1. Derive an expression for acceleration and Tension and then Determine the tension of the rope and acceleration of the system below. m, =12kg m, = 27kg Hs = 0.31 Hx =0.26 %3D 280 62°

1 This loudspeaker has a weight of 70 Newtons and is being held up by two cables. Both cables are at an angle of 25 degrees. This means that they both have the same tension, T. What is the vertical component of the tension in each cable? Ty %D unit What is the horizontal component of the tension in each cable? Tx unit What is the total tension in each cable? T = unit %3D

3. A block of mass m = 5.9 kg is pulled up a 0 = 21° incline as in the figure below with a force of magnitude F = 37 N. (Hint: remember to measure all angles from +x axis.) y a. Draw a free body diagram showing all the forces. NORml Fte F Mass = 5.9k 0-21° F-37N there b. Determine the x and y components of all the forces. X Components of Force f = 37 N Y comporents of Force F=0N X componnt of normal force=ON * Componis of weight=-5.9x 9.8x Sin 210=70. FJN Y Comperents of weight=5.9a 9.8 x Casal. - 53.98 Y Compenents of normal force=mglos H%53.98, c. Write equations summing all the x components and all the y components. F-mg Sm@= mxa 37-20.72= 5.9x a 2.7l6 = Comporunts) Normal force - mg les 0: 05 53.98-53.98-0o d. Find the acceleration of the block if the incline is frictionless. (Give the magnitude of the acceleration. Find the acceleration of the block if the coefficient of kinetic friction between the block and incline is 0.12. (Give the magnitude of the acceleration.) е. 3

2. A 25 kg crate hangs in equilibrium from two strings made from the same material and knotted together as shown. 30° 45° Determine the tension in each of the cables. Note that the tension will be different in each cable.