A crank of length 190mm is initially at 65 degree above the horizontal, and rotates through 35 degree towards the horizontal. A vertically downward force of 160 N acts on the outer end of the crank. Calculate the work done by the force.

φ is the angle between the force ‘F’ and the crank ‘r’

φ₁=180°-90°-65° =25°
φ₂=180°-90°-30° =60°

The work is
dW= M•d φ=F•r•sinφ•dφ
W=∫ F•r•sinφ•dφ =-F•r•cosφ |₂₅⁶⁰= - =160•0.19• (0.5-0.9)=12.16 J

To calculate the work done by the force on the crank, we need to find the distance over which the force acts and the magnitude of the force.

First, let's find the distance over which the force acts. This can be calculated using the arc length formula:

Arc Length = (angle / 360) * 2 * π * radius

In this case, the angle is 35 degrees (since the crank rotates through 35 degrees towards the horizontal) and the radius is the length of the crank, which is given as 190mm or 0.19m.

Arc Length = (35 / 360) * 2 * π * 0.19

Next, let's calculate the magnitude of the force. The force is given as 160 N acting vertically downward. Since the crank makes an angle of 65 degrees above the horizontal, we can find the component of the force along the crank using trigonometry:

Force along the crank = force * cos(angle)

Force along the crank = 160 * cos(65)

Finally, we can calculate the work done by multiplying the distance over which the force acts by the magnitude of the force:

Work Done = Arc Length * Force along the crank

Work Done = ((35 / 360) * 2 * π * 0.19) * (160 * cos(65))

Now you can substitute the values into the equation to get the final result.