physics 1a03 mid-term 2 version 1
TRANSCRIPT
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Name _________________________________
Student Number _________________________________
PHYSICS 1A03 Mid-Term 2 Version 1 Dr. Kari Dalnoki-Veress, Fraser Evans,
Dr. An-Chang Shi DAY CLASS DURATION OF MID-TERM EXAMINATION: 1.5 Hours MCMASTER UNIVERSITY, March 8, 2018 THIS EXAMINATION PAPER INCLUDES 20 MULTIPLE CHOICE QUESTIONS AND 11 PAGES. YOU ARE RESPONSIBLE FOR ENSURING THAT YOUR COPY OF THE PAPER IS COMPLETE. BRING ANY DISCREPANCY TO THE ATTENTION OF YOUR INVIGILATOR. No books, notes, or other aids are permitted.
β’ Mark the version number of this exam on the scantron sheet (1 or 2, see above) β’ If you do not have a 9 digit student number, please put zero's in front of your number i.e. 00xxxxxxx. β’ You must be prepared to show your student card to the exam invigilators. β’ Circle the best answer on this exam paper AND on the computer-readable scan sheet. β’ There is only one correct answer for each question, no penalty for guessing a wrong answer. β’ Return this paper with your answer sheet. β’ A formula sheet is included with this exam paper (Last Page) as well as extra pages for scrap. These
may be removed but must be handed in with your exam. β’ By writing this examination you agree to be bound by the Senate policy of Academic Integrity. β’ All portable communication devices must be off during tests. β’ Only the McMaster standard calculator is allowed. ___________________________________________________________________
COMPUTER SCAN SHEET STUDENT INSTRUCTIONS: IT IS YOUR RESPONSIBILITY TO ENSURE THAT THE ANSWER SHEET IS PROPERLY COMPLETED. YOUR EXAMINATION RESULT DEPENDS UPON PROPER ATTENTION TO THESE INSTRUCTIONS. The scanner, which reads the sheets, senses the bubble shaded areas by their non-reflection of light. A heavy mark must be made, completely filling the circular bubble, with an HB pencil. Marks made with a pen or felt-tip marker will NOT be sensed. Erasers must be thorough or the scanner may still sense a mark. Do NOT use correction fluid on the sheets. Do NOT put any unnecessary marks or writing on the answer sheet. 1. Print your name, student number, course name, section number, instructor name, and the date in the spaces provided at the top of Side 1 (red side) of the sheet. Then you MUST sign the sheet in the space marked SIGNATURE. 2. Mark your student number in the space provided and fill in the corresponding bubble numbers underneath. 3. Mark only ONE choice from the alternatives (a, b, c, d, e) provided for each question. The question number is to the left of the bubbles. Make sure that the number of the question on the scan sheet is the same as the question number on the test paper. 4. Pay particular attention to the Marking Directions on the form.
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Make absolutely sure to fill out the bubble in the version column appropriate for your version of the mid-term exam. Q1. Einswine (m = 20 kg) is having a pushing contest with Physics Girl (m = 70 kg). Physics Girl wins and
pushes Einswine backwards into a mud puddle. Einswine is delighted! How do the magnitudes of the forces they exert on each other compare?
A. Both Einswine and Physics Girl exert zero force on each other. B. Einswine exerts a larger force. C. Physics Girl exerts a larger force. D. The magnitudes of the forces that they exert on each other are the same. E. It is impossible to tell without knowing the net force acting on the system.
Q2. A block is held by a string such that it is in contact with a massless vertical spring (as shown below). The spring rests at its natural equilibrium length. The block is then released so that it falls, compressing the spring by some distance. If we neglect air resistance, which statement below (describing the fall and subsequent spring compression) is correct?
A. The kinetic energy of the ball is always increasing. B. The kinetic energy of the ball is always decreasing. C. The gravitational potential energy decreases at the same rate that the spring potential energy increases. D. The gravitational potential energy decreases at the same rate that the kinetic energy increases. E. The gravitational potential energy decreases as the spring potential energy increases.
Q3. Ben wants to know how much energy his common household appliances are using each day (24 hours).
