pulling on it with a rope that makes a 30 degree angle with the horizontal. The tension in the rope is 69 N and the crate slides a distance of 10 m. How much work is done on the crate by the worker? 600 J
A box slides down an inclined plane with an angle of 37 degrees. The mass of the block is 35 kg, the coefficient of kinetic friction is 0.3, and the length of the ramp is 8 m.
A pool cue striking a stationary billiard ball (m = 0.25 kg) gives the ball a speed of 2 m/s. If the average force of the cue on the ball was 200 N, over what distance does this force act? 0.0025 m
The energy an object possesses due to its position
A 60 kg stuntwoman scales a 40 m tall rock. What is her gravitational potential energy? If she were to jump off the cliff, what would her final velocity be? 24,000 J; 28 m/s
A ball of mass 2 kg is gently pushed off the edge of a table that is 5 m above the floor. Find the speed of the ball as it strikes the floor. 10 m/s
A box is projected up a long ramp with an incline of 37 degrees with an initial speed of 10 m/s. If the surface of the ramp is frictionless, how high up the ramp will the box go? What distance along the ramp will it slide?
A skydiver jumps from a hovering helicopter that’s 3000 m above the ground. If air resistance can be ignored, how fast will he be falling when his altitude is 2000 m? 140 m/s
Wile E. Coyote (m = 40 kg) falls off a 50 m high cliff. On the way down, the force of air resistance has an average strength of 100 N. Find the speed with which he crashes into the ground. 27 m/s
A mover pushes a large crate (m = 75 kg) from the inside of the truck to the back end (distance of 6 m), exerting a steady push of 300 N. If he moves the crate this distance in 20 s, what is his power output? 90 W
What must be the power output of an elevator motor that can lift a total mass of 1000 kg and give the elevator a constant speed of 8.0 m/s? 80,000 W or 80 kW
A golfer strikes a golf ball of mass 0.05 kg and the time of impact between the golf club and the ball is 1 ms. If the ball acquires a velocity of magnitude 70 m/s, calculate the average force on the ball. 3500 N
Inelastic Collisions – Kinetic Energy is not conserved.
Two balls roll toward each other. The red ball has a mass of 0.5 kg and a speed of 4 m/s just before impact. The green ball has a mass of 0.2 kg and a speed of 2 m/s. After the head-on collision, the red ball continues forward with a speed of 2 m/s. Find the speed of the green ball after the collision. Was the collision elastic? 3.0 m/s; no
Given that the radius of the earth is 6.37 x 10 6 m, determine the mass of the earth. 6.1 x 10 24 kg
An artificial satellite of mass m travels at a constant speed in a circular orbit of radius R around the earth (mass M). What is the speed of the satellite? √GM/R
A 0.05 kg block oscillates on a spring whose force (spring) constant is 500 N/m. The amplitude of the oscillations is 4.0 cm. Calculate the maximum speed of the block. 4 m/s
A 2.0 kg block is attached to an ideal spring with a force constant of 500 N/m. The amplitude is 8.0 cm. Determine the total energy of the oscillator and the speed of the block when it’s 4.0 cm from equilibrium. 1.6 J; 1.1 m/s
A block oscillating on the end of a spring moves from is position of maximum stretch to maximum compression in 0.25 s. Determine the period and frequency. 0.5 s; 2 Hz
A student observing an oscillating block counts 45.5 cycles in one minute. Determine its frequency and period. .758 Hz; 1.32s
A 2.0 kg block is attached to a spring whose spring constant is 300 N/m. Calculate the frequency and period. 1.9 Hz; 0.51 s
A block is attached to a spring and set into oscillatory motion and its frequency is measured. If this block were removed and replaced by a second block with ¼ the mass of the first block, how would the frequency of the oscillations compare? f increases by a factor of 2
59.
In the drawing, one cycle is shaded in color. The amplitude A is the maximum excursion of a particle of the medium from the particles undisturbed position. The wavelength is the horizontal length of one cycle of the wave. The period is the time required for one complete cycle. The frequency is related to the period and has units of Hz, or s -1 .
When 2 or more waves meet, they overlap (interfere)
2 Types of interference
Constructive Interference (added together)
Destructive Interference (subtracted from each other)
2 waves, one with amplitude of 8 cm and the other with an amplitude of 3 cm travel in the same direction on a string and overlap. What are the maximum and minimum amplitudes? 11cm; 5 cm
A string of length 12 m that’s fixed at both ends supports a standing wave with a total of 5 nods. What are the harmonic number and wavelength of this standing wave?
66.
LONGITUDINAL SOUND WAVES The area of condensation is the region of compression with increased air pressure The area of rarefaction is the region behind the condensation with decreased air pressure
A vertical column made of cement has a base area of 0.5 m 2 . If the height is 2 m, and the sp. Gravity of cement is 3, how much pressure does this column exert on the ground? 6 x 10 4 Pa
What happens to the gauge pressure if we double the depth below the surface of a liquid? What happens to the total pressure? Gauge pressure increases by a factor of 2; Total pressure increases by less than a factor of 2
A flat piece of wood of area 0.5 m 2 is lying at the bottom of a lake. If the depth of the lake is 30 m, what is the force on the wood due to the pressure? 2 x 10 5 N
If p object < p fluid , then the object will float
A brick with a specific gravity of 2 and volume of 1.5 x 10-3 m3, is dropped into a swimming pool full of water. Explain why the brick will sink. When the brick is lying on the bottom of the pool, what is the magnitude of the normal force on the brick? Specific gravity is greater than 1; 15 N
A glass sphere of specific gravity 2.5 and volume of 10 -3 m 3 is completely submerged in a large container of water. What is the apparent weight of the sphere while immersed? 15 N
A 1 v 1 = A 2 v 2 (flow speed increases when the pipe narrows or inversely proportional)
A pipe carries water. At one point in the pipe, the radius is 2 cm and the flow speed is 6 m/s. What is the flow rate? What is the flow speed where the pipe’s radius changes to 1 cm? 7.5 x 10 -3 m 3 /s; 24 m/s
If the diameter of the pipe increases from 4 cm to 12 cm, what will happen to the flow speed? 1/9 the flowrate
A brass rod 5 m long and 0.01 m in diameter increases in length by 0.05 m when its temperature is increased by 500°C. A similar brass rod of length 10 m has a diameter of 0.02 m. By how much will this rod’s diameter increase if its temperature is increased by 1000°C? 4 x 10 -4 m
An aluminum rod (p = 2.7 x 103 kg/m3 has a radius of 0.01 m and an initial length of 2 m at a temperature of 20°C. Heat is added to raise its temperature to 90°C. Its coefficient of linear expansion is = 25 x 10-6/°C, the specific heat is 900 J/kg°C, and a thermal conductivity of k = 200 J/s m°C.
