On a single, light, vertical cable that does not stretch, a crane is lifting a 1
ID: 2224712 • Letter: O
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 3.45 m/s and acceleration 1.29 m/s2. (a) How do the velocity and acceleration of the BMW compare with those of the Ferrari? Option 1: At any instant they have the same velocity and at all instants they have the same acceleration. Option 2: 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. Option 3: 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. (Please pick the right one from the three options) (b) Find the tension in the cable between the BMW and the Ferrari. _____ N (c) Find the tension in the cable above the Ferrari. ____ NExplanation / Answer
(a) The velocity and acceleration of the two cars are identical. The rigid cable makes their positions identical (except for the fixed height offset), hence x' and x'' (vel and accel) are identical. (b) Force in lower cable is: (1461 kg)(1.31 m/sec^2) + (1461 kg)(9.8 m/sec^2) = 16231 N (c) Force in upper cable is: (1207 kg)(1.31 m/sec^2) + (1207 kg)(9.8 m/sec^2) + 16231 N = 29641 N Note that this final calculation (tension in upper cable) is simply the sum of the accelerations times the sum of the masses.