A cigarettes dispenser requires a south African five-rand (R5) coin with a mass of 9.5 g to dispense one cigarette with a mass of 0.2 g. The design of such a cigarette dispenser is based on a helical spring, of negligible mass, which is found to extend 0.1 mm under a mass of 0.2 g. The spring can support a total mass of a coin. As the customer place money on the dispenser, the spring and coin system displace vertically through 4 mm and release. 1.1. Provide a schematic representation of the mass and spring system.  1.2. Calculate the frequency of natural vibration of the dispenser.  1.3. Determine the velocity of the coin when it is 2 mm below its resting position.

100KN A force of 100 KN is applied on a column as shown. The column is made from two materials. [The top one is a functionally graded material with a linearly varying modulus and densities. Its length is 2 meter. The density and elastic modulus of the top material at point A are 2700 А kg m3 and 72 Gpa, respectively. The density and modulus of kg the top material at point B are 3000 and 100 Gpa. The m 3 В kg bottom material is made from steel (density =7800 and m2 modulus=200GPA). The length of the bottom material is 1m. The cross-sections of both materials comprising the column are cylindrical with a diameter of 0.5 m. C ID (oijj + bị = 0) and considering the weight and the applied force determine: Using equilibrium while The stress distribution in both members

Determine the tension developed in the cable AC required to support the traffic light Express your answer to three significant figures and include the appropriate units. HA ? FAC = Value Units Submit Request Answer Part C Figure 1 of 1 Determine the tension developed in the cable AD required to support the traffic light Express your answer to three significant figures and include the appropriate units. 6 m ? HA 3 m FAD = Value Units 4 m 4 m Submit Request Answer 3 m 4 m 6 m 4 m 3 m y Provide Feedback

From rest a balloon begins to rise. the Balloon experiences a lift due to a buoyant force of 8000 N. 1. Total massof the balloon is 600kg. Find Acceleration. 2. The balloon rises a distance of 10m and loses a mass of 50 kg after a weight is thrown off. Find the acceleration of the balloon after this weight loss 3. Find the initial velocity of the mass in the vertical direction at the timeof the jump. 4. After falling 10 m, find the mass' final velocity as it comesinto contact with the ground. 5.What is the total time the mass takes to hit the ground? 6. Find the heightof the balloon when the mass hits the ground 7. The mass lands 3 m from the baloon, find the horizontal velocity required to land 3m from the balloon. 8. Since the balloon exeperiences equal forces when the mass is thrown off, what is the horizontal velocity the baloon experiences during this act and how far does the balloon travel when the mass comes into contact with the ground?