For P= 100 N, find P in component form.
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- Find the cross product →A × →C for (a) A = 2.0 ^i − 4.0 ^j + ^k and C = 3.0 ^i + 4.0 ^j + 10.0 ^k (b) A = 3.0 ^i + 4.0 ^j + 10.0 ^k and →C = 2.0 ^i − 4.0 ^j + ^k (c) A = −3.0 ^i − 4.0 ^j and →C = −3.0 ^i + 4.0 ^j (d ) →C = −2.0 ^i + 3.0 ^j + 2.0 ^k and A = −9.0 ^j Answer a and bSteel ball with radius of 0.13 m lays on a bottom of the lake 6 m deep. What work is needed to lift the ball to the surface of the lake? Density of steel is 7860kg/m3. The volume of a sphere is Use g = 9.8 m/s2 Calculate answer to two decimals.Answer the following question throughly
- Why is there a blue squiggly line over one of the arrows?A 11 N horizontal force F→ pushes a block weighing 4.1 N against a vertical wall (see the figure). The coefficient of static friction between the wall and the block is 0.56, and the coefficient of kinetic friction is 0.49. Assume that the block is not moving initially. (a) Will the block move? ("yes" or "no") (b) In unit-vector notation Fxî+Fyĵ, what is the force on the block from the wall?The height varies from h to zero according to this function: y(x) = h ( – 1)´ . The constants h and e replace 1.00 m and 3.00 m. There is also a thickness t and a density p. You need two integrals, the total mass and the center of mass. Possibly surprisingly, you don't actually need the numbers t, h, and p. Ax y(x) X The column at x has a mass Am = (density * volume) = y(x) p t Ax. You add all the Am values to get %3D the total mass M. The sum becomes an integral: М — pt y(x) dx For the center of mass, you add each column's x Am, and divide by M: pt Xc х у(x) dx Calculate xc. The only quantity you'll need is e = 5 m.
- 45° Tz T2 T. A cat burglar is planning a daring heist. He will lower himself from a beam as shown in the figure on the left. The burglar weighs 150 lbs. He plans to use a long rope that can withstand a tension of 100 lbs to suspend himself from a shorter rope, reasoning that each segment of the longer rope will only need to support half his weight. (The short rope segment is Kevlar and can easily support the burglar's full weight.) (a) Despite your moral outrage, you decide to set the burglar straight. Compute the tensions T1, T2, and T3 and explain why the plan will not work. (b) As a strictly intellectual exercise, you design an alternative arrangement of ropes that will support the burglar's weight using the same long rope from part (a). In the configuration on the right, what is the maximum angle 0 that will result in a tension of less than 100 lbs in each segment of rope? You may ignore the mass of the rope in parts (a) and (b).Calculate the average kinetic energy for 1. V(x) = x(5-xz) where x € [0,5]By finding the curl, determine which of the following forces are conservative: (a) F = ix +jy + kz (b) F = iy - jx + kz* (c) F = iy + jx + kz' 4.2 _3