Answer :
ANSWER
[tex]\begin{gathered} A)67.24Nm \\ B)58.23Nm \end{gathered}[/tex]EXPLANATION
Parameters given:
Force exerted on door, F = 82N
Width of door, r = 82 cm = 0.82 m
A) Torque is described as a force that tends to cause rotation and it is given mathematically as:
[tex]\tau=r\cdot F\cdot\sin \theta[/tex]where F = force, r = radius, θ = angle between the force and the arm of the lever.
From the question, the radius r is 82 cm (0.82 m) since the door pivots at its edge and because the force is acting perpendicularly, the angle θ is 90 degrees.
Therefore, the torque is:
[tex]\begin{gathered} \tau=0.82\cdot82\cdot\sin 90 \\ \tau=67.24Nm \end{gathered}[/tex]B) Now, the force is acting at an angle of 60 degrees to the face of the door.
This means that θ is 60 degrees.
Therefore, the torque is:
[tex]\begin{gathered} \tau=0.82\cdot82\cdot\sin 60 \\ \tau=58.23Nm \end{gathered}[/tex]