TUTORIAL

PHY 143

PHYSICS FOR ENGINEERING 1

Prepared by: AZMI BIN MOHAMED YUSOFFATHINUL NAJIB BIN AHMAD SA’ADSITI HUSNIAH BINTI CHUMIRANMOHD NOOR BIN MOHD ALIPM LIM KIM POONSITI HAJAR BINTI KHALIDSITI NUR SARAH BINTI RIDHUWANNOR FADHLIN BINTI JAAFARNORAMALIZA BINTI MOHD NOORZUBAINUN BINTI MOHAMED ZABIDI

TUTORIAL 1

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JSG UiTMPPPHYSICAL QUANTITIES

1) Convert the speed of 60 km/h to meter per second. [16.7 m/s]

2) A room is 16 ft long, 1 ft wide and has a ceiling height of 8 ft. If 1 in. = 2.54 cm, what is the volume of the room in cubic centimeter.

[3.6246 X 106 cm3]

3) Express the following quantities in terms of S.I units.a. 3.5 cm/s. b. 2.56 g/cm3.

[0.035 ms-1, 2560 kg.m-3]

4) The sides of a rectangle are 5 inches and 10 inches respectively. Find the area of such rectangle in m2.

[3.2258 x 10-2 m2]

5) A certain brand of house paint claims coverage of 460 ft2/gal. Express this quantity ina. Square meter per literb. S.I base unit.

[11.3 m2/L, 1.13 x 104 m-1]

6) A light year is the distance light travels in one year (light speed = 2.99 x 10 8 ms-1). How many meters are there in 1 light year?

[9.43 x 1015 m]

7) Write the following numbers in scientific notationa. 9064 b. 0.0836 c. 0.00018 d. 10.2185

[9.064 X 103, 8.36 X 10-2, 1.8 X 10-4, 1.02185 X 105]

8) Find the equivalent of 22.4 liters in term of cubic meters. Write the answer in scientific notation.

[2.24 X 10-2 m3]

9) The rated engine output of Proton Persona is 118 hp. Convert this value into watt (W) [given that 1 hp = 550 ft.Ib.f/s; 3.28 ft = 1 m; 2.21 Ib.f = 9.8 N; 1 Nm = 1 J; 1 J/s = 1 W].

[8.77 x 104 W]

10) A room is 20 ft., 2 in. long and 12 ft., 5 in. wide. What is the floor area ina. Square feet. b. Square meter.

If the ceiling is 12 ft., 2(1/2) in. above the floor, what is the volume of the room in cubic meters.

[250.36 ft2, 22.795 m2, 84.82 m3]

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JSG UiTMPPTUTORIAL 2 VECTOR AND SCALAR

1) Find the direction of a vector in term ofa. Angle

b. Bearing

40 0 65 0

9 N 8 N 10 N

c. Poles

N N 10 N

40 0

W E W E 65 0

S 8 N S

25 0

60 0

8 N 12 N

2

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JSG UiTMPP2) A man walks 5 m at 37 0 north of east and then 10 m at 60 0 west of north. What is the

magnitude and direction of his net displacement? [9.27 m, -59.76 0]

3) Three vectors are specified as follows: A is 5 m at 45 0 north of east, B is 7 m at 60 0 east of south and C is 4 m at 30 0 west to south. Find the magnitude and direction of their sum.

[6.4 m at 15.4 0 south of east]

4) Find the resultants vector and its directions:a. F1=10 N, F2=5 N, θ1=25 0, θ2=30 0

b. F1=3 N, F2=7 N, θ1=15 0, θ2=40 0 c. F1=3 N, F2=6 N, F3=5 N, θ1=0 0, θ2=15 0, θ3=45 0 d. F1=10 N, F2=5 N, F3=2 N, F4=2.5 N, θ1=60 0, θ2=0 0, θ3=25.2 0, θ4=77.3 0

[14.98 N 26.67 0, 9.8 N 32.57 0, 13.34 N 22.43 0, 17.19 N 44.03 0]

5) Given vector A and B are in the x-y plane. The magnitude of A is 70 N at 90 0 and B is 120 N at 210 0 counterclockwise. Find

a. A- B b. Find the vector C such that, A-B+C=0

[166.42 N, 51.37 0, Cx = -103.9 Cy = -130]

