A force of 50 N is used to push a wheelchair forward at constant velocity. If the wheelchair is displaced 0.5 m each second, what is the mechanical power expended when transporting the wheelchair?

Question

A force of 50 N is used to push a wheelchair forward at constant velocity.  If the wheelchair is displaced 0.5 m each second, what is the mechanical power expended when transporting the wheelchair?

Quizplus · Accepted Answer

11ecba2d_130f_7ef7_a3bf_0d9174a74e8d_MD0008_00 In some cases, determining the total quantity of work (W) done on or by a system is sufficient for describing the transfer or expenditure of energy. However, most energy-related phenomena do not occur instantaneously. Therefore, power (P) is used to quantify the magnitude of energy transfer or expenditure over time (t): 11ecba2d_130f_7ef8_a3bf_3597f0dafad4_MD0008_00 The SI unit for power is the watt (W), where 1 W is equal to 1 joule (J) of energy expended per second (s) of time. In the context of translational motion, power can be restated in terms of the change in energy per unit of time caused by the application of a force (F) over a distance (d): 11ecba2d_130f_7ef9_a3bf_9bb438ba24de_MD0008_00 The above expression relating power to mechanical work may also be rearranged and expressed in terms of the velocity (v) of the object acted on by the force: 11ecba2d_130f_7efa_a3bf_e9d4f7443171_MD0008_00 Therefore, the power expenditure associated with the motion of an object is equal to the product of the force required to move the object and the velocity at which the object moves. In the prompt, a 50 N force propels a wheelchair forward at a constant velocity. Because the wheelchair is displaced 0.5 m each second, the velocity of the wheelchair is equal to 0.5 m/s. Using this velocity, the power expenditure associated with the motion of the wheelchair is calculated as follows: 11ecba2d_130f_a60b_a3bf_198210831c33_MD0008_00 Because 1 N·m is equal to 1 J, the power required to propel the wheelchair forward is therefore: 11ecba2d_130f_a60c_a3bf_bdb30dbd6a34_MD0008_00 Educational objective: Power is the rate of energy transfer into or out of a system. In the context of translational motion, power is equal to the product of force and velocity.

A Force of 50 N Is Used to Push a Wheelchair