Four small disks A, B, C, and D can slide freely on a frictionless horizontal surface. Disks B, C, and D are connected by light rods and are at rest in the position shown when disk B is struck squarely by disk A, which is moving to the right with a velocity
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Vector Mechanics For Engineers
- The 2.00-kg slender rod shown is hanging in a vertical position and is pin-supported at point A. The slender rod is initially at rest until a 1.000-kg block C, strikes it at its end at point B.The block slides on a frictionless surface with a velocity of 3.50 m/s to the right. After the impact, it slides with a velocity of 1.250 m/s to the right, and the bar rotates with an angular velocity, ω'. Sketch the moment-impulse diagram 1. Which of the following gives the correct kinematic relationship relating the final velocity of the center of the rod, v'G, and its angular velocity, ω'? 2. Which of the following gives the closest value of the coefficient of restitution, e, between the block and the slender rod? 3. Which of the following gives the closest value of the magnitude of the horizontal impulse at the support at point A?arrow_forwardThe 2.00-kg slender rod shown is hanging in a vertical position and is pin-supported at point A. The slender rod is initially at rest until a 1.000-kg block C, strikes it at its end at point B. The block slides on a frictionless surface with a velocity of 3.50 m/s to the right. After the impact, it slides with a velocity of 1.250 m/s to the right, and the bar rotates with an angular velocity, w'. 3.5 m/s с B 1.5 m Answer the following questions given the picture. Please show clear solutions, I want to learn how to solve the problem. 1a. Which of the following gives the correct kinematic relationship relating the final velocity of the center of the rod, v'G, and its angular velocity, w'? A) 1.333 w' B) 0.667 w' C) 1.500 w' D) 0.75 w' 1b. Which of the following gives the closest value of the magnitude of the horizontal impulse at the support at point A? A) 1.125 N-s B) 1.350 N-s C) 0.1180 N-s D) 2.25 N-sarrow_forwardThe arms of a Porter governor are 225 mm long. The upper and lower arms are pivoted to links of 35 mm and 45 mm respectively from the axis of rotation. Each ball has a mass of 4 kg and the sleeve mass is 35 kg. The force of friction on the sleeve of the mechanism is 44 N. Determine the range of speed of the governor for extreme radii of rotation of 115 mm and 145 mm.arrow_forward
- An object of mass m1 slides on a sloped block of mass M2, which in turn slides on a horizontal surface. The slope angle is a constant 3, and both masses are initially at rest. There is no friction between any of the objects, and the masses are subject to the force of gravity -mgêy. Use as co- ordinates the horizontal position x2 of mass m2, and the height y1 of mass m1, as shown in the y4 Y1 M2 x2 diagram to the right. Find the equation of motion of block 2, ä2(t). The expression should only include expressions involving constants: M2, m1, g, and B.arrow_forwardActivity 3. A body that weighs W Newtons falls from rest from a height of 600mm and strikes a spring whose scale is 7.00 N/mm. If the maximum compression of the spring is 150 mm, what is the value of W? Disregard the mass of the spring. (Ans. W=105 N) 600mm 150mmarrow_forwardDisk "A" of weight 5 lb and radius "r=3 in" is at rest and placed in contact with a belt which moves at a constant speed of 57 ft/s. Hk = 0.20 between the disk and the belt. a) USING THE PRINCIPLE OF LINEAR AND ANGULAR IMPULSE AND MOMENTUM, draw the FBD for the before, impulse and after case.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_forwardRequired information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A 3.5-kg slender rod AB and a 2-kg slender rod BC are connected by a pin at B and by the cord AC. The assembly can rotate in a vertical plane under the combined effect of gravity and a couple M applied to rod BC. In the position shown, the angular velocity of the assembly is zero and the tension in cord AC is equal to 26.8 N. 300 mm A 400 mm 400 mm M B Determine the angular acceleration of the assembly. (You must provide an answer before moving to the next part.) rad/s²0. The angular acceleration of the assembly isarrow_forwardQ. The upper and lower arms of Porter governor are 0.25 m each and are pivoted 30 mm from the axis of rotation. The radius of rotation Is 130 mm. The mass of the ball and sleeve are 3 kg and 38 kg respectively. Find the effort and power of the governor.arrow_forward
- The two blocks shown are originally at rest. Neglect the masses of the pulleys and the effect of friction in the pulleys and between the blocks and the incline. Consider WA = 206 lb and WB = 306 lb.arrow_forwardThe 6-lb steel cylinder A of radius r and the 10-lb wooden cart B are at rest in the position shown when the cylinder is given a slightnudge, causing it to roll without sliding along the top surface of the cart. Neglecting friction between the cart and the ground, determine the velocity of the cart as the cylinder passes through the lowest point of the surface at C.arrow_forwardb. The four arms of a porter governor is 250 mm long. The upper and lower arms are pivoted to links 40 mm and 50 mm respectively from the axis of rotation. Each ball has a mass of 5 kg and the sleeve mass is 50 kg. The force of friction on the sleeve of the mechanism is 40 N. Determine the range of speed of the governor for extreme radii of rotation of 125 mm and 150 mm. Consider the force diagrams attached.arrow_forward
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