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...

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.