Question

 The figure below is a long, massless stick with evenly spaced marks. The distance between two adjacent marks is 9.00 cm. In each of the following problems a pivot will be placed at a point on the stick. The pivot will hold that point fixed, but allow the stick to rotate. You will be finding conditions that will keep the stick in static equilibrium given different forces. All forces will be applied to the stick perpendicular to the length of the stick.

 A pivot is placed at Point B and a force of 32.0 N is directed downward perpendicular to the stick at Point D. What is the magnitude and direction of the force which must be applied at point A in order to obtain static equilibrium?

 A pivot is placed at Point E and a force of 16.0 N is directed downward perpendicular to the stick at Point L. What is the magnitude and direction of the force which must be applied at point D in order to obtain static equilibrium?

 A pivot is placed at Point B and a force of 24.0 N is directed downward perpendicular to the stick at Point G. One at a time, each of the following 3 forces are applied to the stick in the manner described. Where must these forces be applied in order to achieve static equilibrium? If the is no point that will work within reason, select the option None.

Answer 1

Magnitude of torque=r*F*sin, where r is position of the point where force is applied, F is force and is the angle between r and F.

For the 24 N force, F=24 N, r = 9*6=54 cm = 0.54 m and =90 deg.

So, torque= 0.54*24*sin90 = 12.96 N-m clockwise.

For equilibrium, a counter clockwise torque of 12.96 N-m is needed.

i)If F=72 N, then r*72*sin90=12.96 => r = 12.96/72 m = 0.18 m= 18 cm.( 2 divisions)

Since counterclockwise torque is needed and the force is downward, this force must be applied at C.

ii)If F=12 N, then r*12*sin90=12.96 => r = 12.96/12 m = 1.08 m= 108 cm.( 12 divisions)

Since counterclockwise torque is needed and the force is upward, this force must be applied act at a point to the right of B. But to the right of B only 7 divisions are there. So, the answer is none.

iii)If F=20.6 N, then r*20.6*sin90=12.96 => r = 12.96/20.6 m = 0.63 m= 63 cm.( 7 divisions)

Since counterclockwise torque is needed and the force is upward, this force must be applied act at a point to the right of B. So, the required point is point F.