Physics Final Pt.2

Older auto-focus cameras sent out a pulse of sound and measured the time interval required for the pulse to reach an object, reflect off of it, and return to be detected. Can air temperature affect the camera's focus? New cameras use a more reliable infrared system. - Yes, the camera may interpret an object as being closer than it actually is on a hot day. - Yes, the camera may interpret an object as being farther away than it actually is on a hot day. - No, the speed of sound in air remains the same regardless of temperature. - No, the effect of such a change in temperature is not great enough to be significant.

- Yes, the camera may interpret an object as being closer than it actually is on a hot day.

A pendulum bob with a mass of 0.43 kg is attached to a 1.5 m long string as shown. As the pendulum bob swings from point A, where the angle 𝜃 = 33°, to point B at the bottom of its arc, determine the change in the gravitational potential energy of the pendulum bob-earth system.

-1.02 J

A baseball with a mass of 151 g is thrown horizontally with a speed of 40.3 m/s (90 mi/h) at a bat. The ball is in contact with the bat for 1.15 ms and then travels straight back at a speed of 46.0 m/s (103 mi/h). Determine the average force (in N) exerted on the ball by the bat. Neglect the weight of the ball (it is much smaller than the force of the bat) and choose the direction of the incoming ball to be positive. (Indicate the direction with the sign of your answer.)

-11331.57 N

An object is traveling such that it has a momentum of magnitude 25.6 kg · m/s and a kinetic energy of 326 J. Determine the following. (a) speed of the object in meters per second (c) mass of the object in kilograms

1.005 kg

The center of mass of a person may be determined by an arrangement such as the one shown in the figure below. A light plank rests on two scales separated by a distance of d = 1.80 m and reading Fg1 = 470 N and Fg2 = 350 N. Determine the distance of the girl's center of mass from her feet.

1.03 m

Two parakeets sit on a swing with their combined center of mass 18.0 cm below the pivot. At what frequency (in Hz) do they swing?

1.17 Hz

A 70-kg boy is surfing and catches a wave which gives him an initial speed of 1.6 m/s. He then drops through a height of 1.60 m, and ends with a speed of 8.5 m/s. How much nonconservative work (in kJ) was done on the boy?

1.34 kg

How much work does a supermarket checkout attendant do on a can of soup he pushes 0.360 m horizontally with a force of 4.60 N? Express your answer in joules and kilocalories.

1.656 J ; 3.96e-4

A torque is applied to a long thin rod making it rotate with an angular acceleration of 7.30 rad/s2 about an axis through its center and perpendicular to its length (see figure (a) below). If the same torque is now applied to make the rod rotate about an axis about one end perpendicular to its length (see figure (b) below), determine the new angular acceleration of the rod.

1.825 rad/s^2

An 8.00 m long beam with a mass of 8.50 kg is suspended horizontally from a post, as shown. The left end of the beam is attached to a frictionless hinge on the vertical post that allows the beam to rotate up and down freely. The right end of the beam is supported by a wire that runs to the top of the post. The wire makes a 50° angle with the vertical post. The beam's shape is symmetric and it is made of a homogeneous material so that its center of mass is located at its geometric center. What tension in the wire is required to support the beam horizontally?

64.8 N

As shown in the figure below, a skateboarder starts at point A on the ramp and rises to point B, a maximum height of h = 3.01 m above the top of the ramp. If the amount of work done against friction is insignificant, determine his initial speed (in m/s) at point A.

7.68 m/s

During a testing process, a worker in a factory mounts a bicycle wheel on a stationary stand and applies a tangential resistive force of 125 N to the tire's rim. The mass of the wheel is 1.30 kg and, for the purpose of this problem, assume that all of this mass is concentrated on the outside radius of the wheel. The diameter of the wheel is 50.0 cm. A chain passes over a sprocket that has a diameter of 9.00 cm. In order for the wheel to have an angular acceleration of 3.70 rad/s2, what force, in Newtons, must be applied to the chain? (Enter the magnitude only.)

701.125 N

With the aid of a string, a gyroscope is accelerated from rest to 25 rad/s in 0.32 s. What is its angular acceleration in rad/s2?

78.12 rad/s^2

A man on a motorcycle plans to make a jump as shown in the figure. If he leaves the ramp with a speed of 38.0 m/s and has a speed of 35.8 m/s at the top of his trajectory, determine his maximum height (h) (in m) above the end of the ramp. Ignore friction and air resistance.

