# 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.

[frac up=”W” down=”sin α”] = [frac up=”P” down=”sin β”] = [frac up=”R” down=”sin γ”]

- Equating 1st and 2nd, we get,

[frac up=”W” down=”sin α”] = [frac up=”P” down=”sin β”] or P = [frac up=”(W . sin β )” down=”sin α”]

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

[frac up=”P” down=”sin β”] = [frac up=”R” down=”sin γ”] or R = [frac up=”(P . sin γ)” down=”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[frac up=”(P1 – P)” down=”P1″] x 100 |
TIE[frac up=”(R1 – R)” down=”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.

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