Physics Exam 1 Ch. 1-5

An electrical motor spins at a constant 2857.0 rev/min. If the armature radius is 2.685 cm, what is the acceleration of the outer edge of the armature?

2402 m/s^2

If two nonzero vectors point in the same direction, their dot product must be zero.

False

For an object in uniform circular motion, its velocity and acceleration vectors are always perpendicular to each other at every point in the path.

True

Approximately how many times does an average human heart beat in a year?

4×10^7

Under what condition is ∣∣∣→A−→B∣∣∣=A+B?

Vectors →AA→ and →BB→ are in opposite directions.

A pilot drops a package from a plane flying horizontally at a constant speed. Neglecting air resistance, when the package hits the ground the horizontal location of the plane will

be over the package.

You swing a bat and hit a heavy box with a force of 1500 N. The force the box exerts on the bat is

exactly 1500 N whether or not the box moves.

A stalled car is being pushed up a hill at constant velocity by three people. The net force on the car is

0

A boy throws a rock with an initial velocity of 2.15m/s2.15⁢ms at 30.0°30.0° above the horizontal. If air resistance is negligible, how long does it take for the rock to reach the maximum height of its trajectory?

0.110 s

If the fastest you can safely drive is 65 mi/h, what is the longest time you can stop for dinner if you must travel 541 mi in 9.6 h total?

1.3 h

You want to swim straight across a river that is 76m76⁢m wide. You find that you can do this if you swim at an angle of θ=28°θ=28° from the upstream direction at a constant rate of 1.5m/s1.5⁢ms relative to the water. At what rate does the river flow? The angle θθ is measured from the river bank (directly upstream is θ=0 while directly across the river is θ=90°).

1.3 m/s

Bumpers on cars are not of much use in a collision. To see why, calculate the average force a bumper would have to exert if it brought a 1200-kg car (a so-called compact model) to a rest in 15 cm when the car had an initial speed of 2.0 m/s (about 4.5 mph). (Bumpers are built with springs that compress to provide a stopping force without, hopefully, denting the metal.)

1.6×10^4N

A new roller coaster contains a loop-the-loop in which the car and rider are completely upside down. If the radius of the loop is 13.2 m, with what minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top? Assume the rider is not strapped to the car.

11.4 m/s

Determine the angle between the directions of vector →A=3.00ˆi+1.00ˆj A→=3.00i^+1.00j^ and vector →B=−3.00ˆi+3.00ˆjB→=−3.00i^+3.00j^.

117 degrees

A 10,000-kg rocket blasts off from earth with a uniform upward acceleration of 2.00m/s22.00⁢ms2 and feels no air resistance. The upward thrust force its engines must provide during this acceleration is closest to

118,000 N.

An 80.0-kg object is falling and experiences a drag force due to air resistance. The magnitude of this drag force depends on its speed, v, and obeys the equation Fdrag=(12.0N⋅s/m)v+(4.00N⋅s2/m2)v2Fdrag=(12.0⁢N⋅sm)v+(4.00⁢N⋅s2/m2)v2. What is the terminal speed of this object?

12.6 m/s

The position of an object is given by x=at3−bt2+ctx=a⁢t3−b⁢t2+c⁢t, where a=4.1m/s3, b=2.2m/s2, c=1.7m/sa=4.1⁢ms3, b=2.2⁢ms2, c=1.7⁢ms, and xx and tt are in SI units. What is the instantaneous acceleration of the object when t=0.7s t=0.7⁢s?

13 m/s^2

A car accelerates from 10.0m/s10.0⁢ms to 30.0m/s30.0⁢ms at a rate of 3.00m/s23.00⁢ms2. How far does the car travel while accelerating?

133 m

A plane has an eastward heading at a speed of 156 m/s (relative to the air). A 20.0 m/s wind is blowing southward while the plane is flying. The velocity of the plane relative to the ground is

157 m/s at an angle 7.31°7.31° south of east.

The position of an object as a function of time is given by x=bt2−ctx=b⁢t2−c⁢t, where b=2.0m/s2b=2.0⁢ms2 and c=6.7m/sc=6.7⁢ms, and xx and tt are in SI units. What is the instantaneous velocity of the object when t=2.2t=2.2?