8.28 m

A 5.50 kg lamp is hung from an 8.00 m long horizontal beam, as shown in the figure. The left end of the beam is attached to a frictionless hinge on a vertical post that allows the beam to rotate up and down freely. The right end of the beam is supported by a wire that runs to the top of a post. The wire makes a 50° angle with the vertical post. The lamp is hung from the beam, 7.70 m away from the vertical post. If the mass of the beam is negligible, what is the tension in the wire?

80.71 N

During a football game, a receiver has just caught a pass and is standing still. Before he can move, a tackler, running at a velocity of +3.7 m/s, grabs and holds onto him so that they move off together with a velocity of +2.0 m/s. If the mass of the tackler is 105 kg, determine the mass of the receiver in kilograms. Assume momentum is conserved.

89.25 kg

An ultracentrifuge accelerates from rest to 100,000 rpm in 1.90 min. (a) What is its angular acceleration in rad/s2? (b) What is the tangential acceleration, in m/s2, of a point 10.80 cm from the axis of rotation? (c) What is the radial acceleration, in m/s2, of this point at full rpm? (d) Express this radial acceleration as a multiple of g.

91.81 rad/s2 9.92 m/s2 1.18e7 m/s2 1.2e6 g

A uniform rod of mass 1.90 kg and length 2.00 m is capable of rotating about an axis passing through its center and perpendicular to its length. A mass m1 = 5.50 kg is attached to one end and a second mass m2 = 2.40 kg is attached to the other end of the rod. Treat the two masses as point particles. (a) What is the moment of inertia of the system in kg · m2? (b) If the rod rotates with an angular speed of 2.60 rad/s, how much kinetic energy, in joules, does the system have? (c) Now consider the rod to be of negligible mass. What is the moment of inertia of the rod and masses combined, in kg · m2? (d) If the rod is of negligible mass, what is the kinetic energy, in joules, when the angular speed is 2.60 rad/s?

a. 8.5 kgm^2 b. 28.73 J c. 7.9 kgm^2 d. 26.702 J

(a) You wish to determine the height of the smokestack of a local coal burning power plant. You convince a member of the maintenance crew to mount the support for a simple pendulum at the top of the stack and you suspend a 1.00 kg mass that just misses the ground at its lowest point from the pendulum cord. If the period of the pendulum is 18.7 s, determine the height of the smokestack. (b) If you had the ability to take this pendulum to the moon, where the acceleration due to gravity is 1.67 m/s2, what would you expect the period of the pendulum to be?

a. 86.806 m b. 45.3 s

(a) What is the length of a simple pendulum that oscillates with a period of 1.2 s on Earth, where the acceleration due to gravity is 9.80 m/s2, and on Mars, where the acceleration due to gravity is 3.70 m/s2? (b) What mass would you need to suspend from a spring with a force constant of 20 N/m in order for the mass-spring system to oscillate with a period of 1.2 s on Earth, where the acceleration due to gravity is 9.80 m/s2, and on Mars, where the acceleration due to gravity is 3.70 m/s2?

a. Le=0.357 m Lm=0.135 m b. mE= 0.73 kg mM= 0.73 kg

You and your family take a road trip on a long holiday weekend. In a certain section of the trip where the road is particularly uneven, the car goes over a bump that is curved downward with a radius of 21.0 m. See diagram below. The mass of the car and its passengers is 1400 kg. (a) When the car is at the highest point of the bump its speed is 8.85 m/s. Determine the magnitude, in N, and the direction of the force exerted by the road on the car at this highest point. (b) If the speed at the highest point is above a certain maximum value the car will lose contact with the road. Calculate this maximum speed in m/s.

a. Magnitude= 8498.5 N Direction= upward b. 14.35 m/s

A thin block of soft wood with a mass of 0.076 kg rests on a horizontal frictionless surface. A bullet with a mass of 4.67 g is fired with a speed of 583 m/s at a block of wood and passes completely through it. The speed of the block is 24 m/s immediately after the bullet exits the block. (a) Determine the speed (in m/s) of the bullet as it exits the block. (b) Determine if the final kinetic energy of this system (block and bullet) is equal to, less than, or greater than the initial kinetic energy. (c) Verify your answer to part (b) by calculating the initial and final kinetic energies of the system in joules.