6) A car is driven east for a distance of 30 km, then north for 40 km and then in a direction 30 0 east of north for 20 km. Determine

a. The magnitude andb. The angle of the car’s total displacement from its starting point

[69.9 km, 55.09 0]

7) Vector A has a magnitude of 8 N and makes an angle of 45 0 with positive x-axis. Vector B also has magnitude 8 N and is directed along the negative x-axis. Using graphical methods, find:

a. The vector sum A+B b. The vector difference A-B

8) Given vector F1 and F2 are in the x-y plane. F1 is 50 N at 45 0 and F2 is 100 N at 120 0

counterclockwise. Find the:a. Magnitude and b. Direction of the resultant vector.

[122.8 N, 96.8 0]

3

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JSG UiTMPPTUTORIAL 3 KINEMATIC

1) A balloon is going up at a steady velocity of 12 ms-1 at a height of 32 m above the ground when an object is dropped from it. How long does it take for the object to reach the ground?

[1.22 s]

2) A ball is thrown vertically upwards with a velocity of 30 ms-1. Calculate:a. The maximum height reach b. The time taken for it to return to the ground.

[45.87 m, 6.12 s]

3) A stone is projected at an angle of 60 0 to the horizontal with a velocity of 30 ms-1. Calculate:

a. The highest point reached b. The range c. The time taken for the flight d. The height of the stone at the instant that the path makes an angle of 30 0 with

the horizontal [34.4 m, 79.5 m, 5.3 s, 22.95 m]

4) A ball is released from rest from the top of a cliff. Taking the top of the cliff as the reference (zero) level and upwards as the positive direction, sketch the motion graphs.

5) A car decelerates uniformly from 20 ms-1 to rest in 4 s, and then reverses with uniform acceleration back to its original starting point, also in 4 s. From the velocity – time graph, calculate the average velocity.

[10 ms-1]

6) A box starts from rest and slides 9.0 m down a hill in 2.5 s. By assuming that the acceleration is constant and the path is straight, determine:

a. The acceleration of the box and b. The time taken to achieve a speed of 24 ms-1

[2.88 ms-2, 8.33 s]

4

velocity - time graph

-30

-20

-10

0

10

20

30

0 2 4 6 8 10

time t / s

velo

city

v /

ms-1

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7) A ball is thrown upward at an angle of 64 O to the horizontal and lands on the top edge of a building that is 10 m away (Figure 1). The top edge is 2.5 m above the throwing point. How fast was the ball thrown?

Figure 1.

8) The instantaneous location of a battery operated toy car moving around a floor is given by the equation:

x(t) = (1.6cm)t3 - (2.4cm)t2 + (3.2cm)t and y(t) = (2.0cm)t2 - (1.2cm)t + (3.0cm).

a. Calculate the magnitude and direction of the instantaneous velocity of the car at t = 2.0 s.

b. What is the magnitude of the car’s acceleration at t=1.0 s? [14.49 ms-1 27.98 0, 6.25 cms-2]

5

10 m

2.5 m

64 0

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JSG UiTMPPTUTORIAL 4 DYNAMICS(Newton’s Laws of motion, linear momentum & collisions)

1) A 5 kg block is pulled along a horizontal surface by a 28 N force to the right. Compute the acceleration of the block if the surface is

a. Smooth, b. Rough with a coefficient of kinetic friction of 0.23 between the block and the

surface. [5.6 ms-2, 3.34 ms-2]

2) An object is pulled with 85 N force inclined at 27 0 along a horizontal surface ABC where AB is smooth but BC is rough.

a. Compute the mass of the object if the object moves with an acceleration of 5 ms -1

along AB.b. When it enters BC the acceleration is reduced to 3 ms-1. Compute the coefficient

of kinetic friction between the object and BC. [15.14 kg, 0.20]

3) Two weights 40 N and 70 N are hung at the ends of a light inelastic string over a light and frictionless pulley. Take g = 10 ms-2.

a. Compute the acceleration of the weights and the tension in the string.b. Determine the weight needed to be added to the 70 N weight in order to increase

the downward acceleration to 5 ms-2. [2.73 ms-2 50.92 N, 50 N]

4) A 4 kg box is pulled along a horizontal surface (μk = 0.23) by a light and inelastic rope over a light and frictionless pulley by a 3 kg hanging mass. Find the acceleration of the box, a AND the tension in the rope T.

