On a single, light, vertical cable that does not stretch, a crane is lifting a 1

Question

On a single, light, vertical cable that does not stretch, a crane is lifting a 1,207-kg Ferrari and, below it, a 1,461-kg BMW Z8. The Ferrari is moving upward with speed 3.70 m/s and acceleration 1.50 m/s2. (a) How do the velocity and acceleration of the BMW compare with those of the Ferrari? At any instant they have the same velocity and at all instants they have the same acceleration. At any instant the BMW Z8 has a higher velocity compared to that of the Ferrari and at all instants they have the same acceleration. At any instant the BMW Z8 has a lower velocity compared to that of the Ferrari and at all instants they have the same acceleration. (b) Find the tension in the cable between the BMW and the Ferrari. N (c) Find the tension in the cable above the Ferrari. N

Explanation / Answer

Since the cable does not stretch, both cars will be accelerating at equal rates. Therefore you can calculate the total unbalanced force for the entire mass. Unbalanced Force=mass x acceleration =(1207 + 1461) x 1.13 =2668 x 1.13 =3014.84N If you then add on the weight of both cars Weight=mass x gravitational acceleration =2668 x 9.8 =26146.4N Tension = W + F =26146.4 + 3014.84 =29161.24N (This is the tension above the ferrari) To calculate the tension between the cars, calculate the unbalanced force for the bottom car Unbalanced Force=mass x acceleration =1461 x 1.13 =1650.93N Then add the weight of the bottom car Weight=mass x gravitational acceleration =1461 x 9.8 =14317.8N Tension=Weight + Unbalanced Force =14317.8 + 1650.93 =15968.73N (This is the tension between the BMW and the Ferrari

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