a. 192.42 m/s b. less than the intial kinetic energy c. KEi= 793.64 J KEf=108.34 J

If during strenuous exercise your heart rate is 152 beats per minute, determine the following. (a) the frequency of your heartbeat (b) the period of your heartbeat

a. 2.53 Hz b. 0.4 s

A mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a stretched position. The position of the mass at any time is described by x = (8.2 cm)cos[2𝜋t/(2.78 s)]. Determine the following. (a) period of the motion (b) frequency of the oscillations (c) first time the mass is at the position x = 0 (d) first time the mass is at the site of maximum compression of the spring

a. 2.78 s b. 0.36 Hz c. 0.695 s d. 1.39 s

(a) Calculate the linear acceleration of a car, the 0.220-m radius tires of which have an angular acceleration of 13.0 rad/s2. Assume no slippage and give your answer in m/s2. (b) How many revolutions do the tires make in 2.50 s if they start from rest? (c) What is their final angular velocity in rad/s? (d) What is the final velocity of the car in m/s?

a. 2.86 m/s^2 b. 6.465 rev c. 32.5 rad/s d. 7.15 m/s

A professional boxer hits his opponent with a 1200 N horizontal blow that lasts 0.170 s. The opponent's total body mass is 119 kg and the blow strikes him near his center of mass and while he is motionless in midair. (a) Determine the impulse (in kg · m/s) the boxer imparts to his opponent by this blow. (b) Determine the opponent's final velocity (in m/s) after the blow. (c) Calculate the recoil velocity (in m/s) of the opponent's 5.0 kg head if hit in this manner, assuming the head does not initially transfer significant momentum to the boxer's body.

a. 204 kgm/s b. 1.71 m/s c. 40.8 m/s

Shoveling snow can be extremely taxing since the arms have such a low efficiency in this activity. Suppose a person shoveling a sidewalk metabolizes food at the rate of 700 W. (The efficiency of a person shoveling is 3%.) (a) What is her useful power output (in W)? (b) How long (in s) will it take her to lift 3,400 kg of snow 1.20 m? (This could be the amount of heavy snow on 60.0 ft of sidewalk.) (c) How much waste heat (in J) will she generate in the process?

a. 21 W b. 1904 s c. 1292816 J

When tightening a bolt, you push perpendicularly on a wrench with a force of 161 N at a distance of 0.140 m from the center of the bolt. (a) How much torque are you exerting in newtons ✕ meters (relative to the center of the bolt)? (b) Convert this torque to footpounds.

a. 22.54 Nm b. 16.6 ft-lb

A uniform rod is attached to a wall by a hinge at its base. The rod has a mass of 2.0 kg, a length of 1.3 m, is at an angle of 23° above the horizontal, and is held in place by a horizontal cord attached to the other end of the rod and bolted to the wall above the base of the rod. (a) Determine the tension in the cord. (b) Determine the horizontal and vertical components of the force exerted on the rod by the hinge.

a. 23.08 N b. Fh=23.08 N Fv=19.6 N

A hammer strikes one end of a thick iron rail of length 5.08 m. A microphone located at the opposite end of the rail detects two pulses of sound, one that travels through the air and a longitudinal wave that travels through the rail. (The speeds of sound in air and in iron are 343 m/s and 5950 m/s, respectively.) (a) Which pulse reaches the microphone first?the pulse traveling through the airthe pulse traveling through the iron rail (b) Find the separation in time between the arrivals of the two pulses.

a. the pulse traveling through the iron rail b. 0.014 s

While leaning out a window that is 6.0 m above the ground, you drop a 0.60 kg basketball to a friend at ground level. Your friend catches the ball at a height of 1.1 m above the ground. Determine the following. (a) the amount of work done (in J) by the force of gravity on the ball (b) the gravitational potential energy (in J) of the ball-earth system, relative to the ground when it is released (c) the gravitational potential energy (in J) of the ball-earth system, relative to the ground when it is caught (d) the ratio of the change (PEf − PE0) in the gravitational potential energy of the ball-earth system to the work done on the ball by the force of gravity

a. 28.812 J b. 35.28 J c. 6.468 d. -1

You hold a softball with a weight of 1.80 N in your hand as shown in the figure. Your arm is moving, but at the instant shown, your arm is horizontal. Consider your forearm and hand to be a uniform rod with a mass of 1.30 kg and the distance between your elbow joint and the ball in your hand is 2L = 25.5 cm. Your biceps exerts an upward, vertical force of 15.0 N on your forearm and is attached a distance of d = 2.20 cm from your elbow (a) Using your elbow joint as the axis of rotation, determine the magnitude of the net torque acting about your elbow due to the weight of your forearm/hand, the weight of the ball, and the force applied by your bicep. (b) In which direction will your forearm and hand rotate, given the signed value of the net torque calculated in part (a)?