He uses his 1200 W microwave for 20 minutes a day. He has his single 100 W lightbulb on for 6 hours a day. He runs his 400,000 W death laser for 5 seconds a day. Which item uses the most energy per day?
A. The microwave. B. The lightbulb. C. The death laser. D. They all use the same amount of energy. E. They create power but do not use any energy.
Q4. You throw a bowling ball with a mass of 5.00 kg straight up from the ground and it reaches a maximum height of 3.00 m. How much kinetic energy does the bowling ball have when it is 2.00 m above the ground? (Assume no air resistance).
A. 24.5 J B. 49.1 J C. 73.6 J D. 98.1 J E. 147 J
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Q5. An object of mass 2m, initially at rest, explodes, breaking into two equal fragments. Which one of the following statements concerning the fragments after the explosion is most correct?
A. They fly off in opposite directions (180 degrees from each other). B. They fly off in the same direction. C. The fragments will have the same speed. D. Both A and C are correct. E. Both B and C are correct.
Q6. You have a class on the 2nd floor of a building. After class, you walk down the stairs to the 1st floor so that you can leave the building. The work done by gravity on you is�
A. β¦positive and independent of the path taken by you. B. β¦negative and independent of the path taken by you. C. β¦positive and depends on the path taken by you. D. β¦negative and depends on the path taken by you. E. β¦zero.
Q7. Einswine (m = 20.0 kg) is trapped at the bottom of a hole. Luckily, Physics Girl comes to save him! She drops a rope down the hole. Einswine grabs onto the rope and Physics Girl starts pulling him vertically upwards. The maximum tension that the rope can withstand is 220.0 N. What is the shortest time, starting from rest, in which Einswine can be lifted out of the hole if the hole is 10.0 m deep? A. 1.20 s B. 4.10 s C. 6.95 s D. 10.6 s E. 16.8 s
Q8. A block is dropped onto a vertical spring. Which net force vs. displacement graph (Fnet,y vs. y) best represents the net force on the block as a function of its distance traveled? Consider only the motion of the block from the time it is dropped until it first comes to rest. The positive direction is upwards.
0 0 0 0 0 y y y y y
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Q9. The diagram below shows 5 different positions of a cart on a roller-coaster ride. The cart rolls freely along the track. Neglecting friction and air resistance, rank the following 5 cart positions in terms of slowest to fastest speed.
A. I, II, III, IV, V B. V, IV, III, II, I C. I, II = IV, III, V D. I, III, II, IV, V E. I, III, II = IV, V
Q10. A block (m = 2.00 kg) slides to the left on a horizontal, frictionless surface. The speed of the block before it touches the spring is 10.0 m/s. When the spring has been compressed by 20.0 cm, the block is still moving to the left, but at 1.00 m/s. What is the spring constant k?
A. 250. N/m B. 750. N/m C. 1550 N/m D. 2450 N/m E. 4950 N/m
Q11. What is the normal force on the block shown? (The block has mass m and P is an applied force pushing
diagonally upwards in the direction shown).
A. mg B. mg β Pcos40Β° C. mg + Pcos40Β° D. mg β Psin40Β° E. mg + Psin40Β°
2.0 kgvk
II
I
IVIII
V
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Q12. Three blocks are in contact with each other on a frictionless, horizontal surface. A horizontal force, F = 10.0 N, is applied to block C so that all three blocks accelerate together. The mass of block A is 5.00 kg, the mass of block B is 2.00 kg, and the mass of block C is 1.00 kg. What is the magnitude of the force by block B on block A?
A. 1.00 N B. 2.50 N C. 3.75 N D. 6.25 N E. 10.0 N
Q13. A spring is stretched by a certain length and then released to return to its original length. It is then stretched by four times that same initial length. Compared to the first stretching, the second stretch requires:
A. Sixteen times as much force. B. Four times as much force. C. Twice as much force. D. The same amount of force. E. Half as much force.
