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Problem Set 11 - Physics - Syracuse University

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<strong>Physics</strong> 2<strong>11</strong> <strong>Problem</strong> <strong>Set</strong> <strong>11</strong> Due Friday, 04/23/04<br />

Last Name:___________________________________ First Name _______________<br />

Workshop time:_____________Location (P=Phys Bldg, A=Archbold) ___________<br />

Please submit your homework on this sheet. If you need more space than is available,<br />

please attach additional sheets of paper.<br />

1. A projectile of mass m moves to the right with speed v i (see below). The projectile<br />

strikes and sticks to the end of stationary rod of mass M and length d that is pivoted<br />

about frictionless axle through its center (see below). Find the angular speed of the<br />

system right after the collision.<br />

Hints: Use angular momentum conservation. See Table 9.2 in your textbook for the<br />

moment of inertia of the rod. Don’t forget that the mass m participates in the<br />

rotation in the final state.<br />

Initial State<br />

m<br />

v i<br />

Final State<br />

d<br />

ω f =?<br />

M<br />

<strong>Physics</strong> 2<strong>11</strong> Spring 2004 <strong>Syracuse</strong> <strong>University</strong> Homework <strong>Problem</strong> <strong>Set</strong> <strong>11</strong> p.1


2. Old MacDonald had a farm, and on that farm he had a gate (see below). The gate is 3m<br />

wide and 1.8m high, with hinges attached to the top and bottom. The guy wire makes<br />

an angle of 300 with the top of the gate and is tightened by a turn buckle to a tension of<br />

200 N. The mass of the gate is 40kg.<br />

(a) Determine the horizontal force exerted on the gate by the bottom hinge.<br />

(b) Find the horizontal force exerted on the gate by the upper hinge.<br />

(c) Determine the combined vertical force exerted by both hinges.<br />

Hints: You should start by drawing extended free-body diagram for the gate. Label<br />

the forces clearly. Write down three equilibrium conditions for the gate before<br />

you try to answer any questions.<br />

Reaction forces from the hinges may have both horizontal and vertical<br />

components. Calculate torque relatively to the upper hinge as one of your<br />

equilibrium conditions (this simplifies algebra to be done).<br />

<strong>Physics</strong> 2<strong>11</strong> Spring 2004 <strong>Syracuse</strong> <strong>University</strong> Homework <strong>Problem</strong> <strong>Set</strong> <strong>11</strong> p.2


Extended free-body diagram for the gate:<br />

Equilibrium conditions:<br />

(a) Solve the equilibrium conditions for the horizontal force exerted on the gate by the<br />

bottom hinge.<br />

(b) Solve the equilibrium conditions for the horizontal force exerted on the gate by the<br />

upper hinge.<br />

(c) Solve the equilibrium conditions for the combined vertical force exerted by both<br />

hinges.<br />

<strong>Physics</strong> 2<strong>11</strong> Spring 2004 <strong>Syracuse</strong> <strong>University</strong> Homework <strong>Problem</strong> <strong>Set</strong> <strong>11</strong> p.3

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