Provide full solutions for each problem below. Remember that a full solution will include a sign convention, appropriate FBD(s), calculations with units carried through and three or four sentences explaining your thought process (ie.what you are doing and why) as you solve each problem. Each problem is worth 15 marks.

1. A storefront sign (m= 30 kg) is supported by two cables. Cable A makes an angle of 30 degrees wrt (with respect to) horizontal. Cable B makes an angle of 50 degrees wrt vertical. Determine the tension in each cable.

1. An Atwood machine consists of a 500 g mass and a 200 g mass connected by a light string over a massless pulley. Determine the acceleration of the system and the tension in the string.

1. A wooden crate (m= 45 kg) is sliding on a long inclined plane which makes an angle of 40 degrees wrt horizontal. The coefficient of kinetic friction between the crate and inclined plane is 0.65. Determine the acceleration of the crate. Assuming the crate begins from rest, how long will it take to travel 3 m down the incline?