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Physics 2A, Prof Beyermann, July 27, 2013 Test Form A
Physics 2A Final Examination
• You have 3 hours to answer 39 multiple-choice questions on the exam. There are 26
conceptual questions worth 1 point each and 13 quantitative questions worth 2 points each.
• This is a closed-book exam, no books or notes are allowed. You may use a calculator,
provided no information is programmed into it. If you need scratch paper, it will be provided
in the front of the room.
• Your answers for the multiple-choice questions must be recorded on a F289-PAR-L Scantron
with a number 2 pencil. Remember to put your name, student ID number and the test
form version letter (lower right-hand corner of this page) on the Scantron.
Physics 2A – Final Exam Formula Sheet
(s represents position along a generic axis, and vectors are denoted with arrows above the symbols)
1. Velocity and Acceleration
v (^) s =
d s dt
a^ s =^
d v (^) s dt
s (^) f = si + v (^) s i
f
∫ dt^ v^ fs =^ vis +^ a^ s
i
f
∫ dt
ω = d^ θ dt
α = d^ ω dt
2. Kinematic Equations (constant acceleration)
Translational v fs = vis + a s Δ t s f = si + 12 ( vis + v fs )Δ t
s (^) f = si + vis Δ t + 12 a (^) s (Δ t ) 2 v (^) fs^2 = vis^2 + 2 a (^) s ( s (^) f − si )
Rotational^ ω^ f =^ ω^ i +^ αΔ t^ θ^ f =^ θ^ i +^12 (^ ω^ i +^ ω^ f )Δ t
θ (^) f = θ (^) i + ω (^) i Δ t + 12 α(Δ t ) 2 ω (^) f^2 = ω (^) i^2 + 2 α( θ (^) f −θ (^) i )
3. Vectors
A = Ax i ˆ + Ay ˆ j Ax = A cos θ Ay = A sin θ A = Ax^2 + Ay^2 tan θ =
Ay Ax A ⋅
B = AB cos θ = Ax Bx + Ay By
A ×
B = AB sin θ
4. Motion on an incline plane a s = ± g sin θ
5. Relative motion r = r^ !+
R v = v^ ! +
V
6. Newton’s Laws of Motion 2 nd^
Fnet =
Fi i
∑ =^ m
a = d ^ p dt
, τ net = I α = dL
dt
3 rd^
FAB = −
FBA
7. Apparent Weight wapp = w 1 +
a (^) y g
8. Static Friction: f s ≤ μ s n Kinetic Friction: f k =μ k n Rolling Friction: f r =μ r n
9. Drag
D = 12 C (^) D ρ Av^2
Physics 2A, Prof Beyermann, July 27, 2013 2
10. Relation Between Rotational and Translational Quantities s = r θ , vt = r ω , at = r α
11. Uniform Circular Motion ( Fnet ) r = mvt
2 r
= mr ω 2 , ( Fnet ) t = 0 , ( Fnet ) z = 0
12. Torque
r ×
F ,
τ = rFt = r ⊥ F = rF sin φ
13. Moment of Inertia I = m n rn^2
n
14. Impulse-Momentum Theorem J s ≡ Fs
i
f
∫ ( t ) dt^ =^ Δ p^ s
15. Momentum Linear: p ≡ m v Angular:
L = r × p ,
L = rp sin φ = rmv sin φ = mrvt = I ω
16. Center of Gravity rcg = 1
M
m (^) n n
r n
17. Hooke’s Law ( Fsp ) s = − k Δ s
18. Newton’s Law of Gravity F = Gm^1 m^^2
r^2
19. Kinetic Energy Linear: K = 12 mv^2 Rotational: K rot = 12 I ω 2
20. Potential Energy Fx = − dU
dx
Elastic: U s = 12 k (Δ s ) 2
Gravitational ( y << r ): U g = mgy Gravitational ( y ~ r ): U g = − Gm^1 m^^2
r
21. Perfectly Elastic Collisions ( vi 2 = 0 ) v f 1 = m^1 −^ m^^2
m 1 + m (^) 2
vi 1 , v f 2 = 2 m^1
m 1 + m (^) 2
vi 1
22. Work W = Fs
i
f
∫ ds^ Work from a Constant Force^ W^ =^
F ⋅ Δ r
23. Work-Energy Equation
Δ E sys = Δ E mech + Δ E th + Δ E chem = W ext where Δ E mech = Δ K + Δ U , Δ E th = − W diss is the work done by dissipative
forces, and W ext is the work done by external forces.
