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- The 10-Ib sphere and 7-ib block (shown in section) are secured to the arm of negligible mass which rotates in the vertical plane about a horizontal axis at O. The 5-Ib plug is released from rest at A and falls into the recess in the block when the arm has reached thehorizontal position. An instant before engagement, the arm has an angular velocity wo = 1.2 rad/s. Determine the angular velocity w(positive if counterclockwise, negative if clockwise) of the arm immediately after the plug has wedged itself in the block.A thin, light string is wrappedaround the outer rim of a uniform hollowcylinder of mass 4.75 kg having innerand outer radii as shown in Fig..The cylinder is then released from rest.(a) How far must the cylinder fall beforeits center is moving at 6.66 m/s? (b) Ifyou just dropped this cylinder withoutany string, how fast would its center bemoving when it had fallen the distancein part (a)? (c) Why do you get twodifferentanswers when the cylinderfalls the same distance in both cases?The 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.
- The double pulley shown in the figure has a mass of 3 kg and a radius of 100 mm rotation. Knowing that when the pulley is at rest, it is applied to the cable in B, a force P of magnitude equal to 24N, determine the speed of the center of the pulley after 1.5 s and the tensile force on cable C.A 5-m-long ladder has a mass of 15 kg and is placed against a house at an angle 0 = 20°. Knowing that the ladder is released from rest, determine the angular velocity of the ladder and the velocity of end A when 0 = 45°. Assume the ladder can slide freely on the horizontal ground and on the vertical wall.A cyclist is riding a bicycle at a speed of 20 mph on a horizontal road. The distance between the axles is 42 in., and the mass center of the cyclist and the bicycle is located 26 in. behind the front axle and 40 in. above the ground. If the cyclist applies the brakes only on the front wheel, determine the shortest distance in which he can stop without being thrown over the front wheel.
- Show that the angular momentum HB of a rigid body about point B can be obtained by adding to the angular momentum HA of that body about point A the vector product of the vector rA/B drawn from B to A and the linear momentum of the body: Further show that when a rigid body rotates about a fixed axis, its angular momentum is the same about any two points A and B located on the fixed axis (HA=HB) if, and only if, the mass center G of the body is located on the fixed axis.A hoop of radius 95mm and mass 100g is rotated via a capacitor driven power source with P(t)=1.61e-1.3tW. (since it is a hoop, it is a special case, and r=rG) Assuming the hoop is accelerated from rest, determine the rotational velocity after t=8.5s. [rad.s-1] Determine the rotational speed of the hoop after t=8.5s if the power source acts to roll the particle from rest on a horizontal surface. [rad.s-1]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'. 1. What gives the correct kinematic relationship relating the final velocity of the center of the rod, v' , and its angular velocity, ω'? 2. What is the coefficient of restitution, e, between the block and the slender rod? 3. What is the magnitude of the horizontal impulse at the support at point A?
- John played croquet with a 0.922-kg. mallet head and you can assume that it can be modelled as a point mass for simplified analysis only in this case. Meanwhile, the mallet's handle has a length of 0.95 m and a mass of 0.63 kg. Helifts the mallet from the ground and swings it down, pivoting around her grasp, to strike the croquet ball. The ball, which is initially at rest, weighs 0.42 kilograms and it has linear velocity of 1.995 meters per second to the right immediately after impact. 1. Which of the following is the most ideally constructed momentum-impulse diagram for the system of croquet ball and mallet together 2. What is the kinematic relationship relating the velocity of the mass center of mallet handle AB vG and its angular velocity ω?A particle M1, weighing 2.4 Ibs, is tied to a thread and describes a circular path in a horizontal plane. The thread, of negligible mass, passes through a hole in the center of the circle and descends vertically. Another particle M2 is attached, weighing 5.0 Ibs, as shown in the figure. If M1 describes a uniform circular motion, with angular velocity w 3.1 rad/s, determine the radius R of the circumference in inches.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?