4. A heavy frictionless cart rolls down an incline. A string is attached to the cart, looped over a pulley and connected to a box on a level surface. The cart has a mass of 10.5 kg and the box has a mass of 6.50 kg. The incline makes an angle of 21.0° above horizontal. If the coefficient of friction between the box and the surface is just 0.085, what is the acceleration of the box? (Include Force diagrams with your answers.) 21.00
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- Two ideal pulleys (massless and frictionless) form a pulley system that can lift a weight by pulling on the end of a massless rope, as shown below. The upper pulley is attached to the ceiling at point A, and the lower pulley is connected to a box of mass M = 10.0kg. (a) What is the tension in the rope if the box is accelerating upwards with a = 2.00 m/s^2? (b) What is the tension force at point A at the ceiling?In the figure, a rectangular slab of slate rests on a bedrock surface inclined at angle 8 = 22.8°. The slab has length L = 48.9 m, thickness T = 6.61 m, and width W = 12.7 m, and 1.0 cm³ of it has a mass of 3.2 g. The coefficient of static friction between slab and bedrock is 0.312. (a) Calculate the component of the gravitational force on the slab parallel to the bedrock surface. (b) Calculate the magnitude of the static frictional force on the slab. By comparing (a) and (b), you can see that the slab is in danger of sliding. This is prevented only by chance protrusions of bedrock. (c) To stabilize the slab, bolts are to be driven perpendicular to the bedrock surface (two bolts are shown). If each bolt has a cross-sectional area of 6.47 cm² and will snap under a shearing stress of 3.59 x 108 N/m², what is the minimum number of bolts needed? Assume that the bolts do not affect the normal force.The answers entered are incorrect. Kindly provide a complete solution. Thank you!
- A "swing" ride at a carnival consists of chairs that are swung in a circle by L = 15.8 m cables attached at an angle of θ = 57.4° to a vertical rotating pole, as the drawing below shows. Suppose the total mass of a chair and its occupant is 161 kg. Calculate the tension in the cable attached to the chair.مجھے E 20 C 4. A 115 kg scaffold is 6.60 m long. It is hanging with two wires, one from each end. A 600 kg box sits 1.70 m from the left end. What is the tension in the right hand side wire? (g = 9.8 m/s²) Newtons $ R F 888 F4 V % 5 T G tv 6: B MacBook Air FG Y Q H & 7 F7 N 8 DII M ( 9 MOSISO FR O O P zoom mes or r ISUIT by mi 04 M nufferIn the figure, a rectangular slab of slate rests on a bedrock surface inclined at angle θ = 28.4°. The slab has length L = 32.4 m, thickness T = 5.92 m, and width W = 14.3 m, and 1.0 cm3 of it has a mass of 3.2 g. The coefficient of static friction between slab and bedrock is 0.385. (a) Calculate the component of the gravitational force on the slab parallel to the bedrock surface. (b) Calculate the magnitude of the static frictional force on the slab. By comparing (a) and (b), you can see that the slab is in danger of sliding. This is prevented only by chance protrusions of bedrock. (c) To stabilize the slab, bolts are to be driven perpendicular to the bedrock surface (two bolts are shown). If each bolt has a cross-sectional area of 6.05 cm2 and will snap under a shearing stress of 3.34 × 108 N/m2, what is the minimum number of bolts needed? Assume that the bolts do not affect the normal force.
- A 10 m long board that has a mass of 20 kg is held up by two vertical ropes. The left rope is 2 m from the left end of the board, and the other rope is 2 m from the right end of the board. A 40 kg box sits 2 m from the right end. Find the tension in the rope on the left.3. The force F required to move a box by pulling on an attached rope that forms an angle w with the horizontal is given by fmg F(w) = cOSw + f sin w where f, m, g > 0 are all constant. (a) Show that the angle wo that minimizes the required force to set the box in motion is given by arctan(f) (b) Show that this minimal force F(wo) is proportional to (a constant multiple of)A block of mass ?=353 gm=353 g is dragged with a string across a rough horizontal table. The string tension is ?=2.63 N,T=2.63 N, and it pulls upward at an angle of ?=44.0∘ϕ=44.0∘ with the horizontal. At one particular instant, the block is moving at a speed of ?=5.70 m/s.v=5.70 m/s. The coefficient of kinetic friction between the block and the table is ?k=0.699. What is the power ?TPT supplied to the block by the string tension? What is the power ?fPf supplied by the force of friction?
- Connected objects with inclined plane problem. Consider the figure where you have two boxes connected by a string over a pulley. The smooth (frictionless) ramp is inclined to a an angle of 35° with the flat ground, and the box on the ramp has a mass of 6.40 kg. The mass of the 6.4 kg hanging box is m = 3.05 kg. You don't need to consider significant figures in your answer, but don't round excessively partway through your calculations. 35° Find (a) the direction and (b) the magnitude of the hanging box's acceleration.It is known that the 10 kg pipe will roll up the ramp and not slide on the ramp when P becomes sufficiently large. Using the rolling assumption, find the minimum P required to cause impending motion of the 10 kg pipe up the ramp. Note that the coefficients of friction for the block/ramp, the pipe/ramp and the pipe/block contacts are each 0.30. 18 kg block 35° 10 kg pipe B μg 0.30 for all contacts