2.1 m/s

The following four forces act on a 4.00 kg object:−→F1=300Neast−→F2=700Nnorth−→F3=500Nwest−→F4=600NsouthF1→=300⁢N⁢eastF2→=700⁢N⁢northF3→=500⁢N⁢westF4→=600⁢N⁢southWhat is the acceleration of the object?

224 N in a direction 26.6°26.6° north of west

Engineers are designing a curved section of a highway. If the radius of curvature of the curve is 194 m, at what angle should the curve be banked so that a car traveling at 29.0 m/s will stay on the road without the aid of frictional forces?

23.9°

A small boat is moving at a velocity of 3.35m/s3.35⁢ms when it is accelerated by a river current perpendicular to the initial direction of motion. If the acceleration of the current is 0.750m/s^2, what will be the new velocity of the boat after 33.5s?

25.3 m/s at 82.4°82.4° from initial direction of motion

The acceleration of an object as a function of time is given by a(t)=(3.00m/s3)ta⁡(t)=(3.00⁢ms3)⁢t, where tt is in seconds. If the object has a velocity 1.00m/s1.00⁢ms at time t=1.00st=1.00⁢s, what is the displacement of the object between time t=2.00st=2.00⁢s and time t=4.00st=4.00⁢s?

27.0 m

A rock is thrown at a window that is located 18.0m18.0⁢m above the ground. The rock is thrown at an angle of 40.0°40.0° above horizontal. The rock is thrown from a height of 2.00m2.00⁢m above the ground with a speed of 30.0m/s30.0⁢ms and experiences no appreciable air resistance. If the rock strikes the window on its upward trajectory, from what horizontal distance from the window was it released?

27.3 m

Vector →A=−1.00ˆi+−2.00ˆjA→=−1.00i^+−2.00j^ and vector →B=3.00ˆi+4.00ˆjB→=3.00i^+4.00j^. What are the magnitude and direction of vector →C=3.00→A+4.00→BC→=3.00A→+4.00B→ ?

3.61 in a direction 33.7°33.7° counterclockwise from the positive x-axis

In addition to 1m=39.37in1⁢m=39.37⁢in, the following exact conversion equivalents are given: 1mile=5280ft1⁢mile=5280⁢ft, 1hour=60min1⁢hour=60⁢min, and 1min=60s1⁢min=60⁢s. If a particle has a velocity of 8.4miles per hour8.4⁢miles per hour, its velocity, in m/sms, is closest to

3.8 m/s

A ball rolls across a floor with an acceleration of 0.100m/s20.100⁢ms2 in a direction opposite to its velocity. The ball has a velocity of 4.00m/s4.00⁢ms after rolling a distance 6.00m6.00⁢m across the floor. What was the initial speed of the ball?

4.15 m/s

A 6.0 kg box slides down an inclined plane that makes an angle of 39°39° with the horizontal. If the coefficient of kinetic friction is 0.19, at what rate does the box accelerate down the slope?

4.7 m/s^2

An airplane flies between two points on the ground that are 500 km apart. The destination is directly north of the origination of the flight. The plane flies with an air speed of 120 m/s. If a constant wind blows at 10.0 m/s due west during the flight, what direction must the plane fly relative to north to arrive at the destination?

4.78°east of north

A car enters a 300-m radius horizontal curve on a rainy day when the coefficient of static friction between its tires and the road is 0.600. What is the maximum speed at which the car can travel around this curve without sliding?

42 m/s

A test rocket is fired straight up from rest with a net acceleration of 20.0m/s220.0⁢ms2. After 4.00 seconds the motor turns off, but the rocket continues to coast upward with no appreciable air resistance. What maximum elevation does the rocket reach?

487 m

A plane flies directly between two cities, A and B, which are separated by 2300 mi. From A to B, the plane flies into a 65 mi/h headwind. On the return trip from B to A, the wind velocity is unchanged. The trip from B to A takes 65 min less than the trip from A to B. What is the airspeed of the plane, assuming it is the same in both directions?

530 mi/h

The acceleration of an object as a function of time is given by a(t)=(3.00m/s3)ta⁡(t)=(3.00⁢ms3)⁢t, where tt is in seconds. If the object is at rest at time t=0.00st=0.00⁢s, what is the velocity of the object at time t=6.00st=6.00⁢s?

