Question

Lever.

We can make a lever by placing a bar on a pivot. Suppose the bar is 5 meters long. A 20 kg kid and an 80 kg adult seat at two terminals of the bar individually. Initially, the bar is along horizontal direction.

A. There are totally three forces exerted on the lever: the force exerted by the kid, the force exerted by the adult and the supporting force exerted at the pivot. What is the value of the arm for the last mentioned above force about the pivot? Then what is the value of the torque generated by the last mentioned above force about the pivot?

B. Suppose the kid seats at the left terminal, the adult seats at the right terminal, then please show the trend of rotation due to the kid (clockwise or counter-clockwise), and also trend due to the adult.

C. If the lever is balanced, what is the position of the pivot? Mass of kid and adult could be denoted as and , the arm could be denoted as

D. Suppose we slightly hit the system, then the lever rotates an angle counter-clockwise. Please solve the arm , in the current case ( is not given explicitly, so keep it in the result as a parameter). Then check whether the system is still in balance (whether the net torque is zero).

E. If we establish a coordinate system, set pivot as origin, then what will be the value of the vertical coordinates of the two person (after the rotation)? Calculate the gravitational potential energy of the system (after the rotation). Is this result related to the angle ?

F. Find the coordinates of the center-of-mass of the system (after rotation). Is this consistent with your result in 4)?

G. If we design an elevator using this model, what will be the advantage of the elevator?

Last mentioned above force= supporting force exerted at the pivot

Answer 1

A. The arm fo foce at pivot about pivot is zero only, and torque is also zero as torque is forceX distance and distance is zero.

B, Since the boy sits at left end, so its weight will create a toque in anticlockwise direction, so it will tend to rotate in anticlockwise direction, similarily the adult weight will tend to rotate clockwise as he sits in the right end.

C. If the lever is balanced, then let the distance of pivot from kid is x then from adult it will be 5-x

for balanced lever, weight of kid X x = weight of adult X (5-x)

solving we get x = 4metre

D. fo other parts see the image below: