Physics
How many molecules are there in a mole of Hydrogen?
1 mol of H2 = 6.022E23 molecules
Convert 1 um to meters
1 um = 0.000001
In the figure, what is the force FmFm supplied by the deltoid muscle so as to hold up the outstretched arm if the mass of the arm is 3.0 kg ? (FjFjis the joint force on the bone of the upper arm-the humerus.)
164 N
An automobile with a linear momentum of 3.0x10^4 kg m/s is brought to a stop in 5.0 s. What is the magnitude of the average braking force?
6000 N braking force
A football player kicks a football in a field goal attempt. When the football reaches its maximum height, what is the relationship between the direction of the velocity and acceleration vectors? Assume air resistance is negligible.
A - At the maximum height, the velocity and acceleration vectors are perpendicular to each other.
On a straight road, a car speeds up at a constant rate from rest to 20 m/s over a 5 second interval and a truck slows at a constant rate from 20 m/s to a complete stop over a 10 second interval. How does the distance traveled by the truck compare to that of the car?
A - The truck travels twice as far as the car.
Newton's second law of motion is expressed by the equation F=m a , where F represents force, m is mass, and a is acceleration. The SI unit of force is, appropriately, called the newton (N). What are the units of the newton in terms of base quantities?
A - kg⋅m/s^2
A race car travels a complete lap on a circular track of radius 500 m in 50 s. a) The average velocity of the race car is b) What is the average speed of the race car?
A) zero B) 63 m/s
The SI base unit for mass is the _______ .
A- kilogram
Using a development similar to Kepler's law of periods for planets orbiting the Sun, find the required altitude in meters of geosynchronous satellites above the Earth's surface. [Hint: The period of such satellites is the same as the Earth's period of rotation.]
Altitude = m
Which figure could represent the velocity versus time graph of a motorcycle whose "speed" is increasing?
B
A leaky faucet drips once each second. At this rate, it takes 1 hour to fill a 1-liter graduated cylinder to the 200-cm^3 mark. What unit conversion do you need in order to calculate the average volume of a single drop in cm^3?
B - 1 hour equals 3600 seconds
Starting from your campsite you walk 3.0 km east, 6.0 km north, 1.0 km east, and then 4.0 km west. How far are you from your campsite?
B - 6.0 km
The figure shows the velocity versus time graph for a car driving on a straight road. Which of the following best describes the acceleration of the car?
B - The acceleration of the car is positive and decreasing.
In the equation z = ct + d, z is measured in meters and t is measured in seconds. What are the dimensions (units) of c?
B - m/s
A girl and a boy are riding on a merry-go-round that is turning at a constant rate. The girl is near the outer edge, and the boy is closer to the center. Who has greater angular displacement?
Both the girl and the boy have the same nonzero angular displacement.
On the Moon, where air resistance is negligible, an astronaut drops a rock from a cliff and notes that the rock has a speed v after falling from its point of release for a time t. Assuming that the rock does not hit the ground first, how fast will it be moving after it has fallen for a time 4t from its point of release?
C - 4v
Which of the following is a vector?
C - Displacement
At what angle, above the horizon, should a cannon be fired in order for the cannon ball to obtain the greatest horizontal range? Assume air resistance is negligible.
C - The cannon should be fired at an angle of 45 degrees above the horizon.
Which of the following is the basis of the current standard for the meter?
C - The meter is defined as the distance that light travels in a specified time interval.
Which of the following do most scientists accept as correct about the Solar System?
C - The sun is a nearby star that consists of a plasma containing mostly H and He.
A red water balloon is thrown horizontally from the top of a bridge. At the same instant, a yellow water balloon is dropped off the bridge from the same height. Compare the time of fall for the two balloons. Assume air resistance is negligible. Assume air resistance is negligible.
C - The two balloons hit the ground at the same time.
A pilot releases a package from a plane flying horizontally at a constant speed. When the package reaches the ground below, what is the horizontal location of the plane with respect to the package? Assume air resistance is negligible.
