4. The drum of a goods hoist has a mass of 900 kg. It has an effective diameter of 1.5 m and a radius of gyration of 0.6 m. The loaded cage has a mass of 550 kg and its frictional resistance in the vertical line of travel is 270 N. A maximum acceleration of 0.9 m/s² is required. Determine: 1. The necessary driving torque on the drum, 2. The tension in the rope during acceleration, and 3. The power devel- oped at a steady speed of 3.6 m/s. [Ans. 4.64 kN-m; 6.16 kN; 22.3 kW]
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- Calculate the horizontal force P required to push the 85-lb lawn mower at constant speed. The center of gravity of the mower is at G, and the coefficients of rolling resistance are 0.12 for the front wheels and 0.18 for the rear wheels.The lower block of mass m2 = 3.2 kg is pulled on by a rope with a tension force of 28 N. The upper block has mass m1 = 1.8 kg. The coefficient of kinetic friction between the lower block and the surface is 0.32. The coefficient of kinetic friction between the lower block and the upper block is also 0.32. What is the acceleration of the 3.2 kg block?A 2.6-kg sphere S is being moved in a vertical plane by a robotic arm. When the angle 0 is 39°, the angular velocity of the arm about a horizontal axis through O is 52 deg/s clockwise and its angular acceleration is 220 deg/s² counterclockwise. In addition, the hydraulic element is being shortened at the constant rate of 520 mm/s. Determine the necessary minimum gripping force Pif the coefficient of static friction between the sphere and the gripping surfaces is 0.61. Compare P with the minimum gripping force P; required to hold the sphere in static equilibrium in the 39° position. 2.0 m Answers: P = i 16.92 N P3 = 20.90 N
- A 2.6-kg sphere S is being moved in a vertical plane by a robotic arm. When the angle 0 is 39°, the angular velocity of the arm about a horizontal axis through O is 52 deg/s clockwise and its angular acceleration is 220 deg/s2 counterclockwise. In addition, the hydraulic element is being shortened at the constant rate of 520 mm/s. Determine the necessary minimum gripping force Pif the coefficient of static friction between the sphere and the gripping surfaces is 0.61. Compare Pwith the minimum gripping force P, required to hold the sphere in static equilibrium in the 39° position. 2.0 m Answers: P = i P3 = NIn a porter governor the mass of the central load is 18 kgand the mass of each ball is 2kg. the top arms (254) mm while the bottom arms are (304) mm long. The friction of the sleeve is 20 N. If the top arms make 45 deg with the axis of rotation in the equilibrium position, find the range of the speed of the governor in that positionA 3.9-kg sphere S is being moved in a vertical plane by a robotic arm. When the angle 0 is 27°, the angular velocity of the arm about a horizontal axis through O is 52 deg/s clockwise and its angular acceleration is 179 deg/s² counterclockwise. In addition, the hydraulic element is being shortened at the constant rate of 600 mm/s. Determine the necessary minimum gripping force P if the coefficient of static friction between the sphere and the gripping surfaces is 0.46. Compare P with the minimum gripping force P required to hold the sphere in static equilibrium in the 27° position. 2.0 m Answers: P= Ps= i Z Z N N
- A block of wood of mass 20 kg is supported as shown in the diagram. If the string suspending the 10 kg mass and connected to the 20 kg mass is light and inextensible and the coefficient of friction, u between the mass and the plane is 0.3 neglecting friction in the pulley (i) Compute the acceleration of the block. (ii) Determine the tension in the rope. 20 kg 10 kg 30°A 1.4-kg sphere S is being moved in a vertical plane by a robotic arm. When the angle e is 37°, the angular velocity of the arm about a horizontal axis through O is 45 deg/s clockwise and its angular acceleration is 166 deg/s² counterclockwise. In addition, the hydraulic element is being shortened at the constant rate of 450 mm/s. Determine the necessary minimum gripping force Pif the coefficient of static friction between the sphere and the gripping surfaces is 0.59. Compare P with the minimum gripping force P; required to hold the sphere in static equilibrium in the 37° position. 1.3 m Answers: P = i N P3 = Nblock C weighs 200lb is lifted by hoisting mechanism. the hoist is wrapped around compound drum B. drum b is rotating as a single unit and weighs 300 lbs. K(bar) is 4ft. a hoist tension (P) is rated 1.0 kips. And its power is being maintained by the power in Motor A. Determine the vertical acceleration of the block C and the resultant force on the bearing at O.
- 1. A cart is being pulled by a motor. The cart has a mass of m = 200 kg. The motor applies a horizontal force of F = 800 N to the center of the right side of the cart. The cart is 1m tall, the total length is 1.5m, the wheels are 1m apart from each other, and the center of mass G is 0.4 m above the floor and on the horizontal center. Ignore friction. If there is no rotational movement of the cart, determine the following: 1. The cart's acceleration 2. The reaction (normal) force at the front pair of wheels. 3. The reaction (normal) force at the rear pair of wheels. F 77 TI TA 3.5-kg sphere S is being moved in a vertical plane by a robotic arm. When the angle is 35°, the angular velocity of the arm about a horizontal axis through O is 53 deg/s clockwise and its angular acceleration is 173 deg/s² counterclockwise. In addition, the hydraulic element is being shortened at the constant rate of 420 mm/s. Determine the necessary minimum gripping force P if the coefficient of static friction between the sphere and the gripping surfaces is 0.41. Compare P with the minimum gripping force P, required to hold the sphere in static equilibrium in the 35° position. p 1.8 m Answers: P = P₁ = i i $ N NA 2.2-kg sphere S is being moved in a vertical plane by a robotic arm. When the angle is 36°, the angular velocity of the arm about a horizontal axis through O is 45 deg/s clockwise and its angular acceleration is 176 deg/s² counterclockwise. In addition, the hydraulic element is being shortened at the constant rate of 550 mm/s. Determine the necessary minimum gripping force P if the coefficient of static friction between the sphere and the gripping surfaces is 0.58. Compare P with the minimum gripping force P, required to hold the sphere in static equilibrium in the 36° position. 1.0 m $ Answers: P= Ps= i i N N