1. A crate possessing a mass of 2.00 x 10exp3 kg is supported by a vertical cable attached to a horizontal boom crane. The angle between the boom and the connecting cable is 57 degrees. Calculate (A) the weight of the crate, (B) the magnitude of the boom thrust, and (C) the magnitude of the tension in the cable.
2. Suppose the angle between the boom and the cable in problem 1 is reduced to 19 degrees. Calculate (A) the weight of the crate, (B) the magnitude of the boom thrust, and (C) the magnitude of the tension in the cable.
3. European boom cranes are designed so that the boom resides at a 45-degree angle to the horizontal. Based on this information, calculate (A) the weight of the same crate referred to in problems 1 and 2, and (B) the magnitude of the boom thrust, and (C) the magnitude of the tension in the cable assuming that the angle between the cable and the boom remain at 45 degrees while the crate is supported by this crane.
4. A pair of filthy, smelly, and otherwise thoroughly objectionable and repulsive gym footwear is suspended from an originally horizontal overhead telephone wire spanning the distance between two adjacent telephone poles. One end of the wire is inclined 17 degrees from the horizontal whereas the other end of the wire is inclined 39 degrees from the horizontal. Assuming the mass of the footwear is 3.73 kg, calculate (A) the weight of the footwear and (B) the respective magnitudes of the tension along each section of the wire.
Answers
1. (A) 1.96 x 10exp4 N
(B) 1.27 x 10exp4 N
(C) 2.34 x 10exp4 N
2. (A) 1.96 x 10exp4 N
(B) 5.69 x 10exp4 N
(C) 6.02 x 10exp4 N
3. (A) 1.96 x 10exp4 N
(B) 1.39 x 10exp4 N
(C) 1.39 x 10exp4 N
4. (A) 36.6 N
(B) 34.3 N (17 degree inclined wire)
(C) 42.2 N (39 degree inclined wire)