a. 3.12 Nm b. Clockwise

A 6.75 kg mass oscillates up and down on a spring that has a force constant of 90 N/m. (a) What is the angular frequency of this spring/mass system? (b) What is the period of this spring/mass system?

a. 3.65 rad/s b. 1.72 s

A child with a weight of 160 N swings on a playground swing attached to 1.90 m long chains. What is the gravitational potential energy (in J) of the child-earth system relative to the child's lowest position at the following times? (a) when the chains are horizontal (b) when the chains make an angle of 29.0° with respect to the vertical (c) when the child is at his lowest position

a. 304 J b. 38.12 J c. 0 J

In a shipping yard, a crane operator attaches a cable to a 1,160 kg shipping container and then uses the crane to lift the container vertically at a constant velocity for a distance of 28 m. Determine the amount of work done (in J) by each of the following. (a) the tension in the cable (b) the force of gravity

a. 318304 b. -318304

A meter stick with a mass of 0.85 kg is held perpendicular to a vertical wall by a cord of length d = 3.8 m attached to the end of the meter stick and also to the wall above the other end of the meter stick. (a) Determine the tension in the cord. (b) Will the tension in the cord will be greater than, less than, or the same as that found in part (a) if the string is shortened? To clarify, when the string is shortened, the location where the string is attached to the wall is lowered so that the meter stick remains horizontal.

a. 4.32 N b. Greater than

As shown in the figure below, object m1 = 1.50 kg starts at an initial height h1i = 0.270 m and speed v1i = 4.00 m/s, swings downward and strikes (in an elastic collision) object m2 = 4.45 kg which is initially at rest. (a) Determine the speed of m1 (in m/s) just before the collision. (b) Determine the velocity (magnitude in m/s and direction) of each ball just after the collision (Assume the positive direction is toward the right. Indicate the direction with the sign of your answer.) (c) Determine the height (in m) to which each ball swings after the collision (ignoring air resistance).

a. 4.61 m/s b. m1-- -2.286 m/s m2-- 2.234 m/s c. m1-- 0.2666 m m2-- 0.2756 m

Because it can go from rest to 24.3 m/s (about 54 mi/h) in 3.6 s, one of the fastest-accelerating animals is the cheetah. If its mass is 50.0 kg, determine the average power developed by the cheetah during the acceleration phase of its motion. Express your answer in the following units. a. watts b. horsepower

a. 4100.65 W b. 5.497 hp

An athlete with a mass of 64.5 kg is in a cross country race, and at one instant he has a speed of 3.80 m/s. (a) What is his kinetic energy at this instant? (b) If he wishes to doubles his speed to reach the finish line, his kinetic energy will change by what factor?

a. 465.69 J b. 4

(a) What is the speed of sound (in m/s) in a medium where a 134 kHz frequency produces a 0.040 cm wavelength? (b) Which substance in this table is this likely to be?

a. 53.6 m/s b. vulcanized rubber

A stunt pilot in an air show performs a loop-the-loop in a vertical circle of radius 2.94 103 m. During this performance the pilot whose weight is 800 N, maintains a constant speed of 2.20 102 m/s. (a) When the pilot is at the highest point of the loop determine his apparent weight in N. (b) At what speed, in m/s, will the pilot experience weightlessness? (c) When the pilot is at the lowest point of the loop determine his apparent weight in N.

a. 543.8 N b. 169.7 m/s c. 2143.8 N

An object with a mass of 58.0 kg is fired with an initial speed of 1.40 102 m/s at an angle of 30.0° above the horizontal from a 122 m high cliff (take ground level to be y = 0 m). (a) Determine the initial total mechanical energy (in J) of the system of the projectile and the earth. (b) If when the projectile is at its maximum height of y = 326 m, it is traveling 99.2 m/s, determine the amount of work (in J) that has been done on the projectile by air resistance. (c) What is the speed (in m/s) of the projectile immediately before it hits the ground, if air resistance does one and a half times as much work on the projectile when it is going down as it did when it was going up?

