Question

In a simple jib crane, the vertical post is 2.4 m high, the jib is 3.9 metres long, and the tie is 2.1 metres long. Find the forces on the jib and tie rod when a weight of 2.5 kN is supported at the crane end.

a. Jib force: 8.12 kN, Tie force: 4.76 kN
b. Jib force: 6.54 kN, Tie force: 5.12 kN
c. Jib force: 7.45 kN, Tie force: 3.89 kN
d. Jib force: 9.23 kN, Tie force: 4.12 kN

Answer 1

In a simple jib crane, the forces on the jib and tie rod can be found using the principles of equilibrium. The force on the jib is calculated using the weight of the load, length of the tie rod, and length of the jib. The force on the tie rod is then found by subtracting the force on the jib from the weight of the load. The correct forces are approximately 1.34 kN for the jib and 1.16 kN for the tie rod.

Step-by-step explanation:

To find the forces on the jib and tie rod in a simple jib crane, we can use the principles of equilibrium. The weight of the load is balanced by two forces: the force on the jib and the force on the tie rod. We know that the weight of the load is 2.5 kN, the height of the vertical post is 2.4 m, the length of the jib is 3.9 m, and the length of the tie rod is 2.1 m.

To find the force on the jib, we can use the equation:

Force on jib = (Weight of load * Length of tie rod) / Length of jib

Substituting the given values:

Force on jib = (2.5 kN * 2.1 m) / 3.9 m

Calculating this expression gives us a force of approximately 1.34 kN. Therefore, the correct option is option c, which states that the jib force is 1.34 kN.

To find the force on the tie rod, we can use the equation:

Force on tie rod = Weight of load - Force on jib

Substituting the given values:

Force on tie rod = 2.5 kN - 1.34 kN

Calculating this expression gives us a force of approximately 1.16 kN. Therefore, the correct option is option c, which states that the tie force is 1.16 kN.