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Two small disks A and B of mass 2 kg and 1 kg, respectively, may slide on a horizontal and frictionless surface. They are connected by a cord of negligible mass and spin about their mass center G. At t = 0, G is moving with the velocity
Fig. P14.53 and P14.54
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Chapter 14 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
- 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_forwardA 30-kg disk A is attached to one end of a spring with stiffness k = 200 N/m at its center G. The other end of the spring is fixed at A. The disk is initially at rest with the spring unstretched. A couple moment of M = 80 Nm is then applied to the disk causing the disk to roll to the left without sliding. Consider the duration of motion when the disk rolls from the position shown (Position 1) to a position (Position 2) when its mass center G has moved 0.5 m to the left. M = 80 N·m 0.5 m G k = 200 N/m 3. Which of the following gives the closest value of the work done by the spring from position 1 to position 2? 4. Which of the following gives the closest value of the work done by the applied couple from position 1 to position 2? -80 Nm -40 Nm 40 Nm 80 Nm ♦ A O 25 Nm -25 Nm 50 Nm -50 Nmarrow_forwardA 30-kg disk A is attached to one end of a spring with stiffness k = 200 N/m at its center G. The other end of the spring is fixed at A. The disk is initially at rest with the spring unstretched. A couple moment of M = 80 Nm is then applied to the disk causing the disk to roll to the left without sliding. Consider the duration of motion when the disk rolls from the position shown (Position 1) to a position (Position 2) when its mass center G has moved 0.5 m to the left. M = 80 N·m 1.875w2^2 3.75w2^2 5.63w2^2 7.50w2^2 0.5 m G k = 200 N/m A 1. Which of the following forces do/does negative work on the disk? I. Applied couple II. Force exerted by the spring III. Normal force IV. Friction between the disk and the horizontal surface 2. Which of the following equations gives the total kinetic energy of the disk at position 2 in terms of its angular velocity, w2? Oarrow_forward
- Two disks each have a mass of 5 kg and a radius of 300 mm. They spin as shown at the rate of w1 = 1200 rpm about a rod AB of negligible mass that rotates about the horizontal z axis at the rate of w2. Determine the maximum allowed value of w2 if the magnitudes of the dynamic reactions at points C and D are not to exceed 350 N each.arrow_forwardSolve B,C,Darrow_forwardA 10 kg , 0.5 m radius wheel is to rotate from rest to a speed of 100 rad/s in 5 s. Determine the tangential force ( N ) created at the rim of the wheel.arrow_forward
- A rod in horizontal position has two equal solid spheres of mass ms and radius R. attached to both ends The mass of the rod is m, and the length of the rod is La. The rod pivots about the left end of the rod where sphere A is attached. Sphere A is free to rotate with the rod at the same angular speed. The rod is released from rest and allowed to swing freely without friction or air resistance. Consider the use of the energy conservation principle. For purposes of finding the moment of inertia, consider the rod to be slender and the rod and sphere to be homogenous. Complete the following tasks: 1) Draw a kinematic diagram, showing the angular velocity the rod and the linear velocity of center of the angular velocity of the rod as it passes through a vertical position, as applicable. 2) Determine the angular velocity in terms of the masses of the rod and sphere, the radius of the sphere and the length of the rod. Barrow_forwardConsider a slender rod AB with a length l and a mass m. The ends are connected to blocks of negligible mass sliding along horizontal and vertical tracks. If the rod is released with no initial velocity from a horizontal position as shown in Fig.A, determine its angular velocity after it has rotated through an angle of θ (see Fig B) using the conservation of energy method. (Hint: Moment of inertia of rod about G = (1/12)ml2 The kinetic energy of a rigid body in plane motion isarrow_forwardDisk A has mass mA = 4.5 kg, radius rA = 278 mm, and initial angular velocity ω0A = 300 rpm clockwise. Disk B has mass mB = 1.0 kg, radius rB = 199 mm, and is at rest when it comes into contact with disk A. Knowing that μk = 0.45 between the disks and neglecting rolling friction ,arrow_forward
- The satellite shown in the figure below has a mass of 250 kg. In its initial configuration, when e = 90°, its radius of gyration around its z-axis is kz= 0.7 m. Att= 0s, the solar panels are raised in such a way that the radius of gyration decreases at a constant rate of 0.05 ms. Assume its mass stays constant during this motion. В 0 = 90° A 0.2 m 1.5 m 0.3 m Suppose the angular velocity around the z-axis of the satellite att = Os equals wz = 2.2 rads, what is the magnitude of the satellite's angular acceleration, angular velocity and angular displacement (around the z-axis) at at t= 3 s?arrow_forwardA 110-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go- round from rest to an angular speed of 0.600 rev/s in 2.00 s? (State the magnitude of the force.) Narrow_forwardFour masses A, B, C and D are attached to a shaft and revolve in the same plane. The masses are 24 kg, 20 kg, 21 kg, and 18 kg, respectively and their radii of rotations are 50 cm, 50 cm, 60 cm and 30 cm. the angular position of the masses B, C, and D are 60º, 135º and 270º from the mass A. the shaft is rotating with a constant angular speed ω = 500 rpm. We need to find : 1. The magnitude and direction of the resultant inertia force before balancing 2. The magnitude and direction of the balancing mass at a radius of 10 cm The magnitude of the resultant force, in Newton, before balancing is = The direction of resultant force before balancing measured in degree CCW from the mass A is = The magnitude of the balancing mass in kg is = The direction of the balancing mass measured in degree CCW from the mass A the magnitude of resultant force after balancing is =arrow_forward
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