54.0 m/s

A rescue plane flying horizontally at 72.6m/s72.6⁢ms spots a survivor in the ocean 182m182⁢m directly below and releases an emergency kit with a parachute. Because of the shape of the parachute, it experiences insignificant horizontal air resistance. If the kit descends with a constant vertical acceleration of 5.82m/s25.82⁢ms2, how far away from the survivor will it hit the waves?

574 m

You push downward on a box at an angle 25°25° below the horizontal with a force of 750 N. If the box is on a flat horizontal surface for which the coefficient of static friction with the box is 0.76, what is the mass of the heaviest box you will be able to move?

59 kg

Estimate the number of pennies that would fit in a box one foot long by one foot wide by one foot tall.

5×10^4

You walk 53m53⁢m to the north, then turn 60° to your right and walk another 45m. Determine the direction of your displacement vector. Express your answer as an angle relative to east.

63°N of E

A block is on a frictionless horizontal table, on earth. This block accelerates at 1.9m/s21.9⁢ms2 when a 90N90⁢N horizontal force is applied to it. The block and table are then set up on the moon where the acceleration due to gravity is 1.62m/s21.62⁢ms2. What is the weight of the block on the moon?

77 N

A helicopter is flying horizontally with a speed of 444 m/s over a hill that slopes upward with a 2% grade (that is, the "rise" is 2% of the "run"). What is the component of the helicopter's velocity perpendicular to the sloping surface of the hill?

8.9 m/s

A ball is projected upward at time t=0.0s t=0.0⁢s, from a point on a roof 90 m above the ground. The ball rises, then falls and strikes the ground. The initial velocity of the ball is 36.2 m/s if air resistance is negligible. The time when the ball strikes the ground is closest to

9.4 s

An object has a position given by→r=[2.0m+(5.00m/s)t]ˆi+[3.0m−(2.00m/s2)t2]ˆjr→=[2.0⁢m+(5.00⁢ms)⁢t]⁢i^+[3.0⁢m−(2.00⁢ms2)⁢t2]⁢j^where quantities are in SI units. What is the speed of the object at time t=2.00st=2.00⁢s?

9.43 m/s

The speed of a wave pulse on a string depends on the tension, FF, in the string and the mass per unit length, μμ, of the string. Tension has SI units of kg⋅m⋅s−2kg⋅m⋅s−2 and the mass per unit length has SI units of kg⋅m−1kg⋅m−1. What combination of FF and μμ must the speed of the wave be proportional to?

F/μ

A monkey is sitting at the top of a tree 20 m above ground level. A person standing on the ground wants to feed the monkey. He uses a bow and arrow to launch the food to the monkey. If the person knows that the monkey is going to drop from the tree at the same instant that the person launches the food, how should the person aim the arrow containing the food? Air resistance is small enough to be ignored.

He should aim it at the monkey.

Suppose that a car traveling to the west (the −x−x direction) begins to slow down as it approaches a traffic light. Which statement concerning its acceleration in the x direction is correct?

Its acceleration is positive but its velocity is negative.

You are standing in a moving bus, facing forward, and you suddenly fall forward as the bus comes to an immediate stop. The force acting on you that causes you to fall forward is

No forces were acting on you to cause you to fall

A box of mass m is pulled with a constant acceleration a along a horizontal frictionless floor by a wire that makes an angle of 15°15° above the horizontal. If T is the tension in this wire, then

T> ma

A ball is thrown directly upward and experiences no air resistance. Which one of the following statements about its motion is correct?

The acceleration is downward during the entire time the ball is in the air.

If the eastward component of vector →A A→ is equal to the westward component of vector →BB→ and their northward components are equal. Which one of the following statements about these two vectors is correct?

The magnitude of vector →A A→ is equal to the magnitude of vector →BB→.

An object is moving forward with a constant velocity. Which statement about this object MUST be true?

The net force on the object is zero.

Two objects have masses m and 5m, respectively. They both are placed side by side on a frictionless inclined plane and allowed to slide down from rest.

The two objects reach the bottom of the incline at the same time.

