bài tập vật lý 1 sư phạm

An electron in a cathode-ray tube accelerates from rest with a constant acceleration of 5,33.. Find b the magnitude of the acceleration of the objects, c the tension in the string, and

TRƯỜNG ĐẠI HỌC SƯ PHẠM

KHOA VẬT LÝ

BÀI TẬP VẬT LÝ 1 CLC

(CƠ & NHIỆT)

DÙNG CHO SINH VIÊN KHỐI CLC

ĐẠI HỌC BÁCH KHOA

LƯU HÀNH NỘI BỘ

Đà Nẵng, 2017

1.1 You run 100 m in 12 s, then turn around and jog 50m back toward the starting point

in 30s Calculate your average speed and your average velocity for the total trip

Đáp số: tốc độ trung bình: 3,57m/s ; vận tốc trung bình: 1,19m/s

1.2 Two train 75 km apart approach each other on parallel tracks, each moving at

15km/h A bird flies back and forth between the trains at 20km/h until the trains pass each other How far does the bird fly?

Đáp số: t = 2,5h ; s = 50km

1.3 Upon graduation, a student throws his cap upward with in initial speed of 14,7m/s

Given that its acceleration is 9,8m/s2 downward (we neglect air resistance)

a) How long does it take to reach its highest point?

b) What is the distance to the highest point?

c) What is the total time the cap is in the air?

Đáp số: a) t 1 = 1,5s ; b) s = 11,0m; c) t = 3s

1.4 On a highway at night you see a stalled vehicle and brake your car to stop with an

acceleration of magnitude 5m/s2 (deceleration) What is the car’s stopping distance if its initial speed is

a) 15 m/s (about 54 km/h); b) 30 m/s

Đáp số: a) s = 22,5m ; b) 90m

1.5 An electron in a cathode-ray tube accelerates from rest with a constant acceleration

of 5,33 1012 m/s2 for 0,15 s The electron then drifts with constant velocity for 0,2 s Finally, it comes to rest with an acceleration of -0,67 1043 m/s2 How far does the

electron travel ?

Đáp số: s = 0,232m

1.6 While standing in an elevator, you see a screw fall from the ceiling The ceiling is

3m above the floor

a) If the elevator is moving upward with a constant speed of 2,2m/s, how long does it take for the screw to hit the floor?

b) How long is the screw in the air if the elevator starts from rest when the screw falls, and moves upward with a constant acceleration of a = 4m/s2 ?

Đáp số: a) t = 0,78s; b) t’ = 0,66s

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CHAPTER 3: MOTION IN TWO DIMENSIONS

2.1 A plane is to fly due north The speed of the plane relative to the air is 200km/h and

the wind is blowing from west to east at 90km/h

a) In which direction should the plane head?

b) How fast does the plane travel relative to the ground

Đáp số: a) Máy bay phải bay theo hướng Tây-Bắc ; b) v pg = 179km/h

2.2 A helicopter drops a supply package to soldiers in a jungle clearing When the

package is dropped, the helicopter is 100m above the clearing and flying at 25 m/s at an angle 0 = 36,90 above the horizontal Choose the origin to be directly below the

helicopter when the package is dropped

a) Where does the package land?

b) If the helicopter flies at constant velocity, where is it when the package lands

c) Find the time t for the package to reach its greatest height h; find h

Đáp số: a) d = 126m ; b) Tọa độ x = 126m, y = 194,5m ; c) t = 1,53s ; h = 111,5m 2.3 A policeman chases a thief across city rooftops They are both running at 5 m/s

When they come to a gap between buildings that is 4m wide and has a drop of 3m The thief, having studied a little physics, leaps at 5 m/s and at 450 and clears the gap easily The policeman did not study physics and he leaps at 5

m/s horizontally

a) Does the policeman clear the gap?

b) By how much does the thief clear the gap?

