A 87 kilogram block is pushed along a rough horizontal surface by a constant hor

Question

A 87 kilogram block is pushed along a rough horizontal surface by a constant horizontal force F as shown above. At time t = 0, the velocity v of the block is 7.1 meters per second in the same direction as the force. The coefficient of sliding friction is 0.20. (a) Calculate the force F necessary to keep the velocity constant. N The force is now changed to a larger constant value F'. The block accelerates so that its kinetic energy increases by 63 joules while it slides a distance of 3.9 meters. (b) Calculate the force F'. N (c) Calculate the acceleration of the block. m/s2

Explanation / Answer

A 10-kilogram block is pushed along a rough horizontal surface by a constant horizontal force F as shown above. At time t = 0, the velocity v of the block is 6.0 meters per second in the same direction as the force. The coefficient of sliding friction is 0.2. Assume g = 10 meters per second squared. a. Calculate the force F necessary to keep the velocity constant. The force is now changed to a larger constant value F'. The block accelerates so that its kinetic energy increases by 60 joules while it slides a distance of 4.0 meters. b. Calculate the force F'. c. Calculate the acceleration of the block a) For constant velocity F = frictional force = µmg = 0.2*10*10 = 20N =============== b) Net Force* distance = increase in energy. (F’-F)*d = 60 => (F’-F) = 60/4 = 15 N And F’= 15+20 = 35 N ===================== C) a = (F’-F)/m =15/10 = 1.5 m/s² or a = 60/(4*10) = 1.5 m/s² ======================

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