Question

(Show all steps please) there is no mass for the box

Equilibrium: A plank, 40 m long rests on two pylons positioned at each end. The plank is inclined at 10 degrees with the left side higher than the right side. The plank is 40 kg. A box rests at a point 5 m from the left side.

A) Draw a free body diagram of the system.

B) Write down an expression for calculating the torque that includes force, the lever arm and the sin function.

C) Use newton’s second law to the sum of the torques on the system.

D) Use newton’s second law to the sum of the forces on the system.

E) Find the force exerted downward on the left most pylon.

Answer 1

A. Following is the FBD of the system

B. net torque about the left pylon can be written as

taking anticlockwise torque to be +ve

T = W2*cos(theta)*5 - N*5 + W1*cos(theta)*20 - T2*40*cos(theta)

C. From newtons second law

T = 0 ( as the plank is stationary)

hence

W2*cos(theta)*5 - N*5 + W1*cos(theta)*20 - T2*40*cos(theta) = 0

D. Also, From newtons second law

N = W2*cos(theta)

hence

W1*cos(theta)*20 - T2*40*cos(theta) = 0

E. W1 = 40*9.81

T2 = 40*9.81*cos(10)*20/40*cos(10)

T2 = 196.2 N

and

T1*40*cos(10) = 40*9.81*cos(10)*20

hence

T1 = 196.2 N