Question
Using equation of newton's second law of motion, derive impulse of a force
Answers
GPT 3.5
Newton's second law of motion states that the force acting on an object is equal to the rate of change of momentum of that object. Mathematically, this can be expressed as:
\[ F = \frac{\Delta p}{\Delta t} \]
Where:
- \( F \) is the force acting on the object
- \( \Delta p \) is the change in momentum of the object
- \( \Delta t \) is the time over which the force acts
To find the impulse of a force, we need to calculate the change in momentum of the object over a certain time interval. The impulse of a force can be defined as the product of the force and the time interval over which the force acts:
\[ J = F \cdot \Delta t \]
By substituting the equation of Newton's second law into the equation for impulse, we get:
\[ J = \left( \frac{\Delta p}{\Delta t} \right) \cdot \Delta t \]
\[ J = \Delta p \]
Therefore, the impulse of a force is equal to the change in momentum of the object.
\[ F = \frac{\Delta p}{\Delta t} \]
Where:
- \( F \) is the force acting on the object
- \( \Delta p \) is the change in momentum of the object
- \( \Delta t \) is the time over which the force acts
To find the impulse of a force, we need to calculate the change in momentum of the object over a certain time interval. The impulse of a force can be defined as the product of the force and the time interval over which the force acts:
\[ J = F \cdot \Delta t \]
By substituting the equation of Newton's second law into the equation for impulse, we get:
\[ J = \left( \frac{\Delta p}{\Delta t} \right) \cdot \Delta t \]
\[ J = \Delta p \]
Therefore, the impulse of a force is equal to the change in momentum of the object.