Physics help – Block, wheel, rope, radius, tension.?
“An 80 N block hangs from a 50-kg solid cylindrical wheel by means of a rope wrapped around the wheel. The wheel has a radius of 0.40 meters and starts from rest to rotate about an axis through its center and perpendicular to the page. Calculate the tension in the rope.”
Honestly I have no idea where to begin. I’m not asking someone to do this for me. Just a point to the right equations would be fantastic. Am I using torque? The answer is 53.9 N.
All problems like this must be started with free-body diagrams.
For the block, in the vertical direction,
net F = ma = (80N/9.8m/s²) · a= mg – T = 80N – T
That is, the net force accelerating the block downward is its weight – the rope tension.
For the wheel, there will be a similar eqn, but since its been decades since I’ve done a rotational moment of inertia problem, I can’t be specific. You are right, though; torque about the wheel will come into play, and you’ll probably use
τ = I·α (see citation)
where τ is the torque
and α is the angular acceleration
and I is the moment of inertia of the wheel
The tension term T that will appear in both eqns will necessarily be equal. You will be able to solve for the acceleration, and then for T.
Hope this gets you started.
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