Đáp số: a) viên cảnh sát vừa chuyển động ngang vừa

rơi, thời gian rơi 3m hết 0,782s, chuyển động

ngang sau 0,782s đạt 3,91m Do đó anh ta không

vượt qua được

b)Tên trộm nhảy lên nên có thời gian 1,22s; chuyển động ngang đạt 4,31m; dài hơn khoảng trống 0,31m)

2.4 A hunter with a gun intends to shoot a monkey hanging from a branch The hunter

aims directly at the monkey’s heart The monkey, hearing the gun discharge lets go of the branch and drops out the tree Assume that the reaction time of the monkey and air

resistance are negligible Find the distance between the monkey’s heart and the point that the bullet hits the monkey

3m

4m

Đáp số: Viên đạn chạm đúng vào vị trí tim con khỉ vì con khỉ và viên đạn cùng rơi tự

do một khoảng như nhau

2.5 A stone is thrown from the top of a building at an angle of 300 to the horizontal and with an initial speed of 20m/s If the height of the building is 45m,

a) How long is the stone “in flight”?

b) What is the speed of the stone just before it strikes the ground?

Đáp số: a) t = 4,22s ; v = 35,9m/s

2.6 It has been said that in his youth George Washington threw a silver dollar across a

river Assuming that the river was 75m wider,

a) What minimum initial speed was necessary to get the coin across the river?

b) How long was the coin in flight?

Đáp số: a) v m = 27,1m/s ; b) t = 3,91s

2.7 An astronaut on a strange planet finds that she can jump a maximum horizontal

distance of 30m if her initial speed is 9m/s What is the acceleration of gravity on the planet?

Đáp số: g = 2,7m/s 2

2.8 The orbit of the moon about the earth is approximately circular, with mean radius of

3,84.108m It takes 27,3 days for the moon to complete one revolution about the earth Find: a) the mean orbital speed of the moon; b) its centripetal acceleration

Đáp số: a) v = 1,02.10 3

m/s ; b) a = 2,72.10 -3 m/s 2

2.9 A worker on the roof of a house drops his hammer, which slides down the roof at a

constant speed of 4m/s The roof makes an angle of 300 with the horizontal, and its lowest point is 10m from the ground What is the horizontal distance traveled by the hammer after it leaves the roof of the house and before it hits the ground?

Đáp số: s = 4,26m

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CHAPTER 4 THE LAWS OF MOTION

4.1 The gravitational force exerted on a baseball is −𝐹𝑔𝑗̂ A pitcher throws the ball with velocity 𝑣𝑖̂ by uniformly accelerating it along a straight horizontal line for a time interval of ∆𝑡 = 𝑡 − 0 = 𝑡 (a) Starting from rest, through what distance does the ball move before its release? (b) What force does the pitcher exert on the ball?

Answer: (a) ∆𝑥 =1

2𝑣𝑡

(b) The magnitude of the force is 𝐹 = 𝑚√(𝑣

𝑡)2+ 𝑔2 and its direction is 𝜃 = 𝑡𝑎𝑛−1( 𝑚𝑔

𝑚𝑣/𝑡) = 𝑡𝑎𝑛−1(𝑔𝑡

𝑣)

4.2 Two forces, 𝐹⃗⃗⃗ = (−6.00𝑖̂ − 4.00𝑗̂) N and 𝐹1 ⃗⃗⃗ = (−3.00𝑖̂ + 7.00𝑗̂) N, act on a 2particle of mass 2.00 kg that is initially at rest at coordinates (−2.00 m, +4.00 m) (a)

What are the components of the particle’s velocity at t = 10.0 s? (b) In what direction

is the particle moving at t = 10.0 s? (c) What displacement does the particle undergo during the first 10.0 s? (d) What are the coordinates of the particle at t = 10.0 s?

