A pendulum is 0.9 m long and the bob has a mass of 1.0 kg. At the bottom of its swing, the bob's speed is 1.5 m/s. What is the tension in the string at the bottom of the swing?

To find the tension in the string at the bottom of the swing, we can use the concept of centripetal force.

First, let's consider the forces acting on the bob at the bottom of the swing.

1. Tension force (T): This is the force exerted by the string on the bob, directed towards the center of the circular path.

2. Gravitational force (mg): This is the force exerted by the Earth on the bob, acting vertically downwards.

At the bottom of the swing, the tension force (T) is providing the centripetal force, which keeps the bob moving in a circular path. The formula for centripetal force is:

Fc = mv^2 / r

where Fc is the centripetal force, m is the mass of the bob, v is the speed of the bob, and r is the radius (length of the pendulum).

From the given information, we know that the mass of the bob (m) is 1.0 kg, the speed (v) is 1.5 m/s, and the length of the pendulum (r) is 0.9 m.

Substituting these values into the formula, we have:

Fc = (1.0 kg) * (1.5 m/s)^2 / 0.9 m

Simplifying this equation, we get:

Fc = 2.5 N

Therefore, the tension in the string at the bottom of the swing is 2.5 N.