A hammer of mass `500g`, moving at `50m//s`, strikes a nail. The nail stops the hammer in a very short time of `0.01 s`. What is the force of the nail on the hammer?

Explanation

To solve the problem of finding the force of the nail on the hammer, we can follow these steps:

### Step 1: Convert the mass of the hammer to kilograms
The mass of the hammer is given as 500 grams. To convert this to kilograms, we use the conversion factor \(1 \text{ kg} = 1000 \text{ g}\).

\[ \text{Mass (m)} = \frac{500 \text{ g}}{1000} = 0.5 \text{ kg} \]

### Step 2: Calculate the initial momentum of the hammer
The initial momentum (\(p_i\)) of the hammer can be calculated using the formula:

\[ p_i = m \times v \]

where \(v\) is the initial velocity of the hammer (50 m/s).

\[ p_i = 0.5 \text{ kg} \times 50 \text{ m/s} = 25 \text{ kg m/s} \]

### Step 3: Determine the final momentum of the hammer
Since the hammer comes to a stop after hitting the nail, its final momentum (\(p_f\)) is:

\[ p_f = 0 \text{ kg m/s} \]

### Step 4: Calculate the change in momentum
The change in momentum (\(\Delta p\)) is given by:

\[ \Delta p = p_f - p_i \]

Substituting the values we have:

\[ \Delta p = 0 - 25 = -25 \text{ kg m/s} \]

### Step 5: Use the impulse-momentum theorem
According to the impulse-momentum theorem, the impulse (force multiplied by time) is equal to the change in momentum:

\[ F \times t = \Delta p \]

Given that the time (\(t\)) taken to stop the hammer is 0.01 seconds, we can rearrange the formula to find the force (\(F\)):

\[ F = \frac{\Delta p}{t} \]

Substituting the values:

\[ F = \frac{-25 \text{ kg m/s}}{0.01 \text{ s}} = -2500 \text{ N} \]

### Step 6: Interpret the result
The negative sign indicates that the force exerted by the nail on the hammer is in the opposite direction to the hammer's motion. Therefore, the magnitude of the force is:

\[ F = 2500 \text{ N} \]

### Final Answer
The force of the nail on the hammer is **2500 N**.

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