Question 17: A non-uniform rod of length l has linear mass density = ox where Ao is a positive constant. The rod is pivoted at point P as shown in Figure 10. The rod is released at rest (7 is the gravitational acceleration). Find the speed of the bottom of the rod when it becomes in the vertical position. P M,l 1
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- The following questions consider the stability of a floating iceberg. Approximate the iceberg as a perfect cylinder of uniform density, If the iceberg has a diameter of 3 meters and a length of 0.5 meters find the location of the metacenter as measured from the bottom of the iceberg. Take the density of sea water to be 1030 kg/m3 and the density of the ice to be 920 kg/m3.Please answer the following question 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.Fluid mechanics, i need solutions in 10 minutes please. MCQ/When a 4 lb weight is placed on the end of a floating wooden beam, the beam tilts at an angle θ= 2.1º with its upper right corner at the surface, as shown in the figure. The floating wooden beam having the dimensions of 8 in x 8 in x 10 ft. What is the buoyant force in 1b? A-230.132 lb B-171.965 lb C-149.002 lb D-233.761 lb E-179.235 lb F-164.682 lb G-186.519 lb H- 222.865 lb I-215.600 lb J-201.063 lb K-237.395 lb L-208.331 lb M-157.401 lb N-193.785 lb
- 01: A 105cm Rod is suspended on a wall with a 5N force pulling upwards, 110 degrees away from the horizontal axis and 5cm from a 50kgm hanging object. Find the location of the C.G. away from the wall. Neglect the Mass of the rod and consider it a rigid body. Assume SSLC. 02: Considering a CCW movement is Positive, what is the total value of the Negative Moments at the point with the 50kgm object? Please answer in four decimal places, in Nm. 03: What is the value of C.G. away from the wall? (in meters, two decimal places)A crane that is 10 meters long is rotating (while loaded), at 1 radians/sec. It is stopped instantly (in 0.1 radian) in the position shown. Due to momentum the load continues to swing. Ignoring the deflection of the crane for this problem. (list all assumptions). The load is 750 lbs. a) The weight of the 10 m crane boom is 3000 lb and the mass moment of inertia is 80 lb ft s^2 about the centroid. Using the parallel axis theory find the mass moment of inertia around the point of rotation. b) What forces and moments are there on the boom at the point of rotation?Data has been gathered from a lifting system used to remove spent RBMK fuel rods from the spent rod pool into long term safe storage. At present the spent rods are winched up from the pool and then lowered into concrete barrels in a second pool. When it is positioned properly the winch is released and the rod is allowed to drop in. The following calculation is based on data gathered from the present set up. Time taken to lowered into concrete barrels = 10 Seconds Winch drum diameter = 0.9m Mass of load = 185 kg Initial velocity = 0 m/s Distance travelled = 6m You have been asked to use this information to determine: The final linear velocity of the load The linear acceleration of the load The final angular velocity of the drum The angular acceleration of the drum The tension force in the cable The torque applied to the drum In determining the above quantities, you should clearly state the formulae used and apply dimensional analysis techniques to show that all values/units used…
- 1.A rotor has an inner radius of 10.0 cm and an outer radius of 25.0 cm. It is fixed to a frictionless axle that goes through its center. The moment of inertia (I) of the rotor is 0.0235 kg m2. A set of 5 constant forces act on the rotor, as shown in the diagram below. (a) Find the net torque acting on the rotor, in units of Nm. Be sure to give both the magnitude and direction. (b) Find the angular acceleration of the rotor, in units of rad/s2. Give both the magnitude and direction. (c) Assuming it starts from rest at t = 0, how long does it take for the rotor to reach an angular speed of 565 revolutions pre minute (rpm)? Give your answer in seconds. (d) At t = 2.50 seconds, how many complete revolutions will the rotor have made?A tentative rule was given about tipping in Testing Experiment Table 8.4, where if a vertical line passing through the object's center of mass is within the object's area of support the object does not tip. According to the rule, the full box of crackers in the following experiment, which has a width of 13 cm and a height of 20 cm, was seen to tip at an angle of: θc=tan−1(13 cm/20 cm)=33∘θ According to the rule, at what angle will a box with the left half filled with crackers begin to tip? Assume the box is light-weight and that the contents remain in the configuration inFOR FIG REFER THE ATTACHED IMAGE The shaft is massless. A thin attached triangular mass ‘m’ is mounted on the shaft. Rotational speed of the shaft is ω. Neglect weight effect of attached mass. Bearings are at A and B. Take Z- axis along the shaft axis. X- axis is vertically downward. Y – axis is horizontal. Take origin at mid-point on the shaft. Question: Under what practical condition can we justify the neglecting of weight of the attached triangular body?
- A block of iron of density 2200 kg/m3 is fully immersed in water as shown in figure 2. Given the density of water is 1000 kg/?3 and the volume of water displaced is Z*10−3 ?3. If (Z is 05+10), Taking in consideration that the gravitational acceleration g = 9.8 m/?2, Calculate the following using Archimedes’ principle: A. What is the value of Z?B. Calculate the upthrust force.C. Determine the mass of the block.D. If half the volume of the block is immersed in water, will the apparent weight of the piece will be lower or greater than in C? Explain your answer.[20] A crane that is 10 meters long is rotating (while loaded), at 1 radians/sec. It is stopped instantly (in 0.1 radian) in the position shown. Due to momentum the load continues to swing. Ignoring the deflection of the crane for this problem. (list all assumptions). The load is 750 lbs. a) The weight of the 10 m crane boom is 3000 lb and the mass moment of inertia is 80 lb ft s^2 about the centroid. Using the parallel axis theory find the mass moment of inertia around the point of rotation. Parallel axis theory can be found in appendix B formula B.6 (pg A9). b) Determine the maximum VERTICAL distance through which the load will swing. (Use the principle of work and energy with the work done by the weight. Two positions needed). c) What is the normal acceleration of the weight immediately after the crane stops (magnitude and direction)? d) What is the maximum energy that can be transmitted back to the crane (boom and load)? e) What forces and moments are there on the boom at the point…Consider a pulley system shown below. Assume there is no slip between the cord and the pulley. I is the mass moment of inertia of the pulley about its own centroidal axis. Find the equations of motion in terms of x. Select all that apply.