A 10-kilogram object is moving along the spiral parameterized by x(u): = u cos u and...

 

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A 10-kilogram object is moving along the spiral parameterized by x(u): = u cos u and y(u) = u sin u in the direction of increasing u. The variable u is not time. When the object is at the origin, its speed is 3 m/s and it is speeding up at the rate of 7 m/s. Compute the following quantities at that point. (You may not necessarily want to compute these in the order they are listed.) (a) The rate of change of arc length, ds/dt. (b) The velocity, v. (c) The tangential acceleration, ar. (d) The normal acceleration, an. (e) The unit tangent, T. (f) The unit normal, . (g) The unit binormal, B. (h) The curvature, K. (i) The torsion, 7. The force on the object. (k) The power being applied to the object. A 10-kilogram object is moving along the spiral parameterized by x(u): = u cos u and y(u) = u sin u in the direction of increasing u. The variable u is not time. When the object is at the origin, its speed is 3 m/s and it is speeding up at the rate of 7 m/s. Compute the following quantities at that point. (You may not necessarily want to compute these in the order they are listed.) (a) The rate of change of arc length, ds/dt. (b) The velocity, v. (c) The tangential acceleration, ar. (d) The normal acceleration, an. (e) The unit tangent, T. (f) The unit normal, . (g) The unit binormal, B. (h) The curvature, K. (i) The torsion, 7. The force on the object. (k) The power being applied to the object.

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To compute the quantities at the given point we need to find the expressions for velocity acceleration and other related vectors Lets calculate them s... View the full answer