[2.91 ms-2, 20.66 N]

Compute the acceleration of the box, a AND the tension in the rope T if the 3 kg mass is placed on a smooth inclined plane with an angle of inclination of 57 0.

[2.24 ms-2, 17.99 N]

5) A 23 kg object is acted on by three forces, F1 = (6i + 3 j) N, F2 = ( 2 i – 7j) N and F = (-5i + 9 j) N. What is the acceleration of this object?

[(0.13 i + 0.22 j) ms-2]

6) a) Two identical balls B1 and B2 of masses 2 kg and 5 kg moving at 12 ms-1 and 4 ms-1 respectively along +X axis. After colliding elastically B2

moves at 6 ms-1. Compute i) Velocity of B1 after collision,

ii) The change in momentum of B1.b) If B2 moves in the opposite direction and the collision is perfectly elastic, calculate the velocities of the balls after collision.

[7 ms-1, -10 kgms-1, 5.14 ms-1, -10.86 ms-1]

7) A 20 g bullet is fired into a wooden block of mass 540 g. The velocity of the bullet just before it strikes the block is 90 ms-1. The bullet is embedded in the block. Determine the velocity of the block with the bullet in it.If the block is hung vertically, compute the change in height of the block before and after the impact.

[3.21 ms-1, 0.53 m]

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8) A car of mass 1030 kg traveling at 125 kmh-1 collided with a 4-WD moving at 80 kmh-1

from opposite direction. Both vehicles were at rest after collision. Find the mass of the 4-WD.If a small truck of mass 2600 kg slammed against the wreckage of the car and the 4- WD, and all three vehicles move together at 20 kmh-1 immediately after the impact, determine the velocity of the truck.What is the loss in kinetic energy in the second collision?

[1609 kg, 40.3 kmh-1, 81.80 kJ]

9) A horizontal force P pushes a 12 kg block up an inclined plane at an angle of inclination of 37 0. The block moves at 3 ms-2. The coefficient of kinetic friction between the plane and the block is 0.26. Compute P.

[131.2 N]

10) Two objects are connected with a light and inelastic string over a light and frictionless pulley as shown in the diagram below. If A and B have masses of 3 kg and 7 kg with the same coefficient of friction of 0.25 on inclines of 33 0 and 42 0 respectively, determine the accelerations of A and B and , the tension in the string.

[1.1 ms-2, 25.5 N]

7

A B

42 033 0

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TUTORIAL 5WORK ENERGY AND POWER

1) A worker pushes a wheelbarrow with a force of 40 N over a distance of 6 m. If a frictional force of 24 N acts on the wheelbarrow, what net work is done on the wheel barrow?

[96 J]

2) A 3 kg block slides down a frictionless plane inclined 30 0 to the horizontal. If the length of the plane’s surface is 1.50 m, calculate

a. The net force acting on the block b. The total work done on the block.

[14.715 N, 22.07 N]

3) A 6 kg block initially at rest is pulled by a constant horizontal force of 12 N. If the surface has a coefficient of kinetic friction of 0.15, by using work-energy theorem, determine the speed of the block after it has moved 3 m.

[1.78 ms-1]

4) An object slides on frictionless inclined plane of angle 30 0 from horizontal. If the initial velocity of the object is 4 ms-1 directed down the incline plane, what is the speed of the object after it slides 2 m down along the plane?

[5.97 ms-1]

5) A block of mass 3 kg initially at rest is pushed up a plane inclined 30 0 to the horizontal by a force F1 = 50 N. The coefficient of kinetic friction between the block and the plane is 0.1, and the block is pushed 1.8 m up the plane. Calculate

a. Work done by F1

b. Work done by the gravitational force c. Work done by the friction force. d. Total work done on the block.

[90 J, -26.49 J, -4.59 J, 58.92 J]

6) A package of mass 5 kg is pushed down a 1.5 m ramp with an initial velocity of 2.2 ms -1. If the ramp is inclined 12 0 below the horizontal and coefficient of the kinetic friction between the package and the ramp is 0.31, calculate,

a. Work done on the package by friction. b. Work done on the package by gravity. c. Work done on package by the normal force. d. Total work done on package. e. The final velocity of the package.

