Question

A massless rod of length L = 2.3 m stands up straight, fixed to the ground by a bolt. A horizontal force of 8.2 N is applied at a vertical distance of L/2 to the right. To counter this force and keep the rod stationary, a wire is fixed at the top of the rod and attached to the ground some distance away to the left, making an angle of 45 degrees to the horizontal.

a) What is the tension in the wire, in N?

Answer: 5.798

b) Calculate the horizontal component of the force of the bolt on the rod, in N, taking right as positive.

Answer: -4.1

c) Calculate the vertical component of the force of the bolt on the rod, in N, taking up as positive.

Answer: 4.1

Suppose you’re building a contraption which contains a solid rod of length L = 11.1 m and mass 4.5 kg. This rod has its lower end barely above the ground at an angle of 23.7 degrees with respect to the horizontal, and is ultimately held up by a rope connected at a distance L/4 from the top of the rod making an angle of 25.4 degrees with respect to the rod. The top of the rod may rotate as it is held in place by a bolt connected to a wall. Calculate the tension in the rope which keeps the rod from touching the ground.

Answer: 188.475

Could you please write down the full solution?

Answer 1

Tension in the string has to be resolve into two component as

T*sin45 as Horizontal part and T*Cos45 as verticle part as shown in figure.

------------------------------------ part (a )----------------------------------

a) To find the Tension we can use the Torque Balance equation taking Bolt point as reference.

where d is verticle distance of the force from the pivot point.

------------------------------------ part (b )----------------------------------

To calculate the Horizontal force on the bolt, we have to balance the force in Horizontal direction

Total Horizontal force in +X direction = 8.2 N

Total Horizontal force in -X direction = F_b + TSin45

Since all force must be balanced so

So the horizontal component of the force of the bolt on the rod is -4.1 N

------------------------------------ part (c )----------------------------------

To calculate the Vertical force on the bolt, we have to balance the force in Verticle direction

Total Verticle force in +Y direction = Fc

Total Verticle force in -Y direction = TCos45

Since all force must be balanced so

So the Vertical component of the force of the bolt on the rod is 4.1 N

------------------------------------ 2nd Question ----------------------------------

There are two force that are acting on the Rod

1) Tension T which is making an angle with the rod and this force has been resolve into two component . Alonf the rod and perpendicular to the rod. This force is acting at a distance L/4 from Top as represented in the fig.

2) Force due to gravity due to the mass of the rod acting at L =L/2, which is also resolved into two component . along thye rod and perpendicular to the rod as shown in fig.

Since the system is at equilibrium so net Torque must be zero. Taking Top of the rod as pivot point we can write it as

So Tension in the string is 188.475 N