D - The plane will be located directly above the package.
A student wants to determine the distance from the lakeshore to a small island. He first draws a 50 m line parallel to the shore. Then, he goes to the ends of the line and measures the angles of the lines of sight from the island relative to the line he has drawn. The angles are 30∘∘ and 40∘∘. How far is the island from the shore?
D = 17.10 m
The gravitational forces of the Earth and the Moon are attractive, so there must be a point on a line joining their centers where the gravitational forces on an object cancel. How far is this distance from the Earth's center in km?
Dearth = km
What is the relationship between mass, volume, and density?
Density is proportional to mass and inversely proportional to volume.
The radius of the earth is 6,380 kilometers. What is the radius of the earth in centimeters?
E - 6.38 x 10^8 cm
Earth's orbit around the Sun is slightly elliptical. Thus, Earth actually gets closer to the Sun during part of the year. What happens to Earth's orbital speed when it is closer to the Sun?
Earth's orbital speed is greater when it is closer to the Sun than when it is farther from the Sun.
A gun is fired and a 50 g bullet is accelerated to a muzzle speed of 100 m/s. If the length of the gun barrel is 0.90 m, what is the magnitude of the accelerating force? (Assume the acceleration to be constant.)
F = 277.78 N
Two force vectors, F⃗ 1=(3.0N)x̂ −(4.0N)ŷ F→1=(3.0N)x^−(4.0N)y^ and F⃗ 2=(−6.0N)x̂ +(4.5N)ŷ F→2=(−6.0N)x^+(4.5N)y^, are applied to a particle. What third force, F⃗ 3F→3 would make the net, or resultant, force on the particle zero?
F3 = 3Nx + -0.5Ny
A certain material has a density of 9 g/cm33. It is formed into a solid rectangular brick with dimensions of 1 cm by 2 cm by 4 cm. a) What is its mass in kilograms? b) If you wanted to make a cube of this same material containing twice the mass of this brick, what would be the length of one side of the cube?
Mass = 0.072kg Side = 2.5 cm
Person B does twice the work of person A, and in one-half of the time. How does the power output of person B compare to person A?
Person B has four times the power output of person A.
A stone thrown off a bridge 20 m above a river has an initial velocity of 12 m/s at an angle of 45° above the horizontal (see the figure). a) What is the range of the stone? b) At what velocity does the stone strike the water?
R = 26.00 m v = 23.15 m/s
A 55 kg gymnast hangs vertically from a pair of parallel rings. a) If the ropes supporting the rings are attached to the ceiling directly above, what is the tension in each rope? b) If the ropes are supported so that they make an angle of 45° with the ceiling, what is the tension in each rope?
T = 269.5 N T = 381.1 N
The same net force is applied to two different objects. The second object has twice the mass of the first object.
The acceleration of object 1 is twice the acceleration of object 2.
In general, how does the coefficient of static friction compare to the coefficient of kinetic friction for the same two materials?
The coefficient of static friction is greater than the coefficient of kinetic friction.
Two equal forces are applied perpendicular to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Which force exerts the greater torque?
The force applied at the doorknob exerts the greater torque.
A large truck collides head-on with a small car. The car is severely damaged as a result of the collision. According to Newton's 3rd Law, how do the forces acting between the truck and car compare during the collision?
The force on the truck is equal to the force on the car.
A large truck collides head-on with a small car. The car is severely damaged as a result of the collision. According to Newton's 3rdrd Law, how do the forces acting between the truck and car compare during the collision?
The force on the truck is equal to the force on the car.
A girl and a boy are riding on a merry-go-round that is turning at a constant rate. The girl is near the outer edge, and the boy is closer to the center. Who has greater linear speed?
The girl has greater linear speed.
Two objects attract each other gravitationally. If the distance between their centers decreases by a factor of 2, how does the gravitational force between them change?
The gravitational force increases by a factor of 4.
Two planets, planet A and planet B, have the same surface gravity. However, planet B has twice the radius of planet A. How does the mass of planet B compare to the mass of planet A?
