A wedge with mass M rests on a frictionless m horizontal tabletop. A block with mass m is placed on the wedge and a horizontal F force F is applied to the wedge. There M is no friction between the block and the wedge. For a = "/7, what must the magnitude of F be if the block is to remain at a constant height above the tabletop? (g is the magnitude of the gravitational acceleration. Take 1 kg, M = 5 kg and g = 10 m/s².) m %3! (a) 29 N (b) 35 N (c) 44 N (d) 60 N (е) 104N
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- Tarzan, who weighs 777 N, swings from a cliff at the end of a 16.5 m vine that hangs from a high tree limb and initially makes an angle of 21.9° with the vertical. Assume that an x axis points horizontally away from the cliff edge and a y axis extends upward. Immediately after Tarzan steps off the cliff, the tension in the vine is 721 N. Just then, what are (a) the force from the vine on Tarzan in unit-vector notation, and (b) the net force acting on Tarzan in unit-vector notation? What are (c) the magnitude and (d) the direction (measured counterclockwise from the positive x-axis) of the net force acting on Tarzan? What are (e) the magnitude and (f) the direction of Tarzan's acceleration just then?Problem 6. A 6.0kg block is placed on top of a 9.0kg block. A horizontal force of 50.0N is applied at an angle to the 9.0kg block, and the 6.0kg block is tied to the wall by a rope. The coefficient of kinetic friction between the two blocks is 0.25, and the coefficient of friction between the 9.0kg block and the ground surface is 0.30. (a) Draw a free body diagram for each block and identify the action-reaction forces between the blocks. (b) Determine the tension in the rope. (c) Determine the magnitude of the acceleration of each block. 6.0kg F = 50.0N 15° 9.0kgA particle, which remains at rest, is acted on by three forces F, G and H. The force F has magnitude 55 N and is directed to the left and up making an angle of 45 degrees with the vertical The force G is directed vertically down and H is directed to the right and up making an angle of 60 degrees with the vertical. Find the magnitude of the vectors G and H, giving your answers to one decimal place. The magnitude of G is N (to 1 d.p.) The magnitude of H is N (to 1 d.p.)
- A 16 kg block of steel is at rest on a horizontal table. The coefficient of static friction between block and table is 0.54. (a) What is the magnitude of the horizontal force that will put the block on the verge of moving? 84.7 N (b) What is the magnitude of a force acting upward 60° from the horizontal that will put the block on the verge of moving? X N (c) If the force acts down at 60° from the horizontal, how large can its magnitude be without causing the block to move? NIn the figure, a rectangular slab of slate rests on a bedrock surface inclined at angle = 25.6°. The slab has length L = 43.4 m, thickness T = 6.23 m, and width W = 13.6 m, and 1.0 cm³ of it has a mass of 3.2 g. The coefficient of static friction between slab and bedrock is 0.351. (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 6.42 cm² and will snap under a shearing stress of 3.57 × 108 N/m², what is the minimum number of bolts needed? Assume that the bolts do not affect the normal force.A sphere of mass 4.7 × 10-4 kg is suspended from a cord. A steady horizontal breeze pushes the sphere so that the cord makes a constant angle of 26° with the vertical. Find (a) the magnitude of that push and (b) the tension in the cord.
- The block shown in the figure is sliding along a frictionless horizontal surface The block's mass is m = 4.80 kg,the magnitude of the applied force is F = 26.5 N, and the angle of the applied force F from the horizontal is θ = 28.0°. Determine the magnitude n of the normal force acting on the block.A sphere of mass 2.9 x 104 kg is suspended from a cord. A steady horizontal breeze pushes the sphere so that the cord makes a constant angle of 20° with the vertical. Find (a) the magnitude of that push and (b) the tension in the cord. (a) Number Units (b) Number i UnitsA sphere of mass 5.4 × 104 kg is suspended from a cord. A steady horizontal breeze pushes the sphere so that the cord makes a constant angle of 18° with the vertical. Find (a) the magnitude of that push and (b) the tension in the cord. (a) Number i Units (b) Number i Units
- A 5.740 kg block of wood rests on a steel desk. The coefficient of static friction between the block and the desk is u, = 0.555 and the coefficient of kinetic friction is µy = 0.305. At time t = 0, a force F = 19.2 N is applied F horizontally to the block. State the force of friction applied to the block by Us,k the table at times t = 0 and t > 0. t = 0 t > 0 N Consider the same situation, but this time the external force F is 38.8 N. Again, state the force of friction acting on the block at times t = 0 and t > 0. %3D t = 0 t > 0 NThe figure below shows an initially stationary block of mass m on a floor. A force of magnitude F = 0.510mg is then applied at upward angle 0 = 19°. (a) What is the magnitude of the acceleration of the block across the floor if the friction coefficients are us = 0.590 and uk = 0.505? m/s? (b) What is the magnitude of the acceleration of the block across the floor if the friction coefficients are ug = 0.395 and uk = 0.295? m/s2In 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.