Consider the figure above, where a rigid beam of negligible mass and 10 m long is supported by a cable attached to a spring. When NO block is hung from the beam, the length L (cable-spring) is equal to 5 m. Assume that immediately after block (weight of 260 N) is hung at the end of the beam the spring does not stretch, calculate the tension under this assumption. Using this tension find how much the spring stretches. Express the amount the spring is stretched in cm. k =8400 N/m.

To solve this problem, we need to analyze the forces acting on the beam and the cable-spring system. Let's consider the different scenarios separately.

Scenario 1: No block hanging from the beam

In this scenario, there is no additional force acting on the beam. Hence, the cable-spring system will be in equilibrium, and the tension in the cable will be equal to the weight of the beam. Since the beam has negligible mass, we can ignore its weight, and the tension in the cable will be zero.

Scenario 2: Block hanging from the beam

Now, let's consider the situation when a block with a weight of 260 N is hung from the end of the beam. In this case, we need to find the tension in the cable and the amount the spring stretches.

Since the system is in equilibrium, the sum of all the forces acting on the beam should be zero. There are two forces acting on the beam:

1. The weight of the block (260 N) acting downwards.
2. The tension in the cable acting upwards.

The equation for the equilibrium is:

Tension in the cable - Weight of the block = 0

Tension in the cable = Weight of the block (260 N)

So, the tension in the cable is 260 N.

To find the amount the spring stretches, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the amount the spring is stretched or compressed.

The equation for Hooke's Law is:

Force = spring constant * displacement

In this case, the force exerted by the spring is equal to the tension in the cable (260 N), and the spring constant (k) is given as 8400 N/m.

260 N = 8400 N/m * displacement

Rearranging the equation, we get:

displacement = 260 N / 8400 N/m

displacement = 0.031 m

Since we need to express the displacement in centimeters, we can convert 0.031 m to cm:

1 m = 100 cm

0.031 m = 0.031 * 100 cm

displacement = 3.1 cm

So, the spring stretches by 3.1 cm when the block is hung from the end of the beam.