The mass of planet B is four times the mass of planet A.
An object is moving with constant velocity. Which of the following best describes the force(s) acting on the object?
The net force acting on the object is zero.
An object moves in a circular path at a constant speed. What is the direction of the net force acting on the object?
The net force is directed toward the center of the circular path.
A person applies a 50 N force on a crate, causing it to move horizontally at a constant speed through a distance of 10 m. What is the net work done on the crate?
The net work done on the crate is zero joules.
If the net work done on an object is positive, what can you conclude about the object's motion?
The object is speeding up.
A constant net torque is applied to a rotating object. Which of the following best describes the object's motion?
The object will rotate with constant angular acceleration.
A planet is discovered orbiting around a star in the galaxy Andromeda at the same distance from the star as Earth is from the Sun. If that star has four times the mass of our Sun, how does the orbital period of the planet compare to Earth's orbital period?
The planet's orbital period will be one-half Earth's orbital period.
A cylindrical rod has equal and opposite forces applied perpendicular to its circular ends. The forces are directed away from the rod, stretching the rod. What type of stress is this rod subject to?
The rod is subject to tensile stress.
A heavy boy and a lightweight girl are balanced on a massless seesaw. The boy moves backward, increasing his distance from the pivot point. What happens to the seesaw?
The side the boy is sitting on will tilt downward.
A jar is completely filled with water, and then it is sealed with a lid. If you push down on the lid with a pressure of 1000 Pa, what happens to the water pressure at the bottom of the jar?
The water pressure at the bottom of the jar will increase by 1000 Pa.
Water flows through a horizontal pipe. The diameter of the pipe at point B is larger than the diameter of the pipe at point A. Where is the water pressure the greatest?
The water pressure is the greatest at point B.
A graph depicts force versus position. What represents the work done by the force over the given displacement?
The work done is equal to the area under the curve.
A spring (spring 1) with a spring constant of 500 N/m is attached to a wall and connected to another weaker spring (spring 2) with a spring constant of 250 N/m on a horizontal surface. Then an external force of = 100 N is applied to the end of the weaker spring (#2). How much potential energy is stored in each spring?
U1 = 10 J U2 = 20 J
The interior storage compartment of a restaurant refrigerator measures 1.3 m high, 1.05 m wide, and 67 cm deep. Determine its volume in cubic feet. Express your answer using two significant figures.
V = 32.30 ft^3
A 5.0 kg box slides a 10 m distance on ice. If the coefficient of kinetic friction is 0.20, what is the work done by the friction force?
W = -98J
A spring has a spring constant of 30 N/m. How much work is required to stretch the spring 2.0 cm from its equilibrium position?
W = 0.006 J
A ball is thrown straight upward. How does the sign of the work done by gravity while the ball is traveling upward compare with the sign of the work done by gravity while the ball is traveling downward?
Work done by gravity is negative while the ball is traveling upward and positive while the ball is traveling downward.
Two separate seismograph stations receive indication of an earthquake in the form of a wave traveling to them in a straight line from the epicenter and shaking the ground at their locations. Station B is 50 km due east of station A. The epicenter is located due north of station A and 30 degrees north of due west from station B. a) Determine the distance from the epicenter to A. b) Determine the distance from the epicenter to B. c) Station C is located an additional 20 km east of B. At what angle does C report the direction of the epicenter to be?
Y = 28.87 km R = 57.73 km θ = 22.41 °
A sports car can accelerate from 0 to 60 mph in 3.9 s. What is the magnitude of the average acceleration of the car in meters per second squared?
a = 6.87 m/s^2
In a laboratory setup, two frictionless carts are placed on a horizontal surface. Cart A has a mass of 500 g and cart B's mass is 1000 g. Between them is placed an ideal (very light) spring and they are squeezed together carefully, thereby compressing the spring by 5.50 cm. Both carts are then released and B's recoil speed is measured to be 0.55 m/s. a) Will cart A's speed be greater than, less than, or the same as B's speed? b) Determine cart A's recoil speed. c) Determine the spring constant of the spring.
