In Fig. 12-69, a package of mass m hangs from a short cord that is tied to the wall via cord 1 and to the ceiling via cord 2. Cord 1 is at angle with the horizontal; cord 2 is at angle. (a) For what value of is the tension in cord 2 minimized? (b) In terms of mg, what is the minimum tension in cord 2
a) The angle of cord 2 with the horizontal i.e. .
b) The minimum tension in cord 2 in terms of mg is the.
From the Free Body Diagram and condition for static equilibrium of the system, we can find the angle and the tension in cord 2.
As the value in the should be minimum, we take derivative at both sides, and we get,
As we know,
The minimum tension in cord 2 in terms of mg is the.
Figure 12-65a shows a uniform ramp between two buildings that allows for motion between the buildings due to strong winds.At its left end, it is hinged to the building wall; at its right end, it has a roller that can roll along the building wall. There is no vertical force on the roller from the building, only a horizontal force with magnitude . The horizontal distance between the buildings is . The rise of the ramp is. A man walks across the ramp from the left. Figure 12-65b gives as a function of the horizontal distance x of the man from the building at the left. The scale of the axis is set by a = 20kN and . What are the masses of (a) the ramp and (b) the man?
A uniform cube of side length rests on a horizontal floor.The coefficient of static friction between cube and floor is m. A horizontal pull is applied perpendicular to one of the vertical faces of the cube, at a distance above the floor on the vertical midline of the cube face. The magnitude of is gradually increased. During that increase, for what values of will the cube eventually (a) begin to slide and (b) begin to tip? (Hint: At the onset of tipping, where is the normal force located?)
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