24. Conservation Laws for an Isolated System
Conservation of energy: Δ E sys = Δ E mech + Δ E th + Δ E chem = 0
Conservation of linear momentum:
Pi =
Pf
Conservation of angular momentum:
Li =
L (^) f
25. Power P =
dE sys dt
F ⋅ v
26. Mathematics If ax^2 + bx + c = 0 then x = − b^ ±^ b^
(^2) − 4 ac 2 a
Law of Cosines: C^2 = A^2 + B^2 − 2 AB cos θ Law of Sines: sin^ ϕ
A
= sin^ φ B
27. Constants g = 9.8 m/s 2 , G = 6.67x10 -11^ Nm 2 /kg 2
Consider what happens when you jump up in the air. Which of the following is the most accurate statement? A) You are able to spring up because the earth exerts a force upward on you which is stronger than the downward force you exert on the earth. B) Since the ground is stationary, it cannot exert the upward force necessary to propel you into the air. Instead, it is the internal forces of your muscles acting on your body itself which propels the body into the air. C) 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. D) It is the upward force exerted by the ground that pushes you up, but this force can never exceed your weight.
Two bodies P and Q on a perfectly smooth horizontal surface are connected by a light cord. The mass of P is
greater than that of Q. A horizontal force F is applied to Q as shown in the figure, accelerating the bodies to the right.
The magnitude of the force exerted by the connecting cord on body P will be A) zero. B) less than F but not zero. C) greater than F. D) equal to F.
- If you jumped out of a plane, you would begin speeding up as you fall downward. Eventually, due to wind resistance, your velocity would become constant with time. After this occurs, the magnitude of the force of wind resistance is A) is much smaller than the force of gravity acting on you. B) is greater than the force of gravity acting on you. C) is slightly smaller than the force of gravity acting on you. D) equal to the force of gravity acting on you.
- Two blocks, A and B, are being pulled to the right along a horizontal surface by a horizontal 100 N pull, as shown in the figure. Both of them are moving together at a constant velocity of 2.0 m/s to the right, and both weigh the same. Which of the figures below shows a correct free-body diagram of the horizontal forces acting on upper block, A?
A)
B)
C)
D)
E)
If you were to move into outer space far from any stars or planets, A) your mass would change, but your weight would not change. B) neither your weight nor your mass would change. C) your weight would change, but your mass would not change. D) both your weight and mass would change. E) None of these is true.
A cyclist is riding up a hill having a constant slope of 30° with respect to the horizon at a constant speed (in a straight line). Which statement is true? A) The net force on the bike (due to gravity, the normal force, and friction) is zero. B) The net force on the bike (due to gravity, the normal force, and friction) is in the opposite direction of motion. C) The net force on the bike (due to gravity, the normal force, and friction) is in the direction of motion. D) None of the above statements are true.
In the figure, a given force F is applied to a rod in several different ways. In which case is the torque due to F about the pivot P greatest? A) 1 B) 2 C) 3 D) 4 E) 5
Suppose that a heavy person and a light person are balanced on a teeter-totter made of a plank of wood. Each person now moves in toward the fulcrum a distance of 25 cm. What effect will this have on the balance of the teeter-totter? A) The light person's end will go down. B) The teeter-totter will remain in balance. C) The heavy person's end will go down. D) One cannot tell whether either end will rise or fall without knowing the relative mass of the plank. E) Only if the plank has significant mass will the light person's end go down.
The figure shows two forces acting on an object. They have magnitudes F1 = 9.6 N and F2 = 3.2 N. What third
force will cause the object to be in equilibrium?
A) 6.4 N at 162° counterclockwise from F1 B) 6.4 N at 108° counterclockwise from F
C) 10 N at 162° counterclockwise from F1 D) 10 N at 108° counterclockwise from F
Three cars, Car X, Car Y, and Car Z, begin accelerating from rest, at the same time. Car X is more massive than Car Y, which is more massive than Car Z. The net force exerted on each car is identical. After 10 seconds, which car has the most amount of momentum? A) They all have the same amount of momentum. B) Car X C) Car Z D) Car Y
You are standing on a skateboard, initially at rest. A friend throws a very heavy ball toward you. You can either catch the object or deflect the object back toward your friend (such that it moves away from you with the same speed as it was originally thrown). What should you do in order to maximize your speed on the skateboard? A) catch the ball B) deflect the ball back C) Your final speed on the skateboard will be the same regardless whether you catch the ball or deflect the ball.
Consider two less-than-desirable options. In the first you are driving 30 mph and crash head-on into an identical car also going 30 mph. In the second option you are driving 30 mph and crash head-on into a stationary brick wall. In neither case does your car bounce off the thing it hits, and the collision time is the same in both cases. Which of these two situations would result in the greatest impact force? A) hitting the other car B) hitting the brick wall C) The force would be the same in both cases. D) We cannot answer this question without more information. E) None of these is true.
