A winch operating at 1kW pulls a box of weight 980N up a smooth slope at a constant speed 2m/s. calculate the angle the slope makes with the horizontal
The winch is operating at 1kW. The work done by the winch in one second is 1 kJ. Assuming the slope is frictionless, the work done is only against the gravitational force of attraction of the Earth on the box which is 980 N.
If we assume the angle of the slope with respect to the horizontal as x, the force with which the box is pulled upwards can be divided into two components: one perpendicular to the ground and one along the ground. The component of the force perpendicular to the ground is equal to 1000*sin x. It is also equal to the weight of the box as the box moves upwards with a constant velocity.
1000* sin x = 980
=> sin x = 980/1000
=> x = arc sin (0.98)
x = 78.52 degrees
The angle made by the slope with the horizontal is 78.52 degrees.