TA: Tomoyuki Nakayama
Wednesday, March 30, 2011
PHY 2048: Physic 1, Discussion Section 1243H
Quiz 8 (Homework Set #10)
Name:
UFID:
Formula sheets are not allowed. Do not store equations in your calculator. You have to solve
problems on your own; memorizing final algebraic expressions from homework assignments and
just plugging numbers into them will not give you full credit. Leave all your work.
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In the figure below right, a 50.0 kg sphere is supported on a frictionless plane inclined at angle θ =
45.0° from the horizontal. Angle φ is 20.0°.
a) What is the tension in the cable?
The ball is in static equilibrium. Hence the net
torque acting on the ball is zero. We choose our
rotational axis at the contact point between the
ball and slope. The balance of torques equation
yields
-TcosφR + MgsinθR = 0
⇒ T = Mgsinθ/cosφ = 369 N
b) What is the normal force on the sphere from the slope?
Since the ball is in equilibrium, the net force exerted on the ball is zero. The balance of forces
equation in the horizontal direction leads to
Tcos(θ-φ) – Nsinθ = 0 ⇒ N = Tcos(θ-φ)/ sinθ= 473 N