A 2.00 kg aluminum block and a 6.00 kg copper block are connected by a light string over a frictionless pulley. The two blocks are allowed to move on a fixed steel block wedge (of angle θ=30.0∘θ=30.0∘) with the aluminum block on the flat of the wedge and the copper block on the angled part. Determine (a) the acceleration of the two blocks and (b) the tension in the string

A m1 = 1.50-kg aluminum block and a m2 = 6.10-kg copper block are connected by a light string over a frictionless pulley. The two blocks are allowed to move on a fixed steel block wedge (of angle  θ = 32.0°)  as shown in the figure. (For aluminum on steel,  μs = 0.61  and  μk = 0.47.  For copper on steel,  μs = 0.53  and  μk = 0.36.)

A 4.15 kg4.15 kg box is suspended from a system of massless wires attached to a ceiling. The first wire makes an angle of ?1=63.0∘θ1=63.0∘ with the ceiling, whereas the second wire makes an angle of ?2=41.5∘θ2=41.5∘ with the ceiling.   Determine the magnitudes of the tensions in the first and second wires, ?1T1 and ?2,T2, respectively.

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.