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1- A toy racing moves with constant speed around the circle shown below. When it is at point A its coordinates are x = 0, y = 3m and its velocity is 6 m/s i. When it is at point B its velocity and acceleration are (respectively)?
The answer is 6 m/s j and 12 m/s^2 i, respectively. I got the magnitudes right, and I understand why its velocity is in the direction of j. However, why is its acceleration is in the direction i?
2- Two blocks (A and B) are in contact on a horizontal frictionless surface. A 36-N constant force is applied to A as shown. The magnitude of the force of A on B is?
3- A 0.20-kg particle moves along the x axis under the influence of a stationary object. The potential energy is given by U(x) = (8.0J/m^2)x^2 + (2.0J/m^4)x^4, where x is in coordinate of the particle. If the particle has a speed of 5.0 m/s when it is at x = 1.0 m, its speed when it is at the origin is?
(Any relations between potential energy and speed?)
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No need. Found the solution.
U(1) = 10 J. Kinetic Energy (x) = 0.5 * m * v ^ 2, so KE(1) = 2.5 J because v = 5 m/s when x = 1.
Mech Energy = U + KE = 12.5 J
When x = 0 then U = 0 and KE = 0.5 * m * v ^ 2.
Mech Energy is conserved, so:
E = 12.5 J --> 12.5 = U + KE --> 12.5 = 0 + 0.5 * m * v ^ 2, so v = 11.48 m/s.