a. 637744.8 J b. -167076.84 J c. 87.11 m/s

(a) What is the final velocity, in m/s, of a hoop that rolls without slipping down a 5.00 m high hill, starting from rest? (b) What would be the final velocity, in m/s, if a disk of the same mass and radius as the hoop rolled down the hill?

a. 7 m/s b. 8.08 m/s

A spring that obeys Hooke's law has a spring force constant of 266 N/m. This spring is then stretched by 28.4 cm. (a) What is the magnitude of the force required to stretch the spring by this distance?

a. 75.54 N b. 10.727

You have a light spring which obeys Hooke's law. This spring stretches 2.96 cm vertically when a 2.30 kg object is suspended from it. Determine the following. (a) the force constant of the spring (in N/m) (b) the distance (in cm) the spring stretches if you replace the 2.30 kg object with a 1.15 kg object (c) the amount of work (in J) an external agent must do to stretch the spring 8.10 cm from its unstretched position

a. 761.47 N/m b. 1.48 cm c. 2.5 J

Sally and Sam are in a spaceship that comes to within 13,000 km of the asteroid Ceres. Determine the force Sally experiences, in N, due to the presence of the asteroid. The mass of the asteroid is 8.7 1020 kg and the mass of Sally is 63 kg. For calculation purposes, assume the two objects to be point masses.

0.02163 N

A box slides from rest down a frictionless ramp inclined at 39.0° with respect to the horizontal and is stopped at the bottom of the ramp by a spring with a spring constant of k = 3.00 104 N/m. If the box has a mass of 12.0 kg and slides 3.00 m from the point of release to the point where it comes to rest against the spring, determine the compression (in m) of the spring when the box comes to rest.

0.122 m

As shown in the figure below, a box of mass m = 5.20 kg is sliding across a horizontal frictionless surface with an initial speed vi = 3.30 m/s when it encounters a spring of constant k = 2550 N/m. The box comes momentarily to rest after compressing the spring some amount xc. Determine the final compression xc (in m) of the spring.

0.15 m

What is the wavelength (in m) of the waves you create in a swimming pool if you splash your hand at a rate of 4.00 Hz and the waves propagate at 0.600 m/s?

0.15 m

A 4.00 gram bullet is fired from a rifle at a horizontal speed of 200 m/s. If the rifle has a weight of 35.0 N and is initially motionless, determine the recoil speed of the rifle.

0.224 m/s

A man holding a rock sits on a sled that is sliding across a frozen lake (negligible friction) with a speed of 0.480 m/s. The total mass of the sled, man, and rock is 93.5 kg. The mass of the rock is 0.300 kg and the man can throw it with a speed of 16.5 m/s. Both speeds are relative to the ground. Determine the speed of the sled (in m/s) if the man throws the rock forward (i.e., in the direction the sled is moving). Determine the speed of the sled (in m/s) if the man throws the rock directly backward.

0.428 m/s ; 0.535 m/s

When a diver gets into a tuck position by pulling in her arms and legs, she increases her angular speed. Before she goes into the tuck position, her angular velocity is 5.5 rad/s, and she has a moment of inertia of 1.9 kg · m2. Once she gets into the tuck position, her angular speed is 19.9 rad/s. Determine her moment of inertia, in kg · m2, when she is in the tuck position. Assume the net torque on her is zero.

0.525 kgm^2

Consider a 92.0 kg ice skater who is spinning on the ice. What is the moment of inertia of the skater, if the skater is approximated to be a solid cylinder that has a 0.140 m radius and is rotating about the center axis of the cylinder.

0.9016 kgm^2

A car with a mass of 980 kg is initially traveling east toward an intersection with a speed of vc = 21.5 m/s and a 1500 kg pickup is traveling north toward the same intersection. The car and truck collide at the intersection and stick together. After the collision, the wreckage (car and truck) moves off in a direction of 40.0° above the x-axis. Determine the initial speed of the truck and the final speed of the wreckage in meters per second. initial speed of the truck final speed of the wreckage

11.79 m/s ; 11.09 m/s

A branch of a tree grows out from the trunk at an angle of 27.5° above the horizontal. Two children hang by their hands from the branch of the tree. The first child has a mass of 48.0 kg and hangs 1.15 m from the tree trunk, as measured along the length of the branch. The second child, with a mass of 35.5 kg, hangs 2.10 m from the tree trunk, also measured along the branch. Determine the magnitude (in N · m) of the net torque exerted on the branch by the children, about an axis located where the branch joins the tree trunk and is perpendicular to the plane formed by the branch and the trunk.