[-22.31 J, 15.30 J, 0 J, -7.01 J, 2.86 ms-1]

7) A sled is dragged along a horizontal path at a constant speed of 1.5 ms -1 by a rope that is inclined at an angle of 30 0 above the horizontal. The total weight of the sled is 470 N, the tension in the rope is 240 N. How much work is done by the rope in a time interval of 10.0 s.

[3.12 kJ]

8) A motor lifts a mass of 70 kg vertically 8 m. It takes 2 minutes to do this.

8

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JSG UiTMPPa. What is the useful work that the motor has done on the mass? b. What is the power produced by the motor? c. If the rope holding the mass now breaks while it is stationary at 8 m high,

calculate the speed of the mass as it reaches the ground. [5.49 kJ, 45.75 Js-1, 12.53 ms-1]

TUTORIAL 6CIRCULAR MOTION

1) A fan turns at a rate of 900 rpm. Finda. The angular speed of any point on one of the fan blades b. Tangential speed of the tip of a blade if the distance from the center of the tip is

200 cm.[94.25 rad/s, 188.5 m/s]

2) A wheel 25.0 cm in radius turning at 120 rpm uniformly increases its frequency to 660 rpm in 9s. Find

a. Constant angular acceleration in rad/s2

b. Tangential acceleration of a point of its rim [6.28 rad/s2, 157 cm/s2]

3) The spin-drier of a washing machine revolving at 900 rpm slows down uniformly to 300 rpm while making 50 revolutions. Find

a. Angular acceleration b. Time required to turn through these 50 revolutions

[-12.57 rad/s2, 5s]

4) A wheel of 40 cm radius rotates on a stationary axle. It is uniformly speeded up from rest to a speed of 900 rpm in a time of 20 s. Find

a. Constant angular acceleration of the wheelb. Tangential acceleration of a point on its rim

[4.71 rad/s2, 1.88 m/s2]

5) A compact disc (CD) rotates at high speed while a laser reads data encoded in a spiral pattern. The disc has radius R = 6.0 cm = 0.060 m, when data are being read, it spins at 1200 rev/min. What is the CD’s angular velocity ω in radians per seconds? How much time is required for it to rotate through 90 O? If it starts from rest and reaches full speed in 4 s, what is its average angular acceleration?

[125.66 rad/s, 12.51 X 10-3 s, 31.42 rad/s2]

6) An airplane propeller is rotating at 1900 rpm.a. Compute the propeller’s angular velocity in rad/s b. How many seconds does it take for the propeller to turn through 35 0? c. If the propeller turning at 18 rad/s, at how many rpm would it be turning? d. What is the period (in seconds) of this propeller?

[198.97 rad/s, 3.07 X 10-3 s, 171.89 rpm, 0.032 s]

7) A wheel turns a constant angular acceleration of 0.640 rad/s2.a. How much time does it take to reach an angular velocity of 8.00 rad/s, starting

from rest?b. Through how many revolutions does the wheel turn in this interval?

[12.5 s, 7.96 rev]

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JSG UiTMPP8) Emilie’s potter’s wheel rotates a constant 2.25 rad/s2 angular acceleration. After 4.00 s, the

wheel rotated through an angle of 60rad. What was the angular velocity of the wheel at the beginning of the 4.00 s interval?

[10.50 rad/s]

TUTORIAL 7STATIC EQUILIBRIUM

1) Each of the objects in Figure 1 is in equilibrium. Find the normal force FN in each case.

[400 N, 250 N, 173.21 N]

2) A 50 N box is slid straight across the floor at constant speed by a force of 25 N, as shown in Figure 2.

a. How large a friction force impedes the motion of the box?b. How large is the normal force? c. Find µk between the box and the floor.

[19.15 N, 33.93 N, 0.56]

10

200 N

30 0Ff

FW = 500 N FN

a

Ff

200 N

FW = 150 N FN

30 0

b

30 0

FW = 200 N

Ff

FN

c

Figure 1

40 0

25 N

Ff

FWFN

Figure 2

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3) Find the tension in each cord in Figure 3 if the weight of the suspended body, W = 200 N

[FA = 146.41 N FB = 179.32 N FC = 200 N, FA = 200 N FB = 282.8 N FC = 200 N]

4) Pulled by the 8 N block shown in Figure 4, the 20 N block slides to the right at constant velocity. Fine µk between the block and the table. Assume the pulley to be frictionless.

