The bob of a simple pendulum of length 1 m has mass 100 g and a speed of 1.4 m/s at the lowest point in its path. Find the tension in the stirng at this instant.

Explanation

To find the tension in the string of a simple pendulum at the lowest point in its path, we can follow these steps:

### Step 1: Identify the forces acting on the bob
At the lowest point of the pendulum's swing, two forces act on the bob:
- The gravitational force (weight) acting downward, \( F_g = mg \)
- The tension in the string acting upward, \( T \)

### Step 2: Calculate the weight of the bob
The mass of the bob is given as 100 g, which we need to convert to kilograms:
\[ m = 100 \, \text{g} = 0.1 \, \text{kg} \]
Now, we can calculate the weight:
\[ F_g = mg = 0.1 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 0.98 \, \text{N} \]

### Step 3: Use centripetal force equation
At the lowest point, the net force acting on the bob is the centripetal force required to keep it moving in a circular path. The centripetal force is given by:
\[ F_c = \frac{mv^2}{r} \]
where:
- \( v = 1.4 \, \text{m/s} \) (speed at the lowest point)
- \( r = 1 \, \text{m} \) (length of the pendulum)

Substituting the values:
\[ F_c = \frac{0.1 \, \text{kg} \times (1.4 \, \text{m/s})^2}{1 \, \text{m}} = \frac{0.1 \times 1.96}{1} = 0.196 \, \text{N} \]

### Step 4: Write the equation for tension
At the lowest point, the tension in the string must support both the weight of the bob and provide the necessary centripetal force. Therefore, we can express the tension as:
\[ T = F_g + F_c \]
Substituting the values we calculated:
\[ T = 0.98 \, \text{N} + 0.196 \, \text{N} = 1.176 \, \text{N} \]

### Final Answer
The tension in the string at the lowest point is:
\[ T = 1.176 \, \text{N} \]

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