In the figure, determine the character of the collision. The masses of the blocks, and the velocities before and after are given. The collision is: A) characterized by an increase in kinetic energy. B) perfectly elastic. C) completely inelastic. D) partially inelastic. E) not possible because momentum is not conserved.
Joe and Bill throw identical balls vertically upward. Joe throws his ball with an initial speed of twice as high as Bill's ball. The maximum height of Joe's ball will be A) eight times that of Bill's ball. B) two times that of Bill's ball. C) equal to that of Bill's ball. D) four times that of Bill's ball. E) roughly 1.3 times that of Bill's ball.
Two cyclists, who weigh the same and have identical bicycles, ride up the same mountain, both starting at the same time. Joe rides straight up the mountain, and Bob rides up the longer road that has a lower grade. Joe gets to the top before Bob. Which statement is true? A) Ignoring friction and wind resistance, the average power exerted by Bob and Joe was the same, but Joe exerted more work in getting there. B) Ignoring friction and wind resistance, the amount of work done by Joe is equal to the amount of work done by Bob, but the average power exerted by Joe is greater than that of Bob. C) Ignoring friction and wind resistance, Bob and Joe exerted the same amount of work, and the average power of each cyclist was also the same. D) Ignoring friction and wind resistance, the amount of work done by Joe is greater than the amount of work done by Bob, and the average power exerted by Joe is greater than that of Bob.
- The figure shows a block of mass m resting on a 20° slope. The block has coefficients of friction !s = 0.55 and
!k = 0.45 with the surface. It is connected via a massless string over a massless, frictionless pulley to a hanging block of mass 2.0 kg. What is the minimum mass m that will stick and not slip?
A) 2.3 kg B) 1.4 kg C) 3.9 kg D) 3.8 kg
- A 90 g bead on a 60 cm long string is swung in a vertical circle about a point 200 cm above the floor. The tension in the string when the bead is at the very bottom of the circle is 2.2 N. A very sharp knife is suddenly inserted, as shown in the figure, to cut the string directly below the point of support. How far to the right of the center of the circle does the ball hit the floor?
A) 200 cm B) 240 cm C) 160 cm D) 190 cm
Spaceman Speff orbits planet X with his spaceship. To remain in orbit at 421 km from the planet's center, he should maintain a speed of 80 m/s. What is the mass of planet X? A) 4.0 × 1016 kg B) 5.1 × 1014 kg C) 5.1 × 1017 kg D) 4.0 × 1019 kg
A force of 16.88 N is applied tangentially to a wheel of radius 0.340 m and gives rise to an angular
acceleration of 1.20 rad/s^2. Calculate the rotational inertia of the wheel. A) 3.59 kg ∙ m^2 B) 5.98 kg ∙ m^2 C) 4.78 kg ∙ m^2 D) 7.17 kg ∙ m^2
A uniform 200 kg beam, 6 m long, is freely pivoted at P. The beam is supported in a horizontal position by a light strut, 5 m long, which is freely pivoted at Q and is loosely pinned to the beam at R. A load of mass is suspended from the end of the beam at S. A maximum compression of 25,000 N in the strut is permitted, due to safety. In the figure, the maximum mass M of the load is closest to: A) 1120 kg B) 1375 kg C) 1175 kg D) 665 kg E) 920 kg
An object attached to a spring is pulled across a frictionless surface. If the spring constant is 45 N/m and the
spring is stretched by 0.88 m when the object is accelerating at 1.4 m/s^2 , what is the mass of the object? A) 28 kg B) 36 kg C) 24 kg D) 31 kg
A 0.140 kg baseball is thrown with a velocity of 26.2 m/s. It is struck with an average force of 5000.0 N, which results in a velocity of 37.0 m/s in the opposite direction. How long were the bat and ball in contact? A) 1.26 × 10 -^2 s B) 1.77 × 10 -^3 s C) 3.02 × 10 -^2 s D) 4.25 × 10 -^3 s
A 1200 kg cannon fires a 100.0 kg cannonball at 35 m/s. What is the recoil velocity of the cannon? Assume that frictional forces are negligible and the cannon is fired horizontally. A) 3.5 m/s B) 3.2 m/s C) 2.9 m/s D) 35 m/s
A traveler pulls on a suitcase strap at an angle 36° above the horizontal. If 908 J of work are done by the strap while moving the suitcase a horizontal distance of 15 m, what is the tension in the strap? A) 92 N B) 85 N C) 75 N D) 61 N