Answer: (a) 𝑣⃗⃗⃗ = (−45.0𝑖̂ + 15.0𝑗̂) (m/s) 𝑓

(b) The direction of motion makes angle θ with the x direction, where θ =

−18.4°+ 180°= 162° from the + x axis

(c) ∆𝑟 = −225𝑖̂ + 75.0𝑗̂ (m)

(d) 𝑟⃗⃗⃗ = (−227𝑖̂ + 79.0𝑗̂) (m) 𝑓

4.3 Three forces acting on an object are given by 𝐹⃗⃗⃗ = (−2.00𝑖̂ + 2.00𝑗̂) N, 𝐹1 ⃗⃗⃗ =2(5.00𝑖̂ − 3.00𝑗̂) N, and 𝐹⃗⃗⃗ = (−45.0𝑖̂) N The object experiences an acceleration of 3magnitude 3.75 m/s2 (a) What is the direction of the acceleration? (b) What is the mass of the object? (c) If the object is initially at rest, what is its speed after 10.0 s? (d) What are the velocity components of the object after 10.0 s?

Answer: (a) 𝑎 is at 181° counter-clockwise from the x axis

(b) m = 11.2 kg

(c) v = 37.5 m/s

(d) 𝑣⃗⃗⃗ = (−37.5𝑖̂ − 0.893𝑗̂) (m/s) 𝑓

4.4 Two objects are connected by a light string that passes over a frictionless pulley as

shown in Fig 1 Assume the incline is frictionless and take m1 = 2.00 kg, m2 =

6.00 kg, and θ = 55.0° (a) Draw free-body diagrams of both

objects Find (b) the magnitude of the acceleration of the

objects, (c) the tension in the string, and (d) the speed of each

object 2.00 s after it is released from rest

Answer: (a)

(b) a = 3.57 m/s2

(c) T = 26.7 N

(d) v f = 7.14 m/s

4.5 A 3.00-kg block starts from rest at the top of a 30.0° incline and slides a distance of

2.00 m down the incline in 1.50 s Find (a) the magnitude of the acceleration of the block, (b) the friction force acting on the block, (c) the coefficient of kinetic friction between block and plane, and (d) the speed of the block after it has slid 2.00 m

traveling in a circular path at uniform speed as shown

in Fig 2 The length of the arc ABC is 235 m, and the

car completes the turn in 36.0 s (a) What is the

acceleration when the car is at B located at an angle

of 35.0o? Express your answer in terms of the unit

vectors 𝑖̂ and 𝑗̂ Determine (b) the car’s average speed

Fig 1

Fig 2

and (c) its average acceleration during the 36.0-s interval

Answer: (a) 𝑎⃗⃗⃗⃗ = (−0.233𝑖̂ + 0.163𝑗̂) (m/s𝑟 2)

(b) v = 6.53 m/s

(c) 𝑎 𝑎𝑣𝑔 = (−0.181𝑖̂ + 0.181𝑗̂) (m/s2)

5.2 Why is the following situation impossible? The object of

mass m = 4.00 kg in Fig 3 is attached to a vertical rod by two

strings of length, ℓ = 2.00 m The strings are attached to the rod

at points a distance d = 3.00 m apart The object rotates in a

horizontal circle at a constant speed of v = 3.00 m/s, and the

strings remain taut The rod rotates along with the object so that

the strings do not wrap onto the rod What If? Could this

situation be possible on another planet?

Answer: By calculation, T b = –5.7 N, where T b is the force

exerted by the lower string on the object This means that the

lower string pushes rather than pulls! The situation is impossible because the speed of the object is too small, requiring that the lower string act like a rod and push rather than like a string and pull

To answer the What if?, we obtain T b = 41.2 N − 2.67g For this situation to be

possible, T b must be > 0, or g < 7.72 m/s2 This is certainly the case on the surface of the Moon and on Mars

5.3 One end of a cord is fixed and a small 0.500-kg object is

attached to the other end, where it swings in a section of a

vertical circle of radius 2.00 m as shown in Fig 4 When θ =

20.0o, the speed of the object is 8.00 m/s At this instant, find

(a) the tension in the string, (b) the tangential and radial

components of acceleration, and (c) the total acceleration (d)

Is your answer changed if the object is swinging down toward

its lowest point instead of swinging up? (e) Explain your

answer to part (d)