[0.4]

5) For the situation shown in Figure 5, find the values of FT1 and FT2 if the object’s weight is 600 N.

11

20 N

8 N

FT2

FT1

50 0

FT1FT2

600 N

Figure 3

A B30 0 45 0

C

W

a

A B90 045 0

C

W

b

Figure 4

Figure 5

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[FT1 = 503.4 N, FT2 = 783.2 N]

6) Figure 6 shows a uniform bar of length L and weight 40 N subjected to several external forces. Another force is needed to put the bar in static equilibrium. Find the magnitude and direction of the force and the location where the force acts on the bar. (Take point A as the reference axis)

[106.27 N 131.2º, 0.33L from A]

7) In Figure 7, AB is a uniform rod of length 6.0 m and weighs 1000 N is hinged at point A with a load of 1500 N hung from point B. the string CD which is tied at C and D keeps the system in equilibrium with the rod AB making and angle of 39 0 with the horizontal. Calculate

a. The tension in string CD b. The magnitude and direction of the reaction force exerted by the wall at A.

[TCD = 2498 N, FN = 2499 N 30.04º]

12

0.20 L 0.60 L 0.20 L

60 N

70 N

50 N 80 N

30º

A B C D

1500 N

4 m

2 m

A

B

C

D

69 0

39 0

Figure 6

Figure 7

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8) In Figure 8, a load of weight W ia attached at a point O to a uniform rod CE of length 100 cm. The rod hangs horizontally from two ropes which is fixed to a point A and B as in figure. If the weight of the load W = 1500 N and the weight of the rod is 500 N, determine :

a. The tension of each rope if the load is 35 cm from Cb. Where the load should be placed in order for the tensions of the two ropes to be

the same

[TAD = 1107.1 N TBC = 892.5 N, 30 cm]

13

W

E D O C

BA

70 cm Figure 8

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TUTORIAL 8 OSCILLATORY MOTION

1) The equation of motion for a mass at end of a particular spring is . Find the displacement, velocity and acceleration of the mass

at a. t = 0s b. t = 3s

[0.30m 0m/s -0.075m/s2, 0.021m -0.15m/s -0.053 m/s2]

2) The equation of motion of a mass is given as x = (0.20m) sin (3t). Find the velocity and acceleration of the mass when the object is +5 cm from its equilibrium position.

[0.58 m/s, -0.45 m/s2]

3) The period of oscillation of a spring and a mass system is 0.50 and the amplitude is 5 cm. Calculate

a. The speed at the equilibrium pointb. The magnitude of the acceleration at the point of maximum extension of the

spring [0.63 m/s, 7.9 m/s2]

4) Block with mass of 200 g is connected to a light horizontal spring of force constant 5 N/m and is free to oscillate on horizontal, frictionless surface.

a. If the block is displaced 5.00 cm from the equilibrium and released from rest, find the period of its motion.

b. Determine the maximum speed and the maximum acceleration of the block.c. Expressed the position, velocity and acceleration of this object as a function of

time, assuming that .[1.26 s, 0.250 m/s 1,25 m/s2, x= (0.05 m) cos 5.00t v= -(0.25 m/s) sin 5.00t,

a= -(1.25 m/s2) cos 5.00t]

5) A block whose mass m is 680 g is fastened to a spring whose spring constant k is 65 N/m. The block is pulled a distance x = 11 cm from its equilibrium position at x = 0 cm on a frictionless surface and released from rest at t = 0 s.

a. What are the angular frequency, the frequency and the period of resulting motion?

b. What is the amplitude of oscillation? c. What is the maximum speed of the oscillating block? d. What is the magnitude am of the maximum acceleration of the block? e. What is the displacement function for the spring system? f. What is the mechanical energy E? g. What are the potential energy U and kinetic energy K of the oscillator when the

block is at x = 5 cm?

