Question

A constant force of 5N acts for 5sec on a mass of 5kg initially at test. Calculate the final momentum

Answer 1

To calculate the final momentum of the mass after a force has acted on it, we can use the following steps:

1. **Calculate the acceleration (a)** using Newton's second law of motion:
\[
F = m \cdot a
\]
where:
- \( F \) = force (5 N)
- \( m \) = mass (5 kg)

Rearranging gives:
\[
a = \frac{F}{m} = \frac{5 \, \text{N}}{5 \, \text{kg}} = 1 \, \text{m/s}^2
\]

2. **Calculate the change in velocity (∆v)** using the formula:
\[
\Delta v = a \cdot t
\]
where:
- \( t \) = time (5 seconds)

So:
\[
\Delta v = 1 \, \text{m/s}^2 \cdot 5 \, \text{s} = 5 \, \text{m/s}
\]

3. **Determine the final velocity (v)** of the mass. Since it starts from rest (initial velocity \( u = 0 \)):
\[
v = u + \Delta v = 0 + 5 \, \text{m/s} = 5 \, \text{m/s}
\]

4. **Calculate the final momentum (p)** using the formula:
\[
p = m \cdot v
\]
Substituting the mass and final velocity:
\[
p = 5 \, \text{kg} \cdot 5 \, \text{m/s} = 25 \, \text{kg m/s}
\]

Thus, the final momentum of the mass is \( \boxed{25 \, \text{kg m/s}} \).