Q14. A fireworks rocket (mass M) is moving at a velocity of v0. The rocket suddenly breaks into two pieces,
which fly off with different velocities. One piece has mass 2M/3 and velocity v1, while the other piece has mass M/3 and velocity v2 (as shown in the diagram). If v1 = 60.0 m/s, what is the magnitude of v0?
A. 34.1 m/s B. 42.5 m/s C. 48.2 m/s D. 54.6 m/s E. 70.0 m/s
M
2M/3
M/3
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Q15. A water balloon is thrown at your 1A03 professorβs face. During the collision, the force is not constant but is given by the graph below. The maximum force experienced by your professorβs face is 50.0 N, with an impulse of 25 N.s during the collision. How long was the water balloon in contact with his face?
A. 0.10 s B. 0.50 s C. 1.0 s D. 2.0 s E. 4.0 s
Q16. An astronaut is at rest in space outside of her spaceship. Using her jetpack, she tries to propel herself back to the ship but realizes that her jetpack is out of fuel. Instead, she decides to throw the jetpack away from the ship, hoping that it will move her towards the ship. If she throws the jetpack away from the ship at a speed of 6 m/s, what speed will the astronaut have back towards the ship? The astronautβs mass is 80 kg and the jetpackβs mass is 40 kg.
A. 1 m/s B. 2 m/s C. 3 m/s D. 6 m/s E. The astronaut wonβt move at all.
Q17. A ladder leans against a wall, as shown below. The ladder has a wheel at the bottom so that it can freely
roll back and forth as if there was no friction. However, in its current position, the ladder is stable and does not move. What direction is the force of static friction on the ladder at the point where the ladder makes contact with the wall?
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Q18. Physics girl is standing on the ground beside a hill of height H. She kicks a block of ice (mass M) along the ground with an initial speed v so that the ice block begins sliding up the hill (no friction). Assuming that energy is conserved, what is the minimum speed that she must kick the ice block with to guarantee that the block reaches the top of the hill?
A. MgH B. β(2MgH) C. β(gH) D. 2gH E. β(2gH)
Q19. A rope is suspended over a smooth (frictionless) pipe. Masses are hung from either end of the rope.
Based on the three cases (A, B, C) in the diagram below, which statement is most correct?
A. The magnitude of the tension in the rope in each of A, B, and C is the same. B. The acceleration of the system in each of A, B, and C is nonzero in magnitude. C. The acceleration of the system in each of A, B, and C is zero. D. More than 1 of the above. E. None of the above.
Q20. Two blocks of mass m1 and m2 are attached by a massless string wrapped around a frictionless pulley as
shown. Block 1 is also attached to a massless spring and sits on a ramp that is inclined at 30Β°. Block 2 is hanging. When the spring is extended by βx = 25.0 cm, the system is at rest in equilibrium. Given that m1 = 3.00 kg, m2 = 10.0 kg, and the spring constant k = 900.0 N/m, what is the force of friction between the ramp and block 1?
A. 127 N [down the ramp] B. 127 N [up the ramp] C. 142 N [down the ramp] D. 142 N [up the ramp] E. 152 N [up the ramp]
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This page is intentionally left blank for your rough work. You may remove these pages from the main exam but must return these with your exam and computer scan sheet.
blank page
This page is intentionally left blank for your rough work. You may remove these pages from the main exam but must return these with your exam and computer scan sheet.
blank page
This page is intentionally left blank for your rough work. You may remove these pages from the main exam but must return these with your exam and computer scan sheet.