14

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JSG UiTMPP[9.8 rad/s 1.6 Hz 0.63 s, 11 cm, 1.1 m/s, 11 m/s2, x= (0.11m) cos (9.8t), 0.39 J,

U=0.085 J, K= 0.31 J]

6) A particle moves to and from between two point A and B that are 24 cm apart and takes 1.2 s to moves from A to B. Find the

a. Amplitude and frequency b. Maximum velocity c. Acceleration when it is 4 cm from A

[12 cm 0.42 Hz, 0.31 m/s, 0.55 m/s2]

7) The velocity of a particle in SHM with amplitude 0.6 m is 4.2 m/s at a displacement of 0.4 m. Find

a. Its velocity at displacement of 2.0 cm b. The frequency and period of motion c. The acceleration at a displacement of 0.4 m.

[± 5.31 m/s, 1.49 Hz 0.67 s, -35.27 m/s2]

8) A particle oscillates with simple harmonic motion along the x-axis. Its position varies with

time according to the equation x= (4.00m) cos where t is in seconds.

a. Determine the amplitude, frequency and the period of the motion.b. Calculate the velocity and acceleration of the particle at any time tc. What are the position and the velocity of the particle at time t=0?

[4m 0.5 Hz 2 s, v=- (4π m/s) sin a= - (4π2 m/s2) cos ,

2.83 m, -8.89 m/s]

9) A 5 kg object on a horizontal frictionless surface is attached to a spring with spring constant 1000 N/m. The object is displaced from equilibrium 50 cm horizontally and given an initial velocity of 10 m/s back toward the equilibrium position.

a. What is the frequency of the motion b. What is the initial potential energy of the block-spring system c. What is the initial kinetic energy d. The amplitude of the oscillation

[2.25 Hz, 125 J, 250 J, 86.6 cm]

10) An oscillator consists of a block of mass 0.5 kg connected to a spring. When set the oscillation with amplitude 35 cm, the oscillator repeats its motion every 0.5 s. Find

a. The period b. The frequency c. The angular frequency d. The spring constant e. The maximum speed f. The magnitude of the maximum force on the block from the spring

[0.5 s, 2 Hz, 12.6 rad/s, 79 N/m, 4.4 m/s, 27.6 N]

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TUTORIAL 9VIBRATION AND WAVE

1) A sinusoidal wave traveling in the positive x direction is described by the following wave equation:

where x and y are in centimeters and t is in seconds.a. Find

i) The amplitudeii) The wave numberiii) The wavelengthiv) The frequencyv) The velocity of the wave

b. Calculate the displacement, y of the wave when t = 0 s and x = 2 cmc. Sketch a graph of y versus x = 0 cm to x = 10 cm at t = 0 s to represent the

motion of the wave [ 5 cm 0.39 cm-1 16 cm 15 Hz 2.4 ms-1, -3.54 cm]

2) The equation of the wave is given as:

where t is in second, y and x in cm. Find: a. The frequencyb. The wavelength of the wave

[4.78 Hz, 0.16 cm]

3) A sinusoidal wave traveling in the right direction has a frequency 10 Hz and wave velocity 20 ms-1. At t = 0 s and x = 0 m, the displacement y = 0 m. At x = 0.5 m the displacement y = -0.02 m. Find

a. Angular frequencyb. Wave lengthc. Wave numberd. Equation for the wave in S.I unit

[20π rads-1, 2 m, π m-1, y = 0.02sin(20πt-πx)]

4) A sinusoidal wave has a frequency 25.0 Hz and the wave velocity is 20.0 ms -1. If two point in the wave phase difference 30 0, what is the distance between the points?

[0.067 m]

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JSG UiTMPP5) A traveling wave moving to the right is shown in Figure 1 when t = 0 s. the frequency of the

wave is 5 cycles per second. The general formula is given by,

where y is the vertical displacement ym the amplitude, k the wave number, ω the a angular frequency and Ф the phase constant.

a. Find the amplitude, the wave number, the wavelength, the angular frequency and the phase constant

b. Give the wave equation for this wave.c. Calculate the y displacement when t = 0.0 s and x = 3.0 cm and 2.4 cm

[1.5 cm 4.0 cm 1.57 cm-1 31.4 rads-1 0, y = 1.5sin(1.57x-31.4t), -1.5 cm; -0.879 cm]