1127.88 Nm

Modern roller coasters have vertical loops like the one shown in the figure below. The radius of curvature is smaller at the top than on the sides so that the downward centripetal acceleration at the top will be greater than the acceleration due to gravity, keeping the passengers pressed firmly into their seats. What is the speed, in m/s, of the roller coaster at the top of the loop if the radius of curvature there is 13.0 m and the downward acceleration of the car is 1.50 g?

13.82 m/s

A mechanic changing the spark plugs in a car notes that the instruction manual calls for a torque with a magnitude of 39 N · m. If the mechanic grasps the wrench as shown in the figure below, determine the magnitude (in N) of the force she must exert on the wrench.

150.1 N

Calculate the angular momentum (in kg·m2/s) of an ice skater spinning at 6.00 rev/s given his moment of inertia is 0.450 kg·m2.

16.965 kgm^2/s

Alice is going on a picnic and is aware that it will be easier to carry the picnic basket if it balances at the center where the handle is attached. She has placed a 1.95-kg container of potato salad at one end and a 0.675-kg package of hot dogs at the other end of a 52.0-cm long basket. Determine where she should place a 1.95-kg container of lemonade so that the basket balances at its center.

17 cm from center, towards the hot dogs

Suppose you start an antique car by exerting a force of 210 N on its crank for 0.275 s. What angular momentum is given to the engine, in kg · m2/s, if the handle of the crank is 0.300 m from the pivot and the force is exerted to create maximum torque the entire time?

17.325 kgm^2/s

A meter stick has a mass of 0.30 kg and balances at its center. When a small chain is suspended from one end, the balance point moves 19.0 cm toward the end with the chain. Determine the mass of the chain.

180.2 g

Radio waves transmitted through space at 3.00 ✕ 108 m/s by the Voyager spacecraft have a wavelength of 0.124 m. What is their frequency (in Hz)?

2.42e9 Hz

During a circus act, an elderly performer thrills the crowd by catching a cannon ball shot at him. The cannon ball has a mass of 49.0 kg and its horizontal component of velocity is 9.00 m/s just before the 65.0 kg performer catches it. If the performer is initially motionless on nearly frictionless roller skates, what is his speed immediately after catching the cannon ball?

2.87 m/s

Several children are on a sled pulled by a four-wheeler across a level snow-covered field. The sled is moving at a constant speed of 9.35 m/s, and the tow rope (parallel to the ground) makes an angle of 35.0°, with respect to the velocity of the sled (see the figure below). If the tension in the rope is 35.0 N, determine the work done (in J) on the sled by the tension in the rope in 11.0 s.

2948.74 J

A sound wave traveling in air has a frequency f and wavelength 𝜆. A second sound wave traveling in air has wavelength 𝜆/2. What is the frequency of the second sound wave?

2f

The specialty of an athlete on the women's track team is the pole vault. She has a mass of 50 kg and her approach speed is 8 m/s. When she is directly above the bar, her speed is 1.5 m/s. Neglecting air resistance and any energy absorbed by the pole, determine the amount(in m) she has raised herself as she crosses the bar.

3.15 m

A gardener is using a tool as shown in the figure to pull weeds. You will notice that the tool is designed with a built-in pivot point about which the torques are applied. If the gardener applies a 1.93 N · m torque (about the pivot point) in order to pull a weed, determine the resistive force (in N) the weed exerts on the weed puller.

32.167 N

Two children playing on a frictionless garden gate invent a new game called "gate". The idea is that they will get on opposite sides of the gate and each push such that the gate does not move. If they both push horizontally and perpendicular to the gate and one child pushes with a force of 160 N at a distance of 0.790 m from the hinges, determine the force the second child must exert in order to keep the gate from moving if she pushes at a distance of 0.390 m from the hinges.

324.1 N

Air temperature in a desert can reach 58.0°C (about 136°F). What is the speed of sound (in m/s) in air at that temperature?

365.8 m/s

Two ice skaters stand facing each other at rest on a frozen pond. They push off against one another and the 48 kg skater acquires a speed of 0.65 m/s. If the other skater acquires a speed of 0.84 m/s, what is her mass in kilograms?

