PROBLEM 7: In the figure, µ = 0.30 for the contact of the 80-kg crate and the ground. Pulleys are frictionless. (a) determine the value of 0 to move the crate (b) Determine the tensile force (in N) in the rope attached to the crate to move the crate. (c) Determine the smallest force (in N) the man must exert on the rope to move the crate. 30°/ 45°
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- The bar ABC is supported by three identical, ideal springs. Note that the springs are always vertical because the collars to which they are attached are free to slide on the horizontal rail. Find the angle at equilibrium if W = kL. Neglect the weight of the bar.The figure shows a steel bar being processed by a rolling mill. Given that P=80kN and r =0.016, determine the force F required to advance the bar at a constant speed.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.
- PROBLEM 7: In the figure, μ = 0.30 for the contact of the 80-kg crate and the ground. Pulleys are frictionless. (a) determine the value of θ to move the crate (b) Determine the tensile force (in N) in the rope attached to the crate to move the crate. (c) Determine the smallest force (in N) the man must exert on the rope to move the crate7. A ladder of length 12 m leaning up against a wall makes a 50 degree angle with the ground. The top of the ladder has sliders so that it can slide up and down the wall. Therefore, consider the top of the ladder to be frictionless. The ladder has a weight of 189 N that acts at its center. Someone weighing Fg = 1000 N is 0.92 m vertically below B, but on the ladder. Another person is on the ground holding the ladder by pushing on it horizontally with a force F. If the coefficient of static friction is 0.32, find the horizontal force F that must be applied at a vertical height of 1.2 m to prevent the ladder from slipping. LL F 1.2 m 12 m 50⁰ Fg B .92 mQ1: In the Figure 1, two forces (P & Q) are acting on the same fixed point A. Find the resultant of these forces and its angle with the horizon by using: (a) Graphical solution. (b) Trigonometric solution. Q = 60 N Figure 1: P 40 N 35 Q2: A block of 15 kg was place on an inclined surface as shown in Figure 2. If the static coefficient of friction between the block and the surface is 0.3, find: (a) the maximum friction force. (b) the equilibrium state of the block. 15 kg Figure 2: 30
- Given the figure shown below, what is the mass of block B on the smooth incline if the system is in static equilibrium? A rope runs from block B up around the frictionless pulley at A down to a 10 kg counterweight. A 1 m B- 1m 10 kg 45°1. The blocks shown in the figure below are separated by a solid strut which is attached to the blocks with frictionless pins. If the coefficient of friction for all surfaces is 0.20, determine the value of horizontal force P to cause motion to impend to the right. Assume that the strut is a uniform rod weighing 100 lb. 200 lb MATHalino.com 30 400 lb 45° MATH5. The figure below represents the anatomy of the lower limb when balanced on your toes and the body weight acts through the tibia. The Achilles Tendon makes an angle (0) of 8° with the vertical and for this foot x1 is 6.2 cm and x2 is 12.3 cm. Calf Muscle Tibia Achilles Tendon Calculate the tension (T) in the Achilles Tendon if a 70 kg man stands on the toes of both feet. Using the values in this example what is the mechanical advantage for this lever and describe what that means in terms of the efficiency of the lever.
- Figure 1 shows a simple system to lift a heavy load. The dimensions a = 3.6 m and b = 1.2 m. The mass of the bar and counterweight is 45000 g, and their weight W acts at the point as shown. The mass of the load being lifted is 20000g (a) (b) If the load is just above the ground, determine the vertical force the person must exert to support the system. If the load is 1 m above the ground, determine the vertical force the person must exert to support the system. 25° Figure 1 20000 g WA puck weighs 8 lb and rests on the center of the frictionless surface of the ramp supported in equilibrium by ropes AC and BC. Determine the normal force the ramp exerts on the puck as well as the tension in each of the two ropes. g Variable Value Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. a b C d e f g9 36.0 in 45.0 in 13.5 in 27.7 in 45.0 in 18.0 in 35.0 in B The normal force acting on the puck is pounds The tension in rope AC is The tension in rope BC is C pounds poundsQ.3) The coefficient of friction between the 100 lb block (shown in figure below) and the incline plane is 0.25 and that between the cord and cylindrical support is 0.3. Determine the range of cylinder weight W for which the system shown below will be in equilibrium. p = 0.3 100 lb p = 0.25 25° W