a) b) VcartA = m/s c) ks = N/m
The displacement of an object is given as a function of time by xx = 3∗t23∗t2 . a) What is the magnitude of the average velocity for Δt=2.5Δt=2.5 s −0−0 s ? b) What is the magnitude of the average velocity for ΔΔ t=5.0t=5.0 s −2.5−2.5 s ?
a) 7.5 m/s b) 22.5 m/s
A car is driven 13 east and then a certain distance due north, ending up at a position θ = 25∘ north of east of its initial position. a) The relative distance traveled by the car due north is b) What distance due north does the car travel? ( Express your answer using two significant figures. )
a) A - less than 13 mi. b) Distance = 6.06 mi
To go to a football stadium from your house, you first drive 1000 m north, then 500 m west, and finally 1500 m south. a) Relative to your home, the football stadium is b) What is the straight-line distance from your house to the stadium?
a) B - south of west. b) Distance = 500sqrt(2)
A baseball player pops a pitch straight up. The ball (mass 200 g) was traveling horizontally at 35.0 m/s just before contact with the bat, and 20.0 m/s just after contact. a) Determine the magnitude of the impulse delivered to the ball by the bat. b) Determine the direction of the impulse delivered to the ball by the bat. Assume the initial direction of the ball is in the −x̂ direction.
a) I or change in P = 8.1 N*s b) theta = 29.74 above + x direction
A 1200 kg automobile travels at 90 km/h. a) What is its kinetic energy? b) What net work would be required to bring it to a stop?
a) Ko = 3.75E5 J b) Wnet = -3.75E5 J
In the Bible, Noah is instructed to build an ark 300 cubits long, 50.0 cubits wide, and 30.0 cubits high. Historical records indicate a cubit is equal to half a yard. a) What would be the dimensions of the ark in meters? b) What would be the ark's volume in cubic meters? ( To approximate, assume that the ark is rectangular. )
a) L = 137.16 m, W = 22.86 m, D = 13.72 m b) V = L*W*D = 43018.75 m^3
A pump lifts 200 kg of water per hour a height of 5.0 m. a) What is the minimum necessary power output rating of the water pump in watts? b) What is the minimum necessary power output rating of the water pump in horsepower?
a) P = 2.72 W b) P = 3.6E-3 hp
Driving a jet-powered car, Royal Air Force pilot Andy Green broke the sound barrier on land for the first time and achieved a record land speed of more than 763 mi/h in Black Rock Desert, Nevada, on October 15, 1997. a) What is this speed expressed in m/s? b) How long would it take the jet-powered car to travel the length of a 300 ft football field at this speed? ( Hint: S = D/t. )
a) S = 341 m/s b) t = 0.268 s
The outside dimensions of a cylindrical soda can are reported as 12.559 cm for the diameter and 5.62 cm for the height. a) How many significant figures will the total outside area have? ( Enter an integer between 1 and 9. ) b) What is the total outside surface area of the can in square centimeters?
a) Significant Figure = 3 b) Surface Area = 469 cm^2
A 1.50 kg mass is placed on the end of a spring that has a spring constant of 175 N/m . The mass-spring system rests on a frictionless incline that is at an angle of 30.0° from the horizontal (see the figure). The system is eased into its equilibrium position, where it stays. a) Determine the change in elastic potential energy of the system. b) Determine the system's change in gravitational potential energy.
a) Us = J b) Ug = J
Imagine that you swing about your head a ball attached to the end of a string. The ball moves at a constant speed in a horizontal circle. a) If the mass of the ball is 0.250 kg, the radius of the circle is 1.50 m, and it takes 1.20 s for the ball to make one revolution, what is the ball's tangential speed? b) What centripetal force are you imparting to the ball via the string?
a) VT = 7.85 m/s b) Fc = 10.3 N
In a pairs figure-skating competition, a 65 kg man and his 45 kg female partner stand facing each other on skates on the ice. a) If they push apart and the woman has a velocity of 1.5 m/s eastward, what is the magnitude of the velocity of her partner? (Neglect friction.) b) What is the direction of the velocity of her partner?