37.143 kg

The center fielder for the school's baseball team throws a 0.150-kg baseball towards home plate at a speed of 30.0 m/s and an initial angle of 40.0°. What is the kinetic energy of the baseball at the highest point of its trajectory?

39.606 J

A cross-country skier slides horizontally along the snow and comes to rest after sliding a distance of 27 m. If the coefficient of kinetic friction between her skis and the snow is 𝜇k = 0.040, determine her speed at the start of the slide.

4.6 m/s

A 25.0 kg child is riding a playground merry-go-round. If the child is 3.00 m from the center of the merry-go-round and has a constant tangential speed of 7.00 m/s. What is the magnitude of the net centripetal force that is necessary to keep her on the merry-go-round at this radius?

408.3 N

A man-made satellite orbits the earth in a circular orbit that has a radius of 22000 km. The mass of the Earth is 5.97e+24 kg. What is the tangential speed of the satellite?

4254.4 m/s

In the diagram, disk 1 has a moment of inertia of 3.8 kg · m2 and is rotating in the counterclockwise direction with an angular velocity of 6.9 rad/s about a frictionless rod passing through its center. A second disk rotating clockwise with an angular velocity of 9.7 rad/s falls from above onto disk 1. The two then rotate as one in the clockwise direction with an angular velocity of 2.8 rad/s. Determine the moment of inertia, in kg · m2, of disk 2.

5.34 kgm^2

Consider a system of a cliff diver and the earth. The gravitational potential energy of the system decreases by 23,000 J as the diver drops to the water from a height of 42.0 m. Determine her weight in newtons.

547.62 N

How many times a minute does a boat bob up and down on ocean waves that have a wavelength of 45.6 m and a propagation speed of 5.28 m/s? (Note: The answer may not be a whole number.)

6.95 times

(a) What is the average useful power output (in W) of a person who does 5.00 ✕ 106 J of useful work in 8.80 h? (b) Working at this rate, how long (in s) will it take this person to lift 2500 kg of bricks 1.30 m to a platform? (Work done to lift his body can be omitted because it is not considered useful output here.)

a. 157.83 W b. 201.8 s

The two rigid objects shown in the figure below have the same mass, radius, and angular speed. If the same braking torque is applied to each, which takes longer to stop?

Hoop takes longer to stop

a) What is the effect on the period of a pendulum if you double its length?

The period is increased by a factor of Sqrt 2

Imagine two circular plates; one is solid and the other has a hole cut out of the center. Both plates have the same radius, same thickness, and same mass. The same force F is applied tangential to the edge of each plate in such a way that the plates rotate about an axis passing through the center and perpendicular to the surface of the plates. Which one of the following statements is true regarding the angular acceleration? - The plate with the hole will have the greater angular acceleration. - Both plates will rotate with the same angular acceleration. - The solid plate will have the greater angular acceleration. Which of the following statements helps to explain the question asked above? (Select all that apply.) - Angular acceleration is directly proportional to the moment of inertia. - The plate with the hole has its mass distributed further out from the axis of rotation, which will increase its moment of inertia. - Angular acceleration is inversely proportional to the moment of inertia. - Both plates will be subjected to the same torque. - Because both plates have the same mass, they will have the same moment of inertia.

a. - The solid plate will have the greater angular acceleration. b. - The plate with the hole has its mass distributed further out from the axis of rotation, which will increase its moment of inertia. - Angular acceleration is inversely proportional to the moment of inertia. - Both plates will be subjected to the same torque.

A 0.40-kg mass is attached to a spring with a force constant of k = 187 N/m, and the mass-spring system is set into oscillation with an amplitude of A = 1.7 cm. Determine the following. (a) mechanical energy of the system (b) maximum speed of the oscillating mass (c) magnitude of the maximum acceleration of the oscillating mass

a. 0.027 J b. 0.368 m/s c. 7.95 m/s^2

A baseball has a mass of 0.15 kg and radius 3.7 cm. In a baseball game, a pitcher throws the ball with a substantial spin so that it moves with an angular speed of 42 rad/s and a linear speed of 35 m/s. Assuming the baseball to be a uniform solid sphere, determine the rotational and translational kinetic energies of the ball in joules. KErotational= KEtranslational=

