A drum (mass m, radius r = 0.5 m) lies in a corner of a wall. The drum is connected to a freely suspended body (mass M) by a rope. The rope leads around a rounded corner of the wall (radius r₂ = 0.2 m). The static friction coefficient between drum and ground, drum and wall as well as rope and wall is μ。 = 0.5. Determine the maximum weight of the body M, up to which the system is still in equilibrium! μο m μο M
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- The coeffient of static friction between the uniform bar AB of weight W and the ground is 0.45. Find the smallest angle and the corresponding force P that would initiate simultaneous tipping and sliding of the bar.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 40-lb spool is suspended from the hanger GA and rests against a vertical wall. The center of gravity of the spool is at G and the weight of the hanger is negligible. The wire wound around the hub of the spool is extracted by pulling its end with the force P. If the coefficient of static friction between the spool and the wall is 0.25, determine the smallest P that will extract the wire.
- Draw the FBD for the bar described in Prob. 5.1 if the bar is homogeneous of mass 50 kg. Count the unknowns.The block of weight W is pulled by the force P inclined at the angle to the horizontal. Find the smallest force P and the corresponding angle that would cause impending sliding of the block. The angle of static friction between the block and the ground is s.Two identical chairs, each weighing 14 lb, are stacked as shown. The center of gravity of each chair is denoted by G. The coefficient of static friction is 0.2 at B (the contact point between the chairs) and 0.35 at A, C, and D. Determine the smallest force P that would cause sliding.
- A ladder of length 2L and mass M is positioned on level ground leaning against a wall such that the angle between the ladder and the horizontal is @. The coefficient of static friction between the ladder and the wall and between the ladder and the ground is jistatic = 0.66. The centre of mass ofthe ladder is halfway along it. For the ladder to be in mechanical equilibrium: Write down equations for the total r- and y-components of the 5 forces acting on the ladder1. 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 TThe 250 lb uniform crate (center of gravity at G) shown in the figure must be moved without tipping. The applied force P is horizontal. 1.5 ft 1.5 ft Determine: a. The largest coefficient of static friction between the crate and the floor that allows the crate to slide and 2.5 ft P. not tip 4.5 ft b. The corresponding magnitude of P 3.5 ft Include all needed FBD's to solve, and put units on your answers.
- 4 10 points A file cabinet weighing 215 lb is being pushed to the right with a horizontal force P applied a distance h from the floor. The width of the file cabinet is w = 15 in., its mass center G is a distance d = 2 ft above the floor, and static friction is insufficient to prevent slipping between the cabinet and the floor. The coefficient of kinetic friction between the cabinet and the floor is Uk = 0.28. Take the value of P to be 70 lb. 01 0!!! 01 Determine the maximum height ʼn at which the cabinet can be pushed so that it does not tip over, and find the corresponding acceleration of the cabinet. The maximum height at which the cabinet can be pushed so that it does not tip over is The acceleration of the cabinet is 1.466 ft/s². 1.7 x ft.A cube with mass of m=80N is on the inclined plane with angle of phi=20 degrees. coeficient of static friction /mu_s = 0.25 coeficient of dynamic friction /mu_k = 0.15 Determine: what is the smallest size of the force F parallel to the inclined plane, which prevents the cube in the slide? what is the smallest size of the force F, which the cube starts to move along the inclined plane up? At what value of the force F starts the cube to rise at a constant speed?The cart and its contents have a total mass of 4500 kg and a center of gravity at G as shown in Figure Q4. The coefficient of static friction between the wheels and the tracks is µ, = 0.4 when the wheels are locked. The normal forces acting on the wheels at (A and B) are independent as to whether the wheels are locked or not. Therefore, 10kN G 0.9 m A20.15 m : 0.6 m 1.5 m Figure Q4: The cart. (a) Draw the free-body diagram of the system. (b) Calculate the normal force acting on the front wheels at B when the brakes at both A and B are locked.