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Unformatted text preview: Physics 1 2nd Midterm 2/28/2008 — 9:30—10:45 Your name 1. (This problem is worth 40 points) An ideal spring with force constant k is attached to the
bottom of a ramp. The ramp is inclined at an angle 0
from the horizontal. A block of mass m is placed on
the ramp in contact with the spring, then pushed down
so that the spring is compressed by a distance a’. The
mass is then released from rest. There is friction
between the ramp and the block. Spring with force constant
compresseda _ .,
distanced I (a) Suppose that the block remains at rest when it is
released from rest. For this situation, explain why the
coefficient of static friction between the block and the ramp must be greater than or equal to
some minimum value. Then calculate this minimum value. Your answer should involve no
quantities other than m, 9, k, d, and g. (It may or may not involve all of these.) For full credit,
show your work and draw a box around your answer. _ F Ema F amt F am a m “it”
Hapﬁ¥£ﬂ5ﬁl ’7 ﬂsZ—iﬁ . H INN ecu?
FM tum? Nadia:wa Law 5° 5% (5 kmth 33 (b) Now suppose that the block begins sliding up the ramp when it is released from rest. The
coefficient of kinetic friction between the block and the ramp is ,uk. In the space below, draw a freebody diagram for the block while it is moving up the ramp and in contact with the spring.
Label each force with what kind of force it is, and state which object exerts that force. Kx Wm (“£11353 i” we (continued on next page) Mi Physics 1 2nd Midterm 2/28/2008 — 9:30—10:45 Your name 1. (continued) (c) When released from rest, the block slides so far up the ramp that it loses contact with the
spring, then comes momentarily to rest at some point up the ramp. Calculate the distance along
the ramp from the initial position of the block to its highest position. Your answer should involve no quantities other than m, 6, k, d, ,uk, and g. (It may or may not involve all of these.) For
full credit, show your work and draw a box around your answer. +Usk‘ 7K4+Ug¥+ SF 0 if 0 tiitai?’ + (ﬂmmgwe  oil‘ﬁos(t%o°)> = o + mastsine +0
W 'l _t_ 2 all (Sine t/MW'CO’Q)‘MQ = Physics 1 2nd Midterm 2/28/2008 —— 9:30—10:45 Your name 2. (This problem is worth 40 points) A small bead of mass m is able to slide without
friction on a circular hoop of wire. The radius of the
hoop is R, and the plane of the hoop is vertical.
When the hoop is rotated around a vertical axis at a
certain rate, the bead rises up along the rotating
hoop until it sits at an angle (1) above the bottom of the hoop. (a) In the space below, draw a freebody diagram YEP—£3] for the bead on the rotating hoop when the bead is at the angle (1). Label each force with what kind of
force it is, and state which object exerts that force. a (3:33“) Hoop rotates around
a vertical axis Hoop, radius R Bead, mass m (b) Calculate the magnitude and direction of the force that the rotating hoop exerts on the bead when the bead is at the angle g2). Your answer should involve no quantities other than m, R, q), and
g. (It may or may not involve all of these.) For full credit, show your work and draw a box around your answer. 2"" Geo/Wilt" U’F 9 i
W) J“ iN .005+M9(>O EL) ww~5i ?oin+ L 4‘0 Swr’iiQ up Coﬂikf)’iﬂw“(0i (continued on next page) Physics 1 2nd Midterm 2/28/2008 — 9:30—10:45 Your name 2. (continued) (0) Calculate the time that it takes the hoop to complete one rotation. Your answer should
involve no quantities other than m, R, g1), and g. (It may or may not involve all of these.) For full credit, show your work and draw a box around your answer. (Hint: The radius of the circle in
which the bead moves is not equal to R.) (d) Suppose that the hoop stops rotating and is held stationary in a vertical plane. The bead is then released from rest, starting at the angle (1) shown in the figure on the previous page. Calculate the speed of the bead as it passes through the low point of the hoop, and find the
magnitude and direction of the net force on the bead as it passes through this point. Your answers should involve no quantities other than m, R, (I), and g. (They may or may not involve all
of these.) For full credit, show your work and draw a box around your answers. . . + : k, +
Kl +0? NM“: Ii direDEOA oi ’FvYQ t5 o + MWVW‘?) *0 t izw +0 Physics 1 2nd Midterm 2/28/2008 — 9:30—10:45 Your name 3. (This problem is worth 20 points)
For each question, draw a circle around the best answer. (a) A car (mass m) moves at constant speed v around a ﬂat, unbanked curve of radius R.
A free—body diagram for the car should include (i) an outward centrifugal force of magnitude mvz/R (ii) an inward centripetal force of magnitude mvz/R (iii) the force of the car’s acceleration (iv g f the above
() none f te bo (b) A ball sits at rest on a horizontal table top. The weight of the ball is equal to the magnitude of the upw ce_ ble to exerts on the ball. Why?
(i) this is a consequence of Newton’s first law
(ii) this is a consequence o ewton’s third law (iii) because we assume that the table top is perfectly rigid
(iv) two of the above three statements are correct
(v) all of the first three statements are correct (0) A roller coaster car of mass 1000 kg starts from rest. During a 50—second ride, the car reaches
a maximum speed of 18 m/s and reaches a maximum height of 40 m before returning to rest at the starting position. What are the total work done on the car and the work due to gravity on the car durini the entire ride? (l k] = 1000 joules) (ii) 162 kJ, 0 (iii) 0, 392 kJ (iv) 162 kJ, 392 k]
(v) none of the above (d) A 12—kg watermelon, initially traveling at 4.0 m/s, moves in a straight line for a distance of
10.0 m in 5.0 seconds. As it moves, it is acted on by three constant forces. During the trip, force
#1 does +24 J of work on the watermelon and force #2 does —l40 J of work on the watermelon.
Which of the following must be true? (i) t okone b 7 force #3 i s tan+20 J
(i) the work done by force #3 is equal to +J
ii) the work done b force # 1s reat than +20 I but less than +44 J
(iv) the work done by force #3 is equal to +44 J (v) the work done by force #3 is greater than +44 J END OF THE EXAM ...
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 Winter '08
 Fridluund
 Physics

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