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By how much does the kinetic energy of particle change as it moves from a point

ID: 1488176 • Letter: B

Question

By how much does the kinetic energy of particle change as it moves from a point with (x,y) coordinates (7m,8m) to another with coordinates (9m, 8m) under the influence of a constant net force vector F = -4N wedge I + 3N wedge j ? Acting on an object is a conservative force with associated potential U = 3x^2 j where x is measured in m. What is the work done by the force on the object as it moves from x= 0 to x = 1m A block of mass m = 2.0 kg is attached to a Hooke's-law spring with force constant k = 8.0 N/m and is on a afractionless horizontal surface . The block is released from rest at position x = +2.5m. What is the speed of the block as it passes through equilibrium (x=0)?

Explanation / Answer

1. F = -4 i + 3 j

S = (9 i + 8 j) - (7 i +8j) = 2 i

Work = F.S = -4*2 = - 8 J

So change in kinetic energy = - 8J

2. Initial potential energy = 3*0^2 = 0

Final potential energy = 3*1^2 = 3 J

change in potential energy = 3 J

Work done by force = - change in potential energy = - 3 J

3. By conservation of energy

0.5kx^2 = 0.5mv^2

=> 8*2.5^2 = 2*v^2

=> v = 5 m/s