Activity 1: Crane

1. Hold the jib of the given crane in a position such that the angle θ between the jib and the pedestal is 60˚.

2. Put a load of 100 grams at the free end of the jib.

3. Attach the other end of the string to points at 2 different positions (A, B) either on the pedestal or the wall.

4. Record the force (F) of the string in Table A for each of the positions.

Table A:

Angle of Jib (Q) = 60o / Position
A / B
Measured Force in string (Newton)
Fmin,60o = (measured) / ______

5. What is the minimum value of F that you measured in the string?

6. Mathematically determine the minimum value of F. Draw a free-body diagram and show all calculations. Omit self-weight of the jib. Tip: regard θ as a constant and then find .

Free body Diagram:

Fmin,60o = (calculated) / ______

7. Compare the mathematical and experiment results, and calculate the relative error. Show calculations.

Relative error (%) =

8. Vary the angle θ to different values such as 45˚, and 75˚. Repeat step 4 with the varying values of θ.

Angle = 45o

Table B

Angle of Jib (Q) = 45o / Position
A / B
Measured Force in string ( N )
Fmin,45o = (measured) / ______

Angle = 75o

Table C

Angle of Jib (Q) = 75o / Position
A / B
Measured Force in string ( N )
Fmin,75o = (measured) / ______

9. Figure out a way to improve the design of the given crane without using the wall (There is not a wall in a real crane) so that the force in the string is reduced. Draw your improved design, if any, on this worksheet.

10. With your improved crane, repeat Step 8.

Improved Design w/ Angle = 60o

Table D

Angle of Jib (Q) = 60o / Position
A / B
Measured Force in string ( N )
Fmin,60o = (measured) / ______

Improved Design w/ Angle = 45o

Table E

Angle of Jib (Q) = 45o / Position
A / B
Measured Force in string ( N )
Fmin,45o = (measured) / ______

Improved Design w/Angle = 75o

Table H

Angle of Jib (Q) = 75o / Position
A / B
Measured Force in string ( N )
Fmin,75o = (measured) / ______

11. Compare the magnitude of the string’s Fmin of the Improved Design to that of the string’s Fmin of the Initial Design (Step 4 and 8).

Initial Design Fmin (measured) / Improved Design Fmin (measured) / Comparisons
Angle of Jib (Q) = 60o
Angle of Jib (Q) = 45o
Angle of Jib (Q) = 75o