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Using a forked rod, a smooth cylinder P, having a mass of 0.4 kg, is forced to move along the vertical slotted path r = (0.6θ) m, where θ is in radians. If the cylinder has a constant speed of υc = 2 m/s, determine the force of the rod and the normal force of the slot on the cylinder at the instant θ = π rad. Assume the cylinder is in contact with only one edge of the rod and slot at any instant. Hint: To obtain the time derivatives necessary to compute the cylinder’s acceleration components ar, and aθ, take the first and second time derivatives of r = 0.6θ. Then, for further information, use Eq. 12-26 to determine
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Chapter 13 Solutions
Practice Problems Workbook For Engineering Mechanics
- The small 1.6-kg block A slides down the curved path and passes the lowest point B with a speed of 3 m/s. If the radius of curvature of the path at B is 2 m, determine the normal force N exerted on the block by the path at this point. PLEASE ANSWER IT COMPLETELY. No rounding off of values unless it is the final answer. Final answers in 3 decimal places.g to be used 9.81 m/s^2 or 32.2 ft/s^2.arrow_forwardDetermine the constant force “f” w/c must be applied to the cord in order to cause the 39lb block to have a speed of 22 ft/a when it has been displaced 0.5 ft upward starting from the rest.arrow_forwardBlock A has a mass mA and is attached to a spring having a stiffness k and unstretched length l0. If another block B, having a mass mB, is pressed against A so that the spring deforms a distance d, determine the distance both blocks slide on the smooth surface before they begin to separate. What is their velocity at this instant?arrow_forward
- The van is traveling at 20 km/h when the coupling of the trailer at A fails. If the trailer has a mass of 250 kg and coasts 45 m before coming to rest, determine the constant horizontal force F created by rolling friction which causes the trailer to stop. Note: 3 decimal points in every answer.arrow_forwardThe 280-Mg jet airliner has three engines, each of which produces a nearly constant thrust of 229 kN during the takeoff roll. Determine the length s of runway required if the takeoff speed is 219 km/h. Compute s first for an uphill takeoff direction from A to B and second for a downhill takeoff from B to A on the slightly inclined runway. Neglect air and rolling resistance.arrow_forwardb)With the radius of curvature (r) at the top of the loop (T) is 1 m. Determine the minimum speed (in m/s) of the box required at point T such that it can stay on the loop.arrow_forward
- It takes 33 s for the 48-Mg tugboat to increase its speed uniformly to 25 km/h, starting from rest. The propeller provides the propulsion force F which gives the tugboat forward motion, whereas the barge moves freely. The barge has a mass of 80 Mg.arrow_forwardThe two spheres each have a mass of 3 kg and are attached to the rod of negligible mass. If a torque M = (6e0.2t )Nm, where t is in seconds, is applied to the rod as shown, determine the speed of each of the spheres in 2s, starting from rest.arrow_forwardIt takes 34 s for the 60-Mg tugboat to increase its speed uniformly to 25 km/h, starting from rest. The propeller provides the propulsion force F which gives the tugboat forward motion, whereas the barge moves freely. The barge has a mass of 84 Mg . (A) Determine the force of the rope on the tugboat. Express your answer to three significant figures and include the appropriate units. (B) Also, determine F acting on the tugboat. Express your answer to three significant figures and include the appropriate units.arrow_forward
- Determine the required height h of the roller coaster so that when it is essentially at rest at the crest of the hill A it will reach a speed of 25 m/s when it comes to the bottom B.arrow_forwardGiven a 1400 kg car traveling along a route with an increasing vertical profile y=0.0003x^2. Determine the x-component of the car's velocity (m/s) and the total force (kN) if the constant velocity is 30 m/s and the distance is 210m. Hint: A line's slope is equal to tan theta, where theta is an angle measured from the x-axis.arrow_forwardDynamic Lesson The ski and the rider, with a total mass of 90 kg, are moving along the curved path in the shape. Since the equation of the curvilinear path is determined as y = 0.08x2 and the speed at x = 10 m is known as 5 m / s, the skier at this pointa) The rate of increase in speed,b) Obtain the value of the Normal force applied to ski.arrow_forward
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