a) Vman = 1.04 m/s b) Westward
An airplane flies due north with an air speed of 250 km/h . A steady wind at 75 km/h blows eastward. (Air speed is the speed relative to the air.) a) What is the plane's ground speed (vpgvpg)?
a) Vpg = 261 km/h b) theta = 16.47 °west of due north
At the instant a ball rolls off a rooftop it has a horizontal velocity component +10.0 m/s of and a vertical component (downward) of 15.0 m/s . a) Determine the angle of the roof. b) What is the ball's speed as it leaves the roof?
a) Vx = 10 m/s Vy = -15 m/s Tan theta = Vy/Vx = tan^-1(-15/10) = -3/2 = 56.31° below the horizontal b) square root Vx^2 + Vy^2 = square root 100 + 225 = square root 325 m/s
An Atwood machine (see the figure) has suspended masses of m1m1 = 0.20 kg and m2m2 = 0.25 kg. a) Under ideal conditions, what will be the magnitude of the acceleration of the smaller mass? b) What will be the direction of the acceleration of the smaller mass?
a) a = 1.089 m/s^2 b) upward
A force F of 10 N acts on two blocks on a frictionless surface. a) What is the acceleration of the system? b) What is the magnitude of the force that block A exerts on block B? c) What is the direction of the force that block A exerts on block B? d) What is the magnitude of the force that block B exerts on block A? e) What is the direction of the force that block B exerts on block A?
a) a = 2 m/s^2 b) Fab = 4 N c) to the right d) Fba = 4 N e) to the left
In an Olympic figure-skating event, a 65 kg male skater pushes a 45 kg female skater, causing her to accelerate at a rate of 2.0 m/s. a) At what rate will the male skater accelerate? b) What is the direction of his acceleration?
a) aM = 1.4 m/s^2 b) opposite to her's
A CD originally at rest reaches an angular speed of 40. rad/s in 5.0 s. a) What is the magnitude of its angular acceleration? b) How many revolutions does the CD make in the 5.0 s?
a) alpha = 8 rad/s^2 b) Nrev = 16 revs
A girl swings back and forth on a swing with ropes that are 4.00 m long. The maximum height she reaches is 2.00 m above the ground. At the lowest point of the swing, she is 0.500 m above the ground. a) The girl attains the maximum speed ________ of the swing. b) What is the girl's maximum speed?
a) at the bottom b) Vmax = 5.42 m/s
A 3.0 kg rod of length 5.0 m has at opposite ends point masses of 4.0 kg and 6.0 kg. a) Will the center of mass of this system be between the 4.0 kg mass and the center, between the 6.0 kg mass and the center, or at the center of the rod? b) Where is the center of mass of the system?
a) between the 6.0 kg mass and the center b) xCM = 2.88 m from the 4.0 kg mass
A ball of mass 200. g is released from rest at a height of 2.00 m above the floor and it rebounds straight up to a height of 0.900 m. a) Determine the magnitude of the the ball's change in momentum due to its contact with the floor. b) Determine the direction of the the ball's change in momentum due to its contact with the floor. c) If the contact time with the floor was 0.0950 s, what was the average force the floor exerted on the ball? d) What was the direction of this force?
a) change in p = 2.1 N*s b) Upward c) Fnet = 22.1 N d) Upward
A 15.0 g rubber bullet hits a wall with a speed of 150 m/s. a) If the bullet bounces straight back with a speed of 120 m/s, what is the magnitude of the change in momentum of the bullet? b) What is the direction of the change in momentum of the bullet?
a) change in p = 4.05 N*s b) in the direction opposite to the initial speed
Two joggers run at the same average speed. Jogger A cuts directly north across the diameter of the circular track, while jogger B takes the full semicircle to meet his partner on the opposite side of the track. Assume their common average speed is 2.70 m/s and the track has a diameter of 150 m. a) How many seconds ahead of jogger B does jogger A arrive? b) How do their travel distances compare? c) How do their displacements compare? d) How do their average velocities compare?