Last page -- formula sheet
Formula Sheet for Physics 1A03
Constants π"#$ = 1.29kg/m3 Patm = 1.013 x 105Pa g = 9.81m/s2
Area and Volume π΄ = ππ), π΄ = 4ππ ), π΄ = 2ππ )
π =43ππ
0, π = ππ )β Other
π₯ =βπ Β± βπ) β 4ππ
2π
sin π =πππππ ππ‘π
βπ¦πππ‘πππ’π π
cosπ =ππππππππ‘βπ¦πππ‘πππ’π π
tan π =πππππ ππ‘πππππππππ‘
sin) π +cos) π = 1 Kinematics π£P = π£# + ππ‘ Ξπ₯ = π£#π‘ +
R)ππ‘)
π£P) β π£#) = 2πΞx
Ξπ₯ =(π£# + π£P)
2 π‘ Forces β οΏ½βοΏ½ = ποΏ½βοΏ½ οΏ½βοΏ½Z = βποΏ½βοΏ½ fs β€ πZπ fk = π^π Work and Energy πΎ = R
)ππ£) πa = πππ¦
π = ΞπΎ πde =R)ππ₯)
π = οΏ½βοΏ½ β Ξπ = πΉΞπ cos π = πΉgΞπ₯ + πΉhΞπ¦ πijkZ = βΞπ E = K + πa +πZ ΞπΈ = πΈP βπΈ# = πkjkmijkZ
π =ΞπΈΞπ‘ = οΏ½βοΏ½ β π£
Momentum π = ππ£ π½ = οΏ½βοΏ½"pdΞπ‘ =β³ π βπ# = βπP Waves, sound, light π¦(π₯, π‘) = π΄cos(ππ₯ Β± ππ‘) π¦(π₯, π‘) = π΄sin(ππ₯ Β± ππ‘) π = 2ππ = 2π/π π = 1 πβ π = 2π/π π = ππ = π/π π = xπ πβ
π =βπΈβπ‘ =
12ππ
)π΄)π
πk =2πΏπ ,πk =
ππ2πΏ, π = 1,2,3,βββ
πk =4πΏπ ,πk =
ππ4πΏ, π = 1,3,5,βββ
π|d"} = |π) β πR| πk = π/π πk = π/π π) sinπ} = πR sinπ#
2π = οΏ½ππk
οΏ½π +12οΏ½ πk
|π) β πR| = π sinπ = οΏ½ππ
οΏ½π +12οΏ½ π
βlow to high, phase shift of Οβ Fluids πΉa = ππ = πππ πΉ|οΏ½jh = πe#οΏ½ππ π = πΉ/π΄ βπ = π β ποΏ½ = ππβ π"|Z = πa"οΏ½ad + π"}οΏ½
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Name _________________________________
Student Number _________________________________
PHYSICS 1A03 Mid-Term 2 Version 1 Dr. Kari Dalnoki-Veress, Fraser Evans,
Dr. An-Chang Shi DAY CLASS DURATION OF MID-TERM EXAMINATION: 1.5 Hours MCMASTER UNIVERSITY, March 8, 2018 THIS EXAMINATION PAPER INCLUDES 20 MULTIPLE CHOICE QUESTIONS AND 11 PAGES. YOU ARE RESPONSIBLE FOR ENSURING THAT YOUR COPY OF THE PAPER IS COMPLETE. BRING ANY DISCREPANCY TO THE ATTENTION OF YOUR INVIGILATOR. No books, notes, or other aids are permitted.
β’ Mark the version number of this exam on the scantron sheet (1 or 2, see above) β’ If you do not have a 9 digit student number, please put zero's in front of your number i.e. 00xxxxxxx. β’ You must be prepared to show your student card to the exam invigilators. β’ Circle the best answer on this exam paper AND on the computer-readable scan sheet. β’ There is only one correct answer for each question, no penalty for guessing a wrong answer. β’ Return this paper with your answer sheet. β’ A formula sheet is included with this exam paper (Last Page) as well as extra pages for scrap. These
may be removed but must be handed in with your exam. β’ By writing this examination you agree to be bound by the Senate policy of Academic Integrity. β’ All portable communication devices must be off during tests. β’ Only the McMaster standard calculator is allowed. ___________________________________________________________________
COMPUTER SCAN SHEET STUDENT INSTRUCTIONS: IT IS YOUR RESPONSIBILITY TO ENSURE THAT THE ANSWER SHEET IS PROPERLY COMPLETED. YOUR EXAMINATION RESULT DEPENDS UPON PROPER ATTENTION TO THESE INSTRUCTIONS. The scanner, which reads the sheets, senses the bubble shaded areas by their non-reflection of light. A heavy mark must be made, completely filling the circular bubble, with an HB pencil. Marks made with a pen or felt-tip marker will NOT be sensed. Erasers must be thorough or the scanner may still sense a mark. Do NOT use correction fluid on the sheets. Do NOT put any unnecessary marks or writing on the answer sheet. 1. Print your name, student number, course name, section number, instructor name, and the date in the spaces provided at the top of Side 1 (red side) of the sheet. Then you MUST sign the sheet in the space marked SIGNATURE. 2. Mark your student number in the space provided and fill in the corresponding bubble numbers underneath. 3. Mark only ONE choice from the alternatives (a, b, c, d, e) provided for each question. The question number is to the left of the bubbles. Make sure that the number of the question on the scan sheet is the same as the question number on the test paper. 4. Pay particular attention to the Marking Directions on the form.