What is the mass of the aluminum rod? 1.7 kg
What is the amount of heat added to the rod? 107,100 J
What is the new length of the rod? 0.0035 m
If we were to use this rod to transfer heat between two objects one side being at 20°C and the other side at 90°C, what would the rate of heat transfer be? 2.2 J/s
In order for the average speed of the molecules in a given sample of gas to double, what must happen to the temperature? Since v is proportional to square root of T, the temperature must quadruple
A cylindrical container of radius 15 cm and height 30 cm contains 0.6 mole of gas at 433 K. How much force does the confined gas exert on the lid of the container? 35 N
92.
THE SECOND LAW OF THERMODYNAMICS: THE LAW OF ENTROPY Heat flows spontaneously from a substance at a higher temperature to a substance at a lower temperature and does not flow spontaneously in the reverse direction.
A heat engine draws 800 J of heat from its high temperature source and discards 450 J of exhaust heat into its cold-temperature reservoir. How much work does this engine perform and what is its thermal efficiency? 350 J; 44%
An inventor proposes a design for a heat engine that operates between a heat source at 500°C and a cold reservoir at 25°C with an efficiency of 2/3. What’s your reaction to the inventor’s claim?
95.
4 types of thermal processes An isobaric process is a process that occurs at constant pressure. An isochoric process is a process that occurs at constant volume. An isothermal process is a process that occurs at constant temperature. An adiabatic process is a process during which no energy is transferred to or from the system as heat at.
Consider two small spheres, one carrying a charge of +1.5nC and the other a charge -2.0 nC, separated by a distance of 1.5 cm. Find the electric force between them. -1.2 x 10 -4 N
A charge q = +3.0 nC is placed at a location at which the electric field strength is 400 N/C. Find the force felt by charge q. 1.2 x 10 -6 N
A dipole is formed by two point charges, each of magnitude 4.0 nC, separated by a distance of 6.0 cm. What is the strength of the electric field at a point midway between them? 8.0 x 10 4 N/C
An object of mass 5g is placed at a distance of 2 cm above a charged plate. If the strength of the electric field is 10 6 N/C, how much charge would the object need to have in order for the electrical repulsion to balance the gravitational pull? 5 x 10 -8 C
A positive charge q 1 = 2 + 10 -6 C is held stationary, while a negative charge q 2 = -1 x 10 -8 C, is released from rest at a distance of 10 cm from q 1 . Find the kinetic energy change of charge q 2 when it’s 1 cm from q 1 . 0.016 J
A 10 nF parallel plate capactior holds a charge of 50 μ C on each plate. What is the electric potential difference between the plates? If the plates are separated by a distance of 0.2 mm, what is the area of each plate? 5000 V; 0.23 m 2
A wire of radius 1mm and length 2 m is made of platinum (resistivity = 1 x 10 -7 Ω• m). If a voltage of 9 V is applied between the ends of the wire, what will be the resulting current? 140 A
A beam of light in air is incident upon a piece of glass striking the surface at an angle of 30 degrees. If the index of refraction of the glass is 1.5, what are the angles of reflection and refraction? 60 ° ; 35 °
Critical Angle - The angle of incidence at which the angle of refraction is 90 °. No light is refracted out and the beam is refracted along the surface.
If the angle of incidence is greater than the critical angle, no beams of light are refracted.
143.
Conceptual Example 4 On the Inside Looking Out A swimmer is under water and looking up at the surface. Someone holds a coin in the air, directly above the swimmer’s eyes. To the swimmer, the coin appears to be at a certain height above the water. Is the apparent height of the coin greater, less than, or the same as its actual height? Light rays are refracted AWAY from the normal when going from a higher index of refraction to a lower index of refraction. When it is the opposite, the light bends TOWARD the normal
Bohr theorized that a photon is emitted only when the electron changes orbits from a larger one with a higher energy to a smaller one with a lower energy
En = Ionization Energy – the minimum amount of energy that must be supplied to release the atom’s electron
How much energy must a ground state electron (n=1) in a hydrogen atom absorb to be excited to the n=4 energy level? 12.8 eV
With the electron in the n=4 level, what wavelengths are possible for the photon emitted when the electron drops to a lower energy level? In what regions of the EM spectrum do these photons lie?
Isotope – Contain the same number of protons but different number of neutrons
The element Neon (atomic number 10) has several isotopes. The most abundant isotope contains 10 neutrons, and two others contain 11 and 12. Write symbols for these three nuclides (a nucleus with a specific number of protons and neutrons
171.
Example 3 The Binding Energy of the Helium Nucleus Revisited The atomic mass of helium is 4.0026u and the atomic mass of hydrogen is 1.0078u. Using atomic mass units, instead of kilograms, obtain the binding energy of the helium nucleus.