a) change t = 31.6 s b) dA = 150 m , dB = 235.5 m c) DA = 150 m , dB = 150 m d) VA = 2.7 m/s , VB = 1.72 m/s
A golf ball is hit with an initial speed of 35 m/s at an angle less than 45oo above the horizontal. a) The horizontal velocity component is ________ the vertical velocity component. b) If the ball is hit at an angle of 37oo, what are the initial horizontal and vertical velocity components?
a) greater than b) Vx = 35cos(37) = 27.95 Vy = 35sin(37) = 21.06
A golf ball is hit with an initial speed of 35 m/s at an angle less than 45° above the horizontal. a) The horizontal velocity component is ________ the vertical velocity component. b) If the ball is hit at an angle of 37°, what are the initial horizontal and vertical velocity components?
a) greater than b) vx = 27.95 m/s vy = 21.06 m/s
To haul a boat out of the water for the winter, a worker at the storage facility uses a wide strap with cables operating at the same angle, θ, (measured from the horizontal) on either side of the boat. a) As the boat comes up vertically and θ decreases, the tension in the cables b) Determine the tension in each cable if the boat has a mass of 500 kg and the angle of each cable is 45° from the horizontal and the boat is being momentarily held at rest. Compare this to the tension when the boat is raised and held at rest so the angle becomes 30°.
a) increases b) T45° = 3474.02 N T30° = 4998 N
In the apparatus shown in the figure , m1 = 10 kg and the coefficients of static and kinetic friction between m1 and the table are 0.60 and 0.40, respectively. a) What mass of m2 will just barely set the system in motion? b) After the system begins to move, what is the acceleration?
a) m2 = 6 kg b) a = 1.23 m/s^2
A crate is dragged 3.0 m along a rough floor with a constant velocity by a worker applying a force of 500 N to a rope at an angle of 30° to the horizontal. a) How many forces are acting on the crate? b) How much work does each of these forces do? c) What is the total work done on the crate?
a) n = 4 b) Wnormal = 0 J Wgravity = 0 J Wworker = 1300 J Wfriction = -1300 J c) Wnet = 0 J
A 1.5 kg object moves up the y-axis at a constant speed. When it reaches the origin, the forces F1=5.0 N at 37° above the + x-axis, F 2=2.5 N in the +x direction, F3=3.5 N at 45° below the -x-axis, and F4=1.5 N in the -y direction are applied to it. a) Will the object continue to move along the y-axis? b) If not, what simultaneously applied force will keep it moving along the y-axis at a constant speed?
a) no b) F5 = 4.02 N at 13° above the -x axis
A 1.5 kg object moves up the yy-axis at a constant speed. When it reaches the origin, the forces F⃗ 1=F→1=5.0 N at 37oo above the + x-axis, F⃗ 2=F→2=2.5 N in the +x direction, F⃗ 3=F→3=3.5 N at 45oo below the -x-axis, and F⃗ 4=F→4=1.5 N in the -y direction are applied to it. a) Will the object continue to move along the y-axis? b) If not, what simultaneously applied force will keep it moving along the y-axis at a constant speed? Find the magnitude and direction of the force.
a) no b) f5 = 4.02 N at 13° above the x-axis
An object initially at rest explodes and splits into three fragments. The first fragment flies off to the west, and the second fragment flies off to the south. a) The third fragment will fly off toward a general direction of b) If the object has a mass of 3.0 kg, the first fragment has a mass of 0.50 kg and a speed of 2.8 m/s, and the second fragment has a mass of 1.3 kg and a speed of 1.5 m/s, what is the speed of the third fragment? c) What is the direction of the third fragment?
a) north of east b) v3 = 2 m/s c) theta = 54.31° north of east
A flight controller determines that an airplane is 20.0 mi south of him. Half an hour later, the same plane is 35.0 mi northwest of him. a) The general direction of the airplane's velocity is ________. If the plane is flying with constant velocity, what is the direction of its velocity during this time? What is the magnitude of its velocity during this time?