page 2 of 11
continued on next page
Make absolutely sure to fill out the bubble in the version column appropriate for your version of the mid-term exam. Q1. Einswine (m = 20 kg) is having a pushing contest with Physics Girl (m = 70 kg). Physics Girl wins and
pushes Einswine backwards into a mud puddle. Einswine is delighted! How do the magnitudes of the forces they exert on each other compare?
A. Both Einswine and Physics Girl exert zero force on each other. B. Einswine exerts a larger force. C. Physics Girl exerts a larger force. D. The magnitudes of the forces that they exert on each other are the same. E. It is impossible to tell without knowing the net force acting on the system.
Q2. A block is held by a string such that it is in contact with a massless vertical spring (as shown below). The spring rests at its natural equilibrium length. The block is then released so that it falls, compressing the spring by some distance. If we neglect air resistance, which statement below (describing the fall and subsequent spring compression) is correct?
A. The kinetic energy of the ball is always increasing. B. The kinetic energy of the ball is always decreasing. C. The gravitational potential energy decreases at the same rate that the spring potential energy increases. D. The gravitational potential energy decreases at the same rate that the kinetic energy increases. E. The gravitational potential energy decreases as the spring potential energy increases.
Q3. Ben wants to know how much energy his common household appliances are using each day (24 hours).
He uses his 1200 W microwave for 20 minutes a day. He has his single 100 W lightbulb on for 6 hours a day. He runs his 400,000 W death laser for 5 seconds a day. Which item uses the most energy per day?
A. The microwave. B. The lightbulb. C. The death laser. D. They all use the same amount of energy. E. They create power but do not use any energy.
Q4. You throw a bowling ball with a mass of 5.00 kg straight up from the ground and it reaches a maximum height of 3.00 m. How much kinetic energy does the bowling ball have when it is 2.00 m above the ground? (Assume no air resistance).
A. 24.5 J B. 49.1 J C. 73.6 J D. 98.1 J E. 147 J
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Q5. An object of mass 2m, initially at rest, explodes, breaking into two equal fragments. Which one of the following statements concerning the fragments after the explosion is most correct?
A. They fly off in opposite directions (180 degrees from each other). B. They fly off in the same direction. C. The fragments will have the same speed. D. Both A and C are correct. E. Both B and C are correct.
Q6. You have a class on the 2nd floor of a building. After class, you walk down the stairs to the 1st floor so that you can leave the building. The work done by gravity on you is�
A. β¦positive and independent of the path taken by you. B. β¦negative and independent of the path taken by you. C. β¦positive and depends on the path taken by you. D. β¦negative and depends on the path taken by you. E. β¦zero.
Q7. Einswine (m = 20.0 kg) is trapped at the bottom of a hole. Luckily, Physics Girl comes to save him! She drops a rope down the hole. Einswine grabs onto the rope and Physics Girl starts pulling him vertically upwards. The maximum tension that the rope can withstand is 220.0 N. What is the shortest time, starting from rest, in which Einswine can be lifted out of the hole if the hole is 10.0 m deep? A. 1.20 s B. 4.10 s C. 6.95 s D. 10.6 s E. 16.8 s
Q8. A block is dropped onto a vertical spring. Which net force vs. displacement graph (Fnet,y vs. y) best represents the net force on the block as a function of its distance traveled? Consider only the motion of the block from the time it is dropped until it first comes to rest. The positive direction is upwards. Answer: B
0 0 0 0 0 y y y y y
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Q9. The diagram below shows 5 different positions of a cart on a roller-coaster ride. The cart rolls freely along the track. Neglecting friction and air resistance, rank the following 5 cart positions in terms of slowest to fastest speed.
