B 1.2 m 0.6 m
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For the pipe assembly of Prob. 4.101, determine (a) the largest permissible value of a if the assembly is not to tip, (b) the corresponding tension in each wire.
(Reference to Problem 4.101):
Two steel pipes AB and BC , each having a mass per unit length of 8 kg/m, are welded together at B and supported by three vertical wires. Knowing that a= 0.4 m, determine the tension in each wire.
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- a PROBLEM 5.96 Consider the composite body shown. Determine (a) the value of when h=L/2, (b) the ratio h/L for which x = L. xThree identical cylinders of radius r are placed inside a hollow cylinder of radius R. All cylinder axes (perpendicular to the paper) are horizontal. There is no friction. The cylinders B and C are on the verge of separating (= infinitesimally separated, as shown). A B (a) From the statics equations for A and B, show that the angle between the normal under B and the vertical is given by tan 0 1 (The same result is obtained for A and C, of course, since B 3/3 and C have mirror image forces on them.) (b) By trigonometry of geometry, show that R must be r(1+2/7 Jin order for B and C to be on the verge of separating. (Find sin 0 and cos 0 from a triangle; don't find 0.) (Problem from a senior-year high school physics book used in England.) ogboProblem 1: A meter stick has mass m = .2 kg (distributed uniformly along its length) and a length of (of course) 1 meter. The stick is placed simultaneously on two weight scales: one at the 20 cm mark (with 0 cm at the far left end of the stick), the other at the 70 cm mark, with no other supports or weights. Remember that a weight scale supplies an upward force, equal to the reading on the scale. Calculate the reading on both scales. Call the reading on the left scale (at 20 cm) FL, and the reading on the right scale (at 70 cm) FR. 20 cm 70 cm
- A block of mass m = 240 kg rests against a spring with a spring constant of k = 550 N/m on an inclined plane which makes an angle of θ degrees with the horizontal. Assume the spring has been compressed a distance d from its neutral position. Refer to the figure. (a) Set your coordinates to have the x-axis along the surface of the plane, with up the plane as positive, and the y-axis normal to the plane, with out of the plane as positive. Enter an expression for the normal force, FN, that the plane exerts on the block (in the y-direction) in terms of defined quantities and g. (b) Denoting the coefficient of static friction by μs, write an expression for the sum of the forces in the x-direction just before the block begins to slide up the inclined plane. Use defined quantities and g in your expression. (c) Assuming the plane is frictionless, what will the angle of the plane be, in degrees, if the spring is compressed by gravity a distance 0.1 m? (d) Assuming θ = 45 degrees and the…(0, 1, 0) is Consider a two-dimensional incompressible flow in the xz plane: u = - ey x Vo, where e the unit vector perpendicular to the xz plane. Denote the two velocity components in the xz plane as u and w in the x, z directions, respectively. Write down the expressions for them in terms of o. If the function of o assumes = x2² calculate the values of u and w at the coordinate x = = 2, z = 1. Ou= Ou= 86 əz > Ou=- - 86 əx W= ap dz 7 W= W= 8p Əz ap əz " ap " əI u = 4, w = -1 u = -1, w = 4 u = −4, w = 1 86 0₂7 86 Ou=- W=- u= -1, w = -4 5 dr =2.16* A golfer hits his ball with speed v at an angle & above the horizontal ground. Assuming that the angle is fixed and that air resistance can be neglected, what is the minimum speed vä(min) for which the ball will clear a wall of height h, a distance d away? Your solution should get into trouble if the angle is such that tan