Answer: (a) T = 20.6 N

(b) a r = 32 0 m/s2 inward

a t = 3.35 m/s2 downward tangent to the circle

(c) a = 32.2 m/s2 inward and below the cord at 5.98°

Fig 3

Fig 4

(d) No change

(e) If the object is swinging down it is gaining speed, and if the object is swinging up it is losing speed, but the forces are the same Therefore, its acceleration

is regardless of the direction of swing

5.4 A person stands on a scale in an elevator As the elevator starts, the scale has a

constant reading of 591 N As the elevator later stops, the scale reading is 391 N Assuming the magnitude of the acceleration is the same during starting and stopping, determine (a) the weight of the person, (b) the person’s mass, and (c) the acceleration

of the elevator

Answer: (a) F g = 491 N

(b) m = 50.1 kg

(c) a = 2.00 m/s2

5.5 A window washer pulls a rubber squeegee down a very tall vertical window The

squeegee has mass 160 g and is mounted on the end of a light rod The coefficient of kinetic friction between the squeegee and the dry glass is 0.900 The window washer presses it against the window with a force having a horizontal component of 4.00 N (a) If she pulls the squeegee down the window at constant velocity, what vertical force component must she exert? (b) The window washer increases the downward force component by 25.0%, while all other forces remain the same Find the squeegee’s acceleration in this situation (c) The squeegee is moved into a wet portion of the

window, where its motion is resisted by a fluid drag force R proportional to its velocity according to R = −20.0v, where R is in newtons and v is in meters per second Find the

terminal velocity that the squeegee approaches, assuming the window washer exerts the same force described in part (b)

Answer: (a) P y = −2.03 N = 2.03 N down

(b) a y = −3.18 m/s2 = 3.18 m/s2 down

(c) v T = = 0.205 m/s down

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CHAPTER 6: ENERGY AND SYSTEM

6.1 A block of mass 𝑚 = 2.50 kg is pushed a distance 𝑑 = 2.20 m along a frictionless,

horizontal table by a constant applied force of magnitude 𝐹 = 16.0 N directed at an angle

𝜃 = 25.08 below the horizontal as shown in Figure P6.1 Determine the work done on the block by

(a) the applied force,

(b) the normal force exerted by the table,

(c) the gravitational force,

(d) the net force on the block

Ans (a) 31.9 J; (b),(c) 0; (d) 31.9 J

Figure P6.1

6.2 The force acting on a particle varies as

shown in Figure P6.2 Find the work done by

the force on the particle as it moves

Ans 50.0 J

6.4 In an electron microscope, there is an electron gun that contains two charged metallic

plates 2.80 cm apart An electric force accelerates each electron in the beam from rest to 9.60% of the speed of light over this distance For an electron passing between the plates

in the electron gun, determine

(a) the kinetic energy of the electron as it leaves the electron gun,

(b) the magnitude of the constant electric force acting on the electron,

(c) the acceleration of the electron,

(d) the time interval the electron spends between the plates

Ans (a) 3.78 × 10−16 𝐽; (b) 1.35 × 10−14 𝑁; (c) 1.48 × 1016 𝑚/𝑠2; (d) 1.94 × 10−9 𝑠

6.5 A single conservative force acts on a 5.00-kg particle within a system due to its

interaction with the rest of the system The equation 𝐹𝑥 = 2𝑥 + 4 describes the force, where 𝐹𝑥 is in newtons and 𝑥 is in meters As the particle moves along the 𝑥 axis from

𝑥 = 1.00 m to 𝑥 = 5.00 m, calculate

(a) the work done by this force on the particle,

(b) the change in the potential energy of the system,

(c) the kinetic energy the particle has at 𝑥 = 5.00 m if its speed is 3.00 m/s at 𝑥 =1.00 m

Ans (a) 40.0 𝐽; (b) −40.0 𝐽; (c) 62.5 𝐽

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CHAPTER 7: CONSERVATION OF ENERGY

7.1 A block of mass 0.250 kg is placed on top of a light, vertical spring of force constant

5 000 N/m and pushed downward so that the spring is compressed by 0.100 m After the block is released from rest, it travels upward and then leaves the spring To what maximum height above the point of release does it rise?