a. 0.0724 J b. 91.875 J

A 0.35-kg mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a compressed position. The record of time is started when the oscillating mass passes through the equilibrium position and the position of the mass at any time is shown in the drawing.Determine the following. (a) amplitude A of the motion (b) angular frequency 𝜔 (c) spring constant k (d) speed of the object at t=2.0s (e) magnitude of the object's acceleration at t=2.0s

a. 0.1 m b. 0.785 rad/s c. 0.216 N/m d. 0 m/s e. 0.062 m/s^2

A transverse wave is traveling through a canal. If the distance between two successive crests is 3.37 m and four crests of the wave pass a buoy along the direction of travel every 21.1 s, determine the following. (a) frequency of the wave (b) speed at which the wave is traveling through the canal

a. 0.1896 Hz b. 0.6389 m/s

A 0.28 kg mass is attached to a light spring with a force constant of 33.9 N/m and set into oscillation on a horizontal frictionless surface. If the spring is stretched 5.0 cm and released from rest, determine the following. (a) maximum speed of the oscillating mass (b) speed of the oscillating mass when the spring is compressed 1.5 cm (c) speed of the oscillating mass as it passes the point 1.5 cm from the equilibrium position (d) value of x at which the speed of the oscillating mass is equal to one-half the maximum value

a. 0.55 m/s b. 0.525 m/s c. 0.525 m/s d. 0.0433 m

A phonograph record accelerates from rest to 34.0 rpm in 4.03 s. (a) What is its angular acceleration in rad/s2? (b)How many revolutions does it go through in the process?

a. 0.883 rad/s^2 b. 1.14 rev

A solid sphere is released from the top of a ramp that is at a height h1 = 2.25 m. It rolls down the ramp without slipping. The bottom of the ramp is at a height of h2 = 1.76 m above the floor. The edge of the ramp is a short horizontal section from which the ball leaves to land on the floor. The diameter of the ball is 0.13 m. (a) Through what horizontal distance d, in meters, does the ball travel before landing? (b) How many revolutions does the ball make during its fall?

a. 1.54 m b. 3.77 rev

A man does 4,470 J of work in the process of pushing his 2.40 103 kg truck from rest to a speed of v, over a distance of 28.0 m. Neglecting friction between truck and road, determine the following. (a) the speed v (in m/s) (b) the horizontal force exerted on the truck (in N)

a. 1.93 m/s b. 159.643 N

The figure shows an overhead view of a 2.10 kg plastic rod of length 1.20 m on a table. One end of the rod is attached to the table, and the rod is free to pivot about this point without friction. A disk of mass 58.0 g slides toward the opposite end of the rod with an initial velocity of 31.0 m/s. The disk strikes the rod and sticks to it. After the collision, the rod rotates about the pivot point. (a) What is the angular velocity, in rad/s, of the two after the collision? (b) What is the kinetic energy, in joules, before and after the collision?

a. 1.98 rad/s b. KEi= 27.87 J KEf= 2.14 J

At the presentation ceremony, a championship bowler is presented a 1.74-kg trophy which he holds at arm's length, a distance of 0.655 m from his shoulder joint. (a) Determine the torque (in N · m) the trophy exerts about the shoulder joint when his arm is horizontal. (Enter the magnitude only.) (b) Determine the torque (in N · m) the trophy exerts about the shoulder joint when his arm is at an angle of 37.0° below the horizontal. (Enter the magnitude only.)

a. 11.17 Nm b. 8.92 Nm

A child bounces in a harness suspended from a door frame by three elastic bands. (a) If each elastic band stretches 0.240 m while supporting a 8.35-kg child at rest, what is the force constant for each elastic band? Assume that each spring supports 1/3 of the child's weight. (b) What is the time for one complete bounce of this child? (c) What is the child's maximum velocity if the amplitude of her bounce is 0.240 m?

a. 113.65 N/m b. 0.983 s c. 1.534 m/s

At t = 0, the instantaneous position of two pulses moving along a taut string with a speed v = 2.62 cm/s are as shown in the diagram below. Each unit on the horizontal axis is 2.0 cm and each unit on the vertical axis is 6.0 cm. (a) At what location will the resultant of the two pulses have minimum amplitude? (b) At what time will the resultant of the two pulses have minimum amplitude? (c) What is the value of this minimum amplitude?

a. 14 cm b. 3.82 s c. 6 cm