A. I, II, III, IV, V B. V, IV, III, II, I C. I, II = IV, III, V D. I, III, II, IV, V E. I, III, II = IV, V
Q10. A block (m = 2.00 kg) slides to the left on a horizontal, frictionless surface. The speed of the block before it touches the spring is 10.0 m/s. When the spring has been compressed by 20.0 cm, the block is still moving to the left, but at 1.00 m/s. What is the spring constant k?
A. 250. N/m B. 750. N/m C. 1550 N/m D. 2450 N/m E. 4950 N/m
Q11. What is the normal force on the block shown? (The block has mass m and P is an applied force pushing
diagonally upwards in the direction shown).
A. mg B. mg β Pcos40Β° C. mg + Pcos40Β° D. mg β Psin40Β° E. mg + Psin40Β°
2.0 kgvk
II
I
IVIII
V
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Q12. Three blocks are in contact with each other on a frictionless, horizontal surface. A horizontal force, F = 10.0 N, is applied to block C so that all three blocks accelerate together. The mass of block A is 5.00 kg, the mass of block B is 2.00 kg, and the mass of block C is 1.00 kg. What is the magnitude of the force by block B on block A?
A. 1.00 N B. 2.50 N C. 3.75 N D. 6.25 N E. 10.0 N
Q13. A spring is stretched by a certain length and then released to return to its original length. It is then stretched by four times that same initial length. Compared to the first stretching, the second stretch requires:
A. Sixteen times as much force. B. Four times as much force. C. Twice as much force. D. The same amount of force. E. Half as much force.
Q14. A fireworks rocket (mass M) is moving at a velocity of v0. The rocket suddenly breaks into two pieces,
which fly off with different velocities. One piece has mass 2M/3 and velocity v1, while the other piece has mass M/3 and velocity v2 (as shown in the diagram). If v1 = 60.0 m/s, what is the magnitude of v0?
A. 34.1 m/s B. 42.5 m/s C. 48.2 m/s D. 54.6 m/s E. 70.0 m/s
M
2M/3
M/3
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Q15. A water balloon is thrown at your 1A03 professorβs face. During the collision, the force is not constant but is given by the graph below. The maximum force experienced by your professorβs face is 50.0 N, with an impulse of 25 N.s during the collision. How long was the water balloon in contact with his face?
A. 0.10 s B. 0.50 s C. 1.0 s D. 2.0 s E. 4.0 s
Q16. An astronaut is at rest in space outside of her spaceship. Using her jetpack, she tries to propel herself back to the ship but realizes that her jetpack is out of fuel. Instead, she decides to throw the jetpack away from the ship, hoping that it will move her towards the ship. If she throws the jetpack away from the ship at a speed of 6 m/s, what speed will the astronaut have back towards the ship? The astronautβs mass is 80 kg and the jetpackβs mass is 40 kg.
A. 1 m/s B. 2 m/s C. 3 m/s D. 6 m/s E. The astronaut wonβt move at all.
Q17. A ladder leans against a wall, as shown below. The ladder has a wheel at the bottom so that it can freely
roll back and forth as if there was no friction. However, in its current position, the ladder is stable and does not move. What direction is the force of static friction on the ladder at the point where the ladder makes contact with the wall? Answer A
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Q18. Physics girl is standing on the ground beside a hill of height H. She kicks a block of ice (mass M) along the ground with an initial speed v so that the ice block begins sliding up the hill (no friction). Assuming that energy is conserved, what is the minimum speed that she must kick the ice block with to guarantee that the block reaches the top of the hill?
A. MgH B. β(2MgH) C. β(gH) D. 2gH E. β(2gH)
Q19. A rope is suspended over a smooth (frictionless) pipe. Masses are hung from either end of the rope.