a) north of west theta = 61.05 ° north of west v = 102.24
You throw a stone vertically upward with an initial speed of 6.0 m/s from a third-story office window. a) If the window is 12 m above the ground, find the time the stone is in flight. b) Find the speed of the stone just before it hits the ground.
a) t = 2.3 s b) v = -16.5 m/s (Downward position)
A football is kicked off the flat ground at 25.0 m/s at an angle of 30.0oo relative to the ground. a) Determine the total time it is in the air. b) Find the angle of its velocity with respect to the ground after it has been in the air for one-fourth of thistime. Repeat for one-half, and three-fourths of this total time. c) For each of these times, determine its speed.
a) t = 2.5 s b) beta1/4 = 16.1°, beta1/2 = 0°, beta3/4= -16.1° c) v1/4= 22.53 m/s , v12 = 21.65 m/s, v3/4 = 22.53 m/s
An object initially at rest experiences an acceleration of 2.00 on a level surface. Under these conditions, it travels 6.00 m. Let's designate the first 3.00 m as phase 1 with a subscript of 1 for those quantities, and the second 3.00 m as phase 2 with a subscript of 2. a) The times for traveling each phase should be related by which condition?
a) t1 > t2 b) t1 = 1.72 s t2 = 0.72 s
The driver of a car sets the cruise control and ties the steering wheel so that the car travels at a uniform speed of 15.0 m/s in a circle with a diameter of 120. m. a) Through what angular distance does the car move in 4.00 minutes?
a) theta = 60 rad b) s = 3600 m
In a pool game, a cue ball traveling at 0.75 m/s hits the stationary eight ball. The eight ball moves off with a velocity of 0.25 m/s at an angle of 37° relative to the cue ball's initial direction (above the +x̂ direction). a) Assuming that the collision is inelastic, at what angle will the cue ball be deflected? b) What will be the cue ball's speed?
a) thetaCueball = 15.23°, below the +x direction b) vCueball = 0.57 m/s
An Olympic skier coasts down a slope with an angle of inclination of 37°. a) Neglecting friction, how many forces are acting on the skier? b) What is the acceleration of the skier? c) If the skier has a speed of 5.0 m/s at the top of the slope, what is his speed when he reaches the bottom of the 35 m long slope?
a) two forces b) a = 5.9 m/s^2 c) v = 20.9 m/s
On a water slide ride, you start from rest at the top of a 45.0 m long incline (filled with running water) and accelerate down at 4.00 m/s22. You then enter a pool of water and skid along the surface for 20.0 m before stopping. a) What is your speed at the bottom of the incline? b) What is the magnitude of the deceleration caused by the water in the pool? c) What was the total time for you to stop in the pool? d) How fast were you moving after skidding the first 10.0 m on the pool water surface?
a) v1 = 18.97 m/s b) a2 = -9 m/s^2 c) t2 = 2.11 s d) v2 = 8.94 m/s
An automobile is traveling on a long, straight highway at a steady 75.0 mph when the driver sees a wreck 180 m ahead. At that instant, she applies the brakes (ignore reaction time). Between her and the wreck are two different surfaces. First there is 100 m of ice, where the deceleration is only 1.00 m/s22. From then on, it is dry concrete, where the deceleration is a more normal 7.00 m/s22. a) What was the car's speed just after leaving the icy portion of the road? b) What is the total distance her car travels before it comes to a stop? c) What is the total time it took the car to stop?
a) v1 = 30.3 m/s b) x total = 166 m c) t total = 7.43 s
At a county fair, two children ram each other head-on while riding on the bumper cars. Jill and her car, traveling left at -3.50 m/s, have a total mass of 325 kg. Jack and his car, traveling to the right at 2.00 m/s, have a total mass of 290 kg. a) Assuming the collision to be elastic, determine the speed of Jill and her car after the collision. Velocities to the left are to be considered negative, and those to the right positive. b) Determine the direction of the velocity of Jack and his car after the collision. Velocities to the left are to be considered negative, and those to the right positive.