6) A type of progressive wave propagates along the x axis through a medium. the displacement, y of the particles of the medium at a distance, x from the source of the wave at time, t is represented by the equation

where x and t are measured in meter and second respectively.Find

a. The amplitude of the waveb. The wavelengthc. The frequency of the waved. The speed of the wave

[4.5 mm, 1.8 mm, 1.02 Hz, 1.84ms-1]

7) A wave source produces harmonic progressive wave. The graph below shown how the displacement y of particle of the medium varies with distance x from the source when wave propagates through the medium. the frequency of the source is 300 Hz. Determined the speed of the wave

17

-2cm 9cm

y

x

Figure 2

1.5

- 1.5

0 2.0

4.0

8.0

y (cm)

x (cm)

Figure 1

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[33ms1]

8) The motion of a wave that propagates to the right is shown In Figure 3. Figure 3(a) is a graph of displacement of the medium, y as the function of the time, t at x = 0. Figure 3(b) is a graph of displacement of the medium, y as a function of position of the wave, x at t = 0. Find the :

a. Amplitudeb. Periodc. Frequencyd. Wavelengthe. Wave velocityf. Initial phase angleg. Wave equation

[5 cm, 0.2 s, 5 Hz, 0.4 cm, 0 rad, (y=5cos(10 t-5 k))cm]

18

-5

0.4

Figure 3(a)

5

0.2

Displacement of medium, y (cm)

time, t (s)

Figure 3(b)

-5 0.4

y

x

5

0.2

Displacement of medium, y (cm)

Position of wave, x (cm)

0.6

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JSG UiTMPP

TUTORIAL 10HEAT

1) A copper container of mass 0.3 kg contains 0.45 kg of water. Container and water are initially at room temperature 20 0C. A 1 kg block of metal is heated to 100 0C placed in the water in the container. The final temperature of the system is 40 0C. Find the specific heat of the metal. (Specific heat of water = 4181 Jkg-1K-1, specific heat of cooper = 388.83 Jkg-

1K-1). [666.03 Jkg-1K-1]

2) A container with heat capacity 750 JK-1 contains 120 g of water at 280 0C. If the container are supplied 7500 J heat energy, find the final temperature if

a. No heat lost to surrounding.b. 12% heat is lost to surrounding. (Given specific heat of water = 4.2 kJkg-1K-1)

[34 0C, 33.3 0C]

3) How much oil at 200 0C must be added to 50 g of the same oil at 20 0C to heat it to 70 0C. [19.2g]

4) A cylinder container contains 80 kg of oil at temperature 30 0C. After 10 kg of the same oil are added at 80 0C, the temperature of the oil becomes 34 0C at equilibrium. Find specific heat capacity of oil if heat capacity of cylinder container is 70 kJkg-1K-1.

[2 kJkg-1K-1]

5) How many kilogram of ice at 0 0C be added to 0.6 kg of water at 100 0C in an insulated 0.1 kg copper calorimeter in order to cool the calorimeter and its contents to 30 0C. (Specific heats of water = 4.2 kJkg-1K-1, specific heats of copper = 0.39 kJkg-1K-1and the heat of fusion of ice is 335 kJ/kg)

[0.39 kg]

6) 5 g of ice at 0 0C added into a empty beaker at 28 0C. The final temperature of the system is 12 0C. Find how many heat lost to the surrounding (Given heat capacity of beaker = 0.15 kJK-1 specific heat capacity of water = 4.2 kJkg-1K-1: the heat of fusion of ice 330 kJ/kg)

[498 J]

7) What is the final temperature when 200 g of ice at –2 0C is dropped into 350 g of water at 40 0C contained in a copper calorimeter (The specific heats of water = 4.2 kJkg -1K-1, the specific heats of ice = 2.1 kJkg-1K-1, the heats capacity of copper = 0.39 kJkg -1K-1and the heat of fusion of ice is 335 kJ/kg)

[2.43 0C]

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____________________________TUTORIAL PHY 143__________________________

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8) How much heat is released when 10 g of steam at 100 0C converts to water at 50 0C (The specific heats of water = 4.2 kJkg-1K-1 and the latent heat of vaporization of water is 2255 kJ/kg)

[24641.5 J]

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