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Disk A rotates in a horizontal plane about a vertical axis at the constant rate
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Vector Mechanics for Engineers: Dynamics
- The system shown below consists of a uniform disk D that has a mass of mp = 3.0 kg and a radius of r = 1.0 meters. The disk is connected by a massless cable to a block. The system is released from rest and the disk starts rolling without sliding with the angular acceleration of a = rad 30 s2 in the clockwise direction. Determine the magnitude of the friction force (in Newtons) developed between the disk and the inclined surface at this instant. Consider 0 = 40° and g = 10 m. mparrow_forwardIn the system shown, a 150 N collar-pulley assembly slides on a horizontal shaft with coefficient of kinetic friction uk =0.10 between the collar and the shaft, and is acted upon by a force P with a magnitude of P = 250N at an angle 0 = 30 as shown. Knowing that the assembly is initially at rest, what is the time when the velocity of collar B reaches to 3 m/s? Also, at this instant, find the tensile force in the cord and the velocity of block A.arrow_forwardA sphere of radius r and mass m has a linear velocity v0 directed to the left and no angular velocity as it is placed on a belt moving to the right with a constant velocity v1. If after first sliding on the belt the sphere is to have no linear velocity relative to the ground as it starts rolling on the belt without sliding, determine in terms of v1 and the coefficient of kinetic friction µk between the sphere and the belt (a) the required value of v0, (b) the time t1 at which the sphere will start rolling on the belt, (c) the distance the sphere will have moved relative to the ground at time t1.arrow_forward
- A 5-kg homogeneous disk with a radius of 0.2 m is connected to a spring (k=50 N/m) as shown. At the instant shown (position 1), the spring is undeformed. The disk is released from rest and rolls without slipping to position 2, which is 0.1 m down the 25-degree incline. A clockwise constant 2 N-m couple is applied to the disk as it rolls down the inclined surface. Note: I disk = mR²2 2 N-m 0.2 5-kg 25° k = 50 N/m 10000000 1. Which of the following forces does negative work on the system? Friction between the disk and the inclined surface + x Mark 0.00 out of 20.00 2. Which of the following best approximates the magnitude of the work done by the spring? 0.250 J + ✓ 3. Which of the following best approximates the work done by the 2 N-m couple? -1.000 J + ✓ 4. Which of the following gives the correct expression of the kinetic energy of the system at position 2 in terms of the disk's angular velocity, w₂? 0.15 w2*2 + 4.53 rad/s + x 5. Which of the following best approximates the magnitude…arrow_forwardDynamic Lecture: The 2 kg BC ring can only move left and right on the frictionless rigid arm. Ring BC is connected to springs with spring constants k = 300 N / m and k ′ = 200 N / m at points AB and CD. The unstretched length of both springs is 600 mm. Since it is known that the springs are not tensioned and starts from rest, find the velocity of the ring BC at the moment when the external force F is applied 200 mm.arrow_forwardH4.arrow_forward
- Object A, mass 12 kg, is attached to a pulley with mass 15 kg and a radius of 0.25 m. The pulley is rotating at 2000 rpm. If object A is to be reduced to half its initial speed, plant By braking the pulley bearings which creates a moment of resistance of 800 N-m. I want to know how far the object will slide down and what is the tension in the rope at that time. 12 kg 0.3 marrow_forwardIn the system that starts to move without speed, the masses of 22.2 kg each reach an angular velocity of 242 rev/min in t second at a radius of R=293 mm with the effect of the 37 N force T. Since the radius of the pulley is r = 63 mm, find t ignoring friction and all masses except the four.arrow_forwardQ2. The cord passes over a massless and frictionless pulley, as shown, carrying a mass 4m at one end and connected to a cylinder of mass 2m and radius of R that rolls on an inclined plane of 30'. What is the acceleration of the cylinder and tensions in the cable? Frictionless pulley 4m 2m ** ******* 30arrow_forward
- A sheep with mass 50 kg is hung on an animal scale system which consists of a helical spring of negligible mass. The stifness (k) of the spring is 60 kN/m. During the hanging operation, the spring and sheep are displaced vertically by 20 mm below the equilibrium position. Calculate the velocity and acceleration of the sheep when it is 10mm below the rest positionarrow_forwardQ5: Determine the speed of slider at position 2 when slider weight 0.75 kg and P=300 N. The slider starts from rest at position land the unstretched length of the spring of modulus is k=210 N/m is 200 mm. Neglect frictions. 200 mm 200 P 250 mm mm 250 mm 15arrow_forwardQ2) The slotted arm pivots about O and maintains the relation between the motions of sliders A and B and their control rods. Each small pivoted block is pinned to its respective slider and is constrained to slide in its rotating slot. Show that the displacement x is proportional to the reciprocal of y. Then estab- lish the relation between the velocities vA and vg. Also, if v, is constant for a short interval of motion, determine the acceleration of B. b y 'Barrow_forward
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