Based on the three cases (A, B, C) in the diagram below, which statement is most correct?
A. The magnitude of the tension in the rope in each of A, B, and C is the same. B. The acceleration of the system in each of A, B, and C is nonzero in magnitude. C. The acceleration of the system in each of A, B, and C is zero. D. More than 1 of the above. E. None of the above.
Q20. Two blocks of mass m1 and m2 are attached by a massless string wrapped around a frictionless pulley as
shown. Block 1 is also attached to a massless spring and sits on a ramp that is inclined at 30Β°. Block 2 is hanging. When the spring is extended by βx = 25.0 cm, the system is at rest in equilibrium. Given that m1 = 3.00 kg, m2 = 10.0 kg, and the spring constant k = 900.0 N/m, what is the force of friction between the ramp and block 1?
A. 127 N [down the ramp] B. 127 N [up the ramp] C. 142 N [down the ramp] D. 142 N [up the ramp] E. 152 N [up the ramp]
page 8 of 11
continued on next page
This page is intentionally left blank for your rough work. You may remove these pages from the main exam but must return these with your exam and computer scan sheet.
blank page
This page is intentionally left blank for your rough work. You may remove these pages from the main exam but must return these with your exam and computer scan sheet.
blank page
This page is intentionally left blank for your rough work. You may remove these pages from the main exam but must return these with your exam and computer scan sheet.
Last page -- formula sheet
Formula Sheet for Physics 1A03
Constants π"#$ = 1.29kg/m3 Patm = 1.013 x 105Pa g = 9.81m/s2
Area and Volume π΄ = ππ), π΄ = 4ππ ), π΄ = 2ππ )
π =43ππ
0, π = ππ )β Other
π₯ =βπ Β± βπ) β 4ππ
2π
sin π =πππππ ππ‘π
βπ¦πππ‘πππ’π π
cosπ =ππππππππ‘βπ¦πππ‘πππ’π π
tan π =πππππ ππ‘πππππππππ‘
sin) π +cos) π = 1 Kinematics π£P = π£# + ππ‘ Ξπ₯ = π£#π‘ +
R)ππ‘)
π£P) β π£#) = 2πΞx
Ξπ₯ =(π£# + π£P)
2 π‘ Forces β οΏ½βοΏ½ = ποΏ½βοΏ½ οΏ½βοΏ½Z = βποΏ½βοΏ½ fs β€ πZπ fk = π^π Work and Energy πΎ = R
)ππ£) πa = πππ¦
π = ΞπΎ πde =R)ππ₯)
π = οΏ½βοΏ½ β Ξπ = πΉΞπ cos π = πΉgΞπ₯ + πΉhΞπ¦ πijkZ = βΞπ E = K + πa +πZ ΞπΈ = πΈP βπΈ# = πkjkmijkZ
π =ΞπΈΞπ‘ = οΏ½βοΏ½ β π£
Momentum π = ππ£ π½ = οΏ½βοΏ½"pdΞπ‘ =β³ π βπ# = βπP Waves, sound, light π¦(π₯, π‘) = π΄cos(ππ₯ Β± ππ‘) π¦(π₯, π‘) = π΄sin(ππ₯ Β± ππ‘) π = 2ππ = 2π/π π = 1 πβ π = 2π/π π = ππ = π/π π = xπ πβ
π =βπΈβπ‘ =
12ππ
)π΄)π
πk =2πΏπ ,πk =
ππ2πΏ, π = 1,2,3,βββ
πk =4πΏπ ,πk =
ππ4πΏ, π = 1,3,5,βββ
π|d"} = |π) β πR| πk = π/π πk = π/π π) sinπ} = πR sinπ#
2π = οΏ½ππk
οΏ½π +12οΏ½ πk
|π) β πR| = π sinπ = οΏ½ππ
οΏ½π +12οΏ½ π
βlow to high, phase shift of Οβ Fluids πΉa = ππ = πππ πΉ|οΏ½jh = πe#οΏ½ππ π = πΉ/π΄ βπ = π β ποΏ½ = ππβ π"|Z = πa"οΏ½ad + π"}οΏ½