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.
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determine the velocity of the coin when it is 2 mm below its resting position
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- A. A motorcycle and rider have a combined mass of 350kg. The wheels each have a mass of 20kg, diameter of 500mm and radius of gyration of 200mm. The rider accelerates uniformly from 5m/s to 25m/s over a distance of 100m, whilst climbing a hill of slope 1 in 20. The average resistance to motion, including drag, is 105 N. 1. Determine the total work done as the motorcycle ascends the incline. 2. Calculate the amount of power developed during the climb. B. At another point in its journey, the motorcycle and rider travel at 80 km/h around a left-hand bend of radius 30m. Calculate: 1. The angular velocity of each of the wheels. 2. The moment of inertia of each wheel. 3. The magnitude and effect of the gyroscopic torque produced on the bike.A proposal is made to use a giant spring in the bottom of an elevator shaft as a means of safely "catching" a falling elevator car. The car freefalls until it hits a spring, which is then compressed until the car stops. The car's loaded weight is 20.0 kN. The elevator will service 20 floors. Distance between floors is 4 m. The deceleration rate of the car should not exceed 10 g's as it is being stopped. (a) determine the requirements for the spring constant and the amount the spring will compress in order to catch the falling car in the worst-case scenario. (b) what do you think about this proposal? Is it practical?An Olympic lifter (m = 103kg) is holding a lift with a mass of 350 kg. The bar exerts a purely vertical force that is equally distributed between both hands. Each arm has a mass of 9 kg, are 0.8m long and form a 40° angle with the horizontal. The CoM for each arm is 0.5 m from hand. Assuming the lifter is facing us in the diagram below, his right deltoid inserts 14cm from the shoulder at an angle of 13° counter-clockwise from the humerus. Find the force right deltoid
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- Consider the system formed by three ideal springs, a rigid rod of negligible mass and a body of mass M, as illustrated in the figure. The two springs attached to the ceiling are identical and have spring constant K1 = 2 kg/s2 and natural length L1 = 10 cm, while the third has spring constant K2 = 3 kg/s2 and natural length L2 = 20 cm. Assume that the mass M and the rod oscillate only along the vertical x-axis and that the gravitational acceleration is uniform with magnitude g=10 m/s2. What is the mass oscillation period? Choose the closest value.The photo shown was theset-up of the chocolateexperiment you haveconducted before. What mechanical property wastested? Can you relate thisconcept to the suspensionbridges? How?Under some circumstances, when two parallel springswith constants k1 and k2 support a single mass, theeffective spring constant of the system is given byk 4k1k2/(k1 + k2). A mass weighing 20 pounds stretchesone spring 6 inches and another spring 2 inches. Thesprings are first attached to a common rigid supportand then to a metal plate. As the figure illustrates(see image), the mass is attached to the center of the plate in the distributiondouble spring. Determine the constant of theeffective spring for this system. find the equationof motion if the mass is initially released fromequilibrium position with downward speed of2 ft/sec.
- A block of mass M1 resting on an inclined plane is connected by a string and pulleys to another block of mass M2 as shown in Fig. Find the tension in the string and acceleration of the blocks. Assume the coefficient of friction between the blocks M1 and the plane to be 0.2. M1=1500N , M2=1000N . Angle of inclined glane = 45 degreesA light, plastic sphere with mass m = 9.00 g and density r = 4.00 kg/m3 is suspended in air by thread of negligible mass. (a) What is the tension T in the thread if the air is at 5.00C and p = 1.00 atm? The molar mass of air is 28.8 g>mol. (b) How much does the tension in the thread change if the temperature of the gas is increased to 35.0C? Ignore the change in volume of the plastic sphere when the temperature is changed.Let’s look at a simplified model of a car that’s dropped onto the ground. Model the suspension as a single linear spring and the rest of the vehicle as a single lumped mass. The car is dropped from a height of h1 = 0.9m. What is the maximum mass m for which the suspension does not bottom out? Assume a maximal allowable suspension travel of 10 cm and a spring constant of k = 2.4x10^6 N/m.