Question
A cable raises a mass of 120.0 kg with an acceleration of $1.3 \textrm{ m/s}^2$. What force of tension is in the cable?

$1330 \textrm{ N}$

Solution Video

OpenStax College Physics for AP® Courses Solution, Chapter 4, Problem 17 (Test Prep for AP® Courses) (1:42)

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Video Transcript

This is College Physics Answers with Shaun Dychko. The force of tension in the cable will be the force it exerts upwards on this mass so we’ll label that <i>Fc</i> for cable and then there’s a force downwards due to gravity which is mass times gravitational field strength <i>g</i>. The acceleration upwards is 1.3 meters per second squared and the mass is 120.0 kilograms. So the net force is the up forces which is that due to the cable minus the down forces which is that due to gravity equals mass times acceleration. I’ve written plus <i>Fg</i> on both sides here because we’re solving for the force due to the cable. So that’s <i>ma</i> plus <i>Fg</i> and then substituting <i>mg</i> in place of <i>Fg</i> and then factoring out the <i>m</i> because that’s the sleek thing to do, it’s more concise, and you have mass times acceleration plus acceleration due to gravity. So that’s 120.0 kilograms times 1.3 plus 9.8, giving us 1330 Newton. It has three significant figures here because this sum in here is 11.1 meters per second squared and this will be precise to the ones place since this number is precise to the ones place, this number has more precision but I didn’t bother writing the digits that’s our constant <i>g</i>. So this number has three significant figures which is what you have to consider when you’re multiplying by this number which has four significant figures. And so three significant figures times four significant figures will get three significant figures in our answer.