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What is the power required to give a body of a mass 'm' a forward acceleration 'a' when it ismoving with velocity 'V' up a frictionless trackinclined at an angle 'O' to the horizontal? |
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Answer» Power = Work done / time = Force x velocityThe track is frictionless, so no frictional force acts on the mass.If the track was horizontal, the power required to give the mass m a forward ACCELERATION a when it is moving with velocity v is given byPower = Force x velocity = (ma) x v = mavBut in this case, the track is inclined at an angle O to the horizontal. The COMPONENT of the WEIGHT of the mass (against motion) along the track is mg SIN O. Therefore, a force is required to keep the mass stationary (from moving down along the inclined track). This force should be equal in magnitude to the component of the weight so that the RESULTANT acceleration (when considering only the component of the weight and this force) is zero.This force would result in a power of mg sin O x v = mgv sin O.So total power = mav + mgv sinO |
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