A hammer weighing of 1 kg moving with the speed of 10 m/s strikes the head of the nail driving it 10 cm into wall. Neglecting the mass of the nail, calculate the impluse.
Impulses = mass*change in speed
Impulse = 1kg * 10m/s = 10 kgm/s
To calculate the impulse, we need to use the impulse-momentum principle, which states that the impulse experienced by an object is equal to the change in its momentum.
The formula for impulse is given by:
Impulse = Force * Time