Problem Set 11 - Physics - Syracuse University
Problem Set 11 - Physics - Syracuse University
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