State the definition of power.
A force $F$ acts for a time $t$ to move an object through a displacement $x$ at constant velocity $v$, in the same direction as the force. The work done by the force is $W$. Use the definition of power to show that the power $P$ transferred by the force is $P = Fv$.
A block is drawn up a slope by a wire connected to a motor, as shown in Fig. 3.1. The useful power output of the motor is $56\,\text{W}$. The block has a weight of $430\,\text{N}$ and moves with constant velocity along the slope at an angle of $11^{\circ}$ to the horizontal. Assume that there are no resistive forces opposing the block’s motion. Calculate the tension $T$ in the wire.
Calculate the speed of the block.
The rate at which the block’s gravitational potential energy increases is the same as the useful power output of the motor. One reason for this is that no work is done against resistive forces. By considering the motion of the block, state one further reason for this.
The motor’s efficiency is $80\%$. Calculate the time taken for an input energy of $1.2\,\text{kJ}$ to be delivered to the motor.