On a horizontal frictionless floor, a worker of weight 0.900 kN pushes horizontally with a force of 0.200 kN on a box weighing 1.80 kN. As a result of this push, which statement could be true?

The worker will accelerate at 2.17m/s22.17⁢ms2 and the box will accelerate at 1.08m/s21.08⁢ms2, but in opposite directions.

Consider what happens when you jump up in the air. Which of the following is the most accurate statement?

When you push down on the earth with a force greater than your weight, the earth will push back with the same magnitude force and thus propel you into the air.

You are seated in a bus and notice that a hand strap that is hanging from the ceiling hangs away from the vertical in the backward direction. From this observation, you can conclude that

You cannot conclude anything about the direction of the velocity of the bus.

A 615 N student standing on a scale in an elevator notices that the scale reads 645 N. From this information, the student knows that the elevator must be moving

You cannot tell if it is moving upward or downward.

In order to lift a bucket of concrete, you must pull up harder on the bucket than it pulls down on you.

false

On the earth, when an astronaut throws a 0.250-kg stone vertically upward, it returns to his hand a time T later. On planet X he finds that, under the same circumstances, the stone returns to his hand in 2T. In both cases, he throws the stone with the same initial velocity and it feels negligible air resistance. The acceleration due to gravity on planet X (in terms of g) is

g/2

Two identical objects A and B fall from rest from different heights to the ground and feel no appreciable air resistance. If object B takes TWICE as long as object A to reach the ground, what is the ratio of the heights from which A and B fell?

hA/hB=1/4

Jan and Len throw identical rocks off a tall building at the same time. The ground near the building is flat. Jan throws her rock straight downward. Len throws his rock downward and outward such that the angle between the initial velocity of the rock and the horizon is 30°30°. Len throws the rock with a speed twice that of Jan's rock. If air resistance is negligible, which rock hits the ground first?

hit at same time

If an object travels at a constant speed in a circular path, the acceleration of the object is

larger in magnitude the smaller the radius of the circle.

Two particles, A and B, are in uniform circular motion about a common center. The acceleration of particle A is 8.5 times that of particle B. The period of particle B is 2.0 times the period of particle A. The ratio of the radius of the motion of particle A to that of particle B is closest to

rA/rB=2.1rA/rB=2.1

Two objects are dropped from a bridge, an interval of 1.0 s apart, and experience no appreciable air resistance. As time progresses, the DIFFERENCE in their speeds

remains constant

Suppose the force of the air drag on an object is proportional to the speed of the object and in the direction opposite the object's velocity. If you throw an object upward, the magnitude of its acceleration is greatest

right after the object is released

A string is attached to the rear-view mirror of a car. A ball is hanging at the other end of the string. The car is driving around in a circle, at a constant speed. Which of the following lists gives all of the forces directly acting on the ball?

tension and gravity

A 20-ton truck collides with a 1500-lb car and causes a lot of damage to the car. During the collision

the force of on the truck due to the collision is exactly equal to the force on the car.

The current definition of the standard second of time is based on

the frequency of radiation emitted by cesium atoms.

While an object is in projectile motion (with upward being positive) with no air resistance,

the horizontal component of its velocity remains constant and the vertical component of its acceleration is equal to −g−g.

Alice and Tom dive from an overhang into the lake below. Tom simply drops straight down from the edge, but Alice takes a running start and jumps with an initial horizontal velocity of 25 m/s. Neither person experiences any significant air resistance. Just as they reach the lake below,

the speed of Alice is larger than that of Tom.

A ball is tossed vertically upward. When it reaches its highest point (before falling back downward)

the velocity is zero, the acceleration is directed downward, and the force of gravity acting on the ball is directed downward.

Two identical stones are dropped from rest and feel no air resistance as they fall. Stone A is dropped from height h, and stone B is dropped from height 2h. If stone A takes time t to reach the ground, stone B will take time

t√2

The period of a pendulum is the time it takes the pendulum to swing back and forth once. If the only dimensional quantities that the period depends on are the acceleration of gravity, g, and the length of the pendulum, ℓ, what combination of g and ℓ must the period be proportional to? (Acceleration has SI units of m⋅s−2m⋅s−2.)

√ℓ/g