a) vJill = 1.69 m/s b) vJack = 3.81 m/s
After landing, a jetliner on a straight runway taxis to a stop at an average velocity of −35−35 km/h. If the plane takes 7.007.00 s to come to rest, what are the plane's initial velocity and acceleration?
a) vo = -19.44 m/s b) a = 2.78 m/s^2
A fixed 0.15 kg solid-disk pulley with a radius of 0.075 m is acted on by a net torque of 6.4 m⋅N. What is the angular acceleration of the pulley?
alpha = 1.52E4 rad/s^2
In 2004 two Martian probes successfully landed on the Red Planet. The final phase of the landing involved bouncing the probes until they came to rest (they were surrounded by protective inflated "balloons"). During one of the bounces, the telemetry (electronic data sent back to Earth) indicated that the probe took off at 25.0 m/s at an angle of 20 oo and landed 110 m away (and then bounced again). Assuming the landing region was level, determine the acceleration due to gravity near the Martian surface.
gMARS = 3.65 m/s^2
A rolling object
has a zero velocity at the point or line of contact.
The figure shows the applied force versus elongation for a typical metal under tension. Four points on the figure, A through D, have been identified. Which point represents the elastic limit of the material?
point C
You measure the length of a distant car to be subtended by an angular distance of 1.5°. If the car is actually 5.0 m long, approximately how far away is the car?
r = 192 m
A ball with a horizontal speed of 1.0 m/s rolls off a bench 2.0 m high. How long will the ball take to reach the floor? How far from a point on the floor directly below the edge of the bench will the ball land?
t = 0.64 s x = 0.64 m
An object is at rest on a tabletop. Earth pulls downward on this object with a force equal in magnitude to mgmg. If this force serves as the action force, what is the reaction force in the action-reaction pair?
the object pulling upward on Earth
A motor boat's speed in still water is 2.0 m/s. The driver wants to go directly across a river with a current speed of 1.5 m/s. At what angle upstream should the boat be steered?
theta = 41.41° with respect to the current's direction
Two gear wheels with radii of 25. cm and 60. cm have interlocking teeth. How many radians does the smaller wheel turn when the larger wheel turns 4.0 rev ?
theta_small = 60.3 rad
For the apparatus shown in the figure , what is the minimum value of the coefficient of static friction between the block m3 and the table that would keep the system at rest if m1 = 0.25 kg, m2 = 0.50 kg, and m3 = 0.75 kg?
uS= 0.33
A rotating cylinder about 16. km long and 7.0 km in diameter is designed to be used as a space colony. With what angular speed must it rotate so that the residents on it will experience the same acceleration due to gravity as on Earth?
w = 0.053 rad/sec
A merry-go-round makes 24 revolutions in a 3.0 minute ride. a) What is its average angular speed in rad/s? b) What are the tangential speeds of two people 4.0 m and 5.0 m from the center, or axis of rotation?
w = 0.84 rad/sec vT @ 4.0 m = 3.4 m/s vT@ 5.0 m = 4.2 m/s
Calculate the value for x in the following equation where y = 2:
x = 2
The polar coordinates of a point are (5.3 , 32°). What are the point's Cartesian coordinates?
x = 4.5 m y = 2.8 m
A uniform meterstick pivoted at its center has a 100. gg mass suspended at the 25.0 cm position, similar to this picture. a) At what position should a 75.0 gg mass be suspended to put the system in equilibrium?
x = 83.33 cm m = 62.5 g
A boy throws a stone straight upward with an initial speed of 15.0 m/s. What maximum height will the stone reach before falling back down?
y = 11.5 m
A vertical spring with a force constant of 300. N/m is compressed 6.0 cm and a 0.25 kg ball placed on top. The spring is released and the ball flies vertically upward. How high does the ball go?
y = 22 cm
