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Unformatted text preview: Homework No. 7
Calculating work CHANG 1 The 2 Kg collar slides up the smooth vertical rod from A to B under the action of the constant force F = 50 N with angle θ = 30˚ as shown. The collar is attached to a linear spring that has a spring constant k = 24 N/m and an unstretched length of 1.6 m. Find (a) the work done by the 50 N force, (b) the work done by gravity, and (c) the work done by the spring. Ans: (a) 65.0 J (b) –29.4 J (c) –7.8 J CHANG 2 A linear spring (k = 2000 N/m) with an unstretched length of 1.5 m is attached to the 50 Kg block as shown. A constant horizontal force F = 250 N is applied as shown on the block as the block moves from A to B along the ramp. The coefficient of friction on the surface is μk = 0.5 between the block and the incline. Find the work done (a) by the applied force F, (b) by gravity, (c) by friction, (d) by the spring on the block from A to B. Use cos36.87° = 0.8 and sin36.87° = 0.6. Ans: (a) –200 J (b) 294 J (c) –271 J (d) 400 J B F θ A 1.5 m 2m
0.8 m A F 1.8 m B
36.87° Power CHANG 3 A force F is applied parallel to the incline to push the 50 Kg box up the ramp as shown. The kinetic coefficient of friction is μk = 0.4 between the box and the ramp, and the angle of the incline is θ = 30˚. The box starts from rest and moves with a constant acceleration of a = 1.5 m/s2 from A to B in 8 s. (a) Find the average power by F for the motion from A to B. (b) Find the instantaneous power of F when the box reaches point B. Ans: (a) 2.94 kW (b) 5.88 kW B A F θ Y&F 6.99 **(a) (b) (c) only** Ans: (a) 358 N (b) 47.2 hp (c) 4.06 hp Note: Unit conversions: 1 hp = 746 W, and 1 km/h = 1000/3600 m/s. ...
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