How much work does it take to slide a crate 20 m along a loading dock by pulling on it with a 200-N force at an angle of 30 degrees from the horizontal?

A cylindrical tank half full of water is lying on its side. If the radius of the tank is 1m and the length is 2m, find the force against the end. Sketch the situation.

Answer Preview 73.25 73.25 51.27 Result correct correct incorrect

On the graph to the right, draw a coordinate axis. Draw in the two force vectors. Show by adding the vectors graphically that the net force on the central ring is zero. Verify this algebraically by showing that the sum of the. components is also zero. L +) = N the position. Now, notice that you can slide the ring back and forth along the r axis, placing it at any distance, and the ring will stay in place. This means that every point along the r axis is an equilibrium point. Explain why this is the case. The forces Cancel it does not matter FYEN Now we're going to change the axes. Remove the two pulleys, and place them at angles of 90° and 270°, respectively. Keeping the z axis along = 0, we've now placed the forces along the y axis. Repeat the earlier analysis with the new forces. 1D Trial 2 Results Force Magnitude (N) Direction (6) 0297 F₁ F₂ 0.48A/ 1 80 13 JEN Vector 0.294160 GrMB.NK 1800 F 11800

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Let a be the vector of length 126 that when drawn in standard position makes a 164° angle with the positive x-axis. Let b be the vector of length 36 that when drawn in standard position makes a 288° angle with the positive x-axis. Find the length of v = a + b and the angle ? that v makes with the positive x-axis when drawn in standard position. Round your approximations to three decimal places.

Consider a denolition crane with a 35-pound ball suspended from a 40-foot cable that weighs 6 pounds per foot. Exercise (a) Find the work required to wind up 15 feet of the apparatus. Step 1 Note that in the current situation, as the cable is pulled, the following things happen. 1. The ball gets lifted with a constant constant force. 2. The cable that is wound up gets lifted with a variable variable force. 3. The cable that doesn't get wound up is lifted with a constant constant force. Step 2 Calculate the work done, W,, in pulling up the ball while winding up 15 ft of the apparatus. W, = force x distance = 35 x 15 = 525 525 ft-lb Step 3 Consider an elemental length Ay, of the cable that gets wound up. As the cable weighs 6 pounds per feet: Weight = 6 Ay. Suppose it is at a vertical distance y from the winding engine, then Distance moved = (6 15 -) ft. a e Type here to search

Let f(x, y) = xex - y and P = (9, 81). (a) Calculate || Vfp||- ||Vfel| =| (b) Find the rate of change of f in the direction Vfp. (c) Find the rate of change of f in the direction of a vector making an angle of 45° with Vfp.

Find the work done by the force F = 2i - 7j in moving an object from the point (2, 1) to the point (9, -16). W =