# EXPERIMENT

### OBJECTIVE:

To Verify Lami’s theorem by finding the forces in the different members of a Jib-crane.

### APPARATUS REQUIRED:

Jib Apparatus, Weight, Meter Rod, Set Square, Pencil etc.

### THEORY: Lami’s Theorem states that If three coplanar concurrent forces are acting on a body and keeps the body in Equilibrium, then each force is proportional to the sine of the angle between the other two forces. ### PROCEDURE:

• Take the initial reading of forces in the compression spring balance of rod and tension spring balance of the tie rod.
• Suspend a known weight ‘w’ with the help of weight hanger.
• Take final reading of force in jib rod and tie rod of spring balance.
• From the final reading subtract the initial reading to get observed value of the forces in rod and tie rod.
• Measure the length of jib rod from the point on the platform, the position where string is attached, length of the tie rod and vertical height of the post.
• From the above measurement, draw the space diagram to a suitable scale and name the member by bow’s notation.
• Measure the internal angles contained between the two forces in vector diagram.
• Measure angle α, β and γ and apply Lami’s theorem to find out the forces in the member e.g.

W/sin α = P/sin β = R/sin γ

• Equating 1st and 2nd, we get,

W/sin α = P/sin β  or  P = (W . sin β )/sin α

• Similarly, equating 2nd and 3rd, we get,

P/sin β = R/sin γ or R = (P . sin γ)/sin β

• Compare the calculated values of forces with observed values and determine the percentage error.
• Repeat the experiment either by changing the load or by varying the length of the vertical post.

### OBSERVATION TABLE:

 S. No. Weight on post (W in kg) Length of members of jib crane (in cm) Initial Reading (I) (in kg) Final Reading (F) (in kg) Observed Value (F-I) (in kg) Calculated Force (in kg) Percentage Error of Force (in percentage) JIB TIE POST JIB TIE JIB TIE JIB TIE JIB TIE JIB (P1 – P)/P1 x 100 TIE (R1 – R)/R1 x 100

### PRECAUTIONS:

• Initial reading of the spring balance of tie rod and jib rod should be taken carefully.
• Weight should be suspended gently without any jerk.
• Measure the length of each member of jib crane with an extensible string.
• The spring balance  should be sensitive to give correct reading.
• The space and force diagram should be drawn correctly.