Ans 10.2 m

7.2 A 20.0-kg cannonball is fired from a cannon with muzzle speed of 1 000 m/s at an

angle of 37.0° with the horizontal A second ball is fired at an angle of 90.0° Use the isolated system model to find

(a) the maximum height reached by each ball,

(b) the total mechanical energy of the ball–Earth system at the maximum height for each ball Let 𝑦 = 0 at the cannon

Ans (a) 𝑏𝑎𝑙𝑙 1: 1.85 × 104 𝑚, 𝑏𝑎𝑙𝑙 2: 5.10 × 104 𝑚; (b) 1.00 × 107 𝐽

7.3 A bead slides without friction around a

loop-the-loop (Fig P7.1) The bead is released from rest at a

height ℎ = 3.50𝑅

(a) What is its speed at point A?

(b) How large is the normal force on the bead at

point A if its mass is 5.00 g?

7.4 A block of mass m 5 5.00 kg is released

from point A and slides on the frictionless track

shown in Figure P7.2 Determine

(a) the block’s speed at points B and C

(b) the net work done by the gravitational

force on the block as it moves from point A to

point C

Ans (a) 𝑣𝐵 = 5.94 𝑚/𝑠, 𝑣𝐶 = 7.67 𝑚/𝑠;

7.5 A crate of mass 10.0 kg is pulled up a rough incline with an initial speed of 1.50 m/s

The pulling force is 100 N parallel to the incline, which makes an angle of 20.0° with the horizontal The coefficient of kinetic friction is 0.400, and the crate is pulled 5.00 m (a) How much work is done by the gravitational force on the crate?

(b) Determine the increase in internal energy of the crate–incline system owing to friction

(c) How much work is done by the 100-N force on the crate?

(d) What is the change in kinetic energy of the crate?

(e) What is the speed of the crate after being pulled 5.00 m?

Ans (a) −168 𝐽; (b) 184 𝐽; (c) 500 𝐽; (d) 148 𝐽; (e) 5.65 𝑚/𝑠

7.6 A 40.0-kg box initially at rest is pushed 5.00 m along a rough, horizontal floor with a

constant applied horizontal force of 130 N The coefficient of friction between box and floor is 0.300 Find

(a) the work done by the applied force,

(b) the increase in internal energy in the box–floor system as a result of friction,

(c) the work done by the normal force,

(d) the work done by the gravitational force,

(e) the change in kinetic energy of the box,

(f) the final speed of the box

Ans (a) 650 𝐽; (b) 588 𝐽; (c),(d) 0; (e) 62.0 𝐽; (f) 1.76 m/s

7.7 The coefficient of friction between the block of

mass 𝑚1 = 3.00 kg and the surface in Figure P7.3

is 𝜇𝑘 = 0.400 The system starts from rest What is

the speed of the ball of mass 𝑚2 = 5.00 kg when it

has fallen a distance ℎ = 1.50 m?

Ans 3.74 m/s

Figure P7.3

7.8 The electric motor of a model train accelerates the train from rest to 0.620 m/s in

21.0 ms The total mass of the train is 875 g

(a) Find the minimum power delivered to the train by electrical transmission from the metal rails during the acceleration

(b) Why is it the minimum power?

Ans (a) 8.01 𝑊

7.9 An older-model car accelerates from 0 to speed 𝑣 in a time interval of Δ𝑡 A newer,

more powerful sports car accelerates from 0 to 2𝑣 in the same time period Assuming the energy coming from the engine appears only as kinetic energy of the cars, compare the power of the two cars

Ans The power of the sports car is four times that of the older-model car

7.10 A roller-coaster car shown in Figure P7.4 is released from rest from a height ℎ and then moves freely with negligible friction The roller-coaster track includes a circular loop of radius R in a vertical plane