The drawing shows two identical systems of objects; each consists of the same th
ID: 2190398 • Letter: T
Question
The drawing shows two identical systems of objects; each consists of the same three small balls connected by massless rods. In both systems the axis is perpendicular to the page, but it is located at a different place, as shown. The same force of magnitude F is applied to the same ball in each system (see the drawing). The masses of the balls are m1 = 9.6 kg, m2 = 6.9 kg, and m3 = 7.9 kg. The magnitude of the force is F = 435 N. (a) For each of the two systems, determine the moment of inertia about the given axis of rotation. (b) Calculate the torque (magnitude and direction) acting on each system. (c) Both systems start from rest, and the direction of the force moves with the system and always points along the 4.00-m rod. What is the angular velocity of each system after 5.93 s?Explanation / Answer
The drawing shows an A-shaped ladder. Both sides of the ladder are equal in length. This ladder is standing on a frictionless horizontal surface, and only the crossbar (which has a negligible mass) of the “A” keeps the ladder from collapsing. The ladder is uniform and has a mass of 20.3 kg. Determine the tension in the crossbar of the ladder.
The weight of the ladder is (20.3 kg)(9.81 m/s²) = 199 N, and for the purposes of this problem, we can treat it as a single force acting downward at the apex of the ladder.
I looked at this for a while before deciding that the apex itself would actually be the most efficient place to sum the moments. Let's see how it works out.
We'll denote the crossbar tension as Fc. Note that half of the ladder's weight is reacted vertically at each point where it touches the ground. Our sign convention will be clockwise = positive, counterclockwise = negative.
M = (199/2 N)(4.00sin15º m) (Fc)(3.00cos15º m) = 0
Solving for Fc, we get 35.5 N.
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