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Unformatted text preview: Physics 212, Homework 1
Required Problems. Chapter 1U: 37, 95, 101, 1GB. lﬂﬁ Problem 3'? u i la. Two blocks with mass ml = ﬂﬂkg and m2 = ltlﬂltg sit on frictionless inclines of St} degrees and 66 degrees respectively, as shown below. They are connected by a
string passing over a pulley with radius 0.25 In and moment of inertia I. .,. __ _ m». _ .__
lp,_,:I.:.  .___. ___ : J .. (.5. — I..—r'L./'. J (ali‘Draw a free—body diagram for each of the two blocks and the pulley.
{b} Find Pm and PH, the tensions in the two parts of the string. (c) Find the net torque acting on the pulley, and determine its moment of inertia, 1
I. lc. We assume that the length of the string stays constant, so the blocks and pulley
must all move together. This means that at any time the speed of both blocks (m
and ﬁg) and the tangential speed {wit} of the pulley. Also ﬂ‘ff : ﬂﬁlf‘ﬁo‘in the same
time interval the accelerations of both blocks and the tangential acceleration of the
pulley must be equal, a“ = efﬁng. —— i . . 5.9 2a. The balance of forces and Newton's second law (F = Ina] apply to both blocks. be
cause they show translational motion, whereas the balance of torques and r = la.
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goes through 2E] revolutions in 1 min. Find: (a) Its angular acceleration, a
(1)) its final speed, wf 1c. We assume that the acceleration is constant over the 1 min period. This will allow
us to use rotational kinematics. 2a. Rotational kinematics apply.
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301. I “if” ’ ‘ ' 1. J. 1'“ c I; Problem ID] 1a. A roll of paper has radius 7".6 cm and moment of inertia l = 2.9 X lﬂ‘akgmz.
A force of 3.2 N is exerted on the end of the roll for 1.3 s, causing the paper to
unroil (with no tearing). A constant friction torque of I11] m‘N is exerted on the
roll, which gradually brings it to a stop. Assuming that the papEr’s thickness is
negligible, calculate {a} the length of paper that unrolls during the time that the force is applied [b]: the length of paper that unrolls from the time the force ends to the time when
the roll has stopped moving lc We assume that the thickness of paper is negligible, so the moment of inertia of
the roll does not change as the paper enrolls. Now, the citI13.r effect of the entailed
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of radius 31) m and moment of inertia loos kg‘mE. The platform rotates without
friction with angular velocity 21] rad!r s. The person walks radially,»r to the edge of the platform. {a} Calculate the angular velocity when the person read‘tes the edge. (b) lCompare the rotational kinetic energies of the System of platform plus person
before and after the person's walk. 1c. We are told that the person walks radially to the edge of the platform — this means
we can assume that the act of walking does not exert a torque on the platform. So.r
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«Estes other} bah». weftads eweﬁne Problem 105 la. A cord connected at one end to a block which can slide on an inclined plane has
its other end wrapped around a cylinder resizing in a depression at the top of the
plane as shown below. Determine the speed of the block after it has traveled 1.312}
m along the plane, starting from rest. Solve the problem both (a) if there is no friction
(b) if the coefﬁcient of friction between all surfaces is p = DIES. 1c. We know that the cord is wrapped around the cylinder. This means that any time
the block travels a certain distance clown the incline, it unwraps an amount of
string of equal length. So, the distance traveled by a point on the edge of the
pulley [or R times the angular distance 9} is equal to the distance traveled by the
block. We also assume that the depression in the inclined plane is exactly the right
shape so that the string pulls the block only parallel to the incline, and pulls the pulley only tangentially to its surface. QCA ' bﬂjgﬁeﬁ Twigr5 i; ﬁg [Flur magi/1 E i.. . I. _,l. _ u Lg} l€ r1
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 Winter '08
 DEMAREE
 Physics, Angular Momentum, Moment Of Inertia, Angular Acceleration, Pulley, inertia loos kg‘mE

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