(2013) A rubber cord of a Y– shaped object has a cross sectional area of 4 x 10-6 m² ? And relaxation length of 100 mm. If the arms of the catapult are 70 mm apart, calculate the: - tension in the rubber. - force required to stretch it when the rubber cord is pulled back until its length doubles.

PROBLEM 1: The uniform beam has a mass of 50 kg per meter of length. Support at A is roller and support at B is hinge. Use acceleration due to gravity = 9.81 m/s2. [1] Calculate the reaction at A. (ANSWER: 1.86 KN) [2] Calculate the horizontal reaction at B. (ANSWER: 0.00 KN) [3] Calculate the vertical reaction at B. (ANSWER: 2.84 KN)

A current problem in the U.S. Air Force is the neck/shoulder fatigue experienced by pilots. To be able to fly missions at night, the pilots wear night vision goggles, which are attached to the front of the helmet. Unfortunately, these are heavy, causing a large downward torque of the head, which must be counteracted by the neck muscles, which then fatigue. To alleviate this problem, many pilots have started attaching random lead weights to the back of the helmet. Find the appropriate weight that would best balance the head and minimize neck fatigue – You must show your free body diagram. Assumptions: a) center of gravity of goggles is 20 cm in front of neck pivot point, b) load of goggles1.0 kg mass, c) center of gravity of lead weight is 10 cm behind neck pivot point, d) load of bare helmet 3 kg mass, e) center of gravity of helmet is 2 cm in front of neck pivot, f) load of head 4.0 kg mass, and g) center of gravity of head is right at neck pivot point.  Answer: ___________________

A alank of wood is fixed to a wall using a hinge. When the angle between the plank and the wall is 45°, a spring is attached to the wood 25cm from the hinge and fixed to the wall so that it is horizontal (Diagram A). The wood is then pushed downwards until it is perpendicular to the wall (Diagram B). The force exerted by the spring, depends on its length. As the spring stretches, the force it exerts increases. A graph showing this relationship is below. 70 Diagram B 60 Diagram A spring 50 90° 20 25cm 45 90° 10 25cm hinge 10 35 15 20 25 30 Spring Length (cm) (a) Calculate the length of the spring in Diagrams A and B. (b) Calculate the torque produced by the spring on the plank of compare the values. around the hinge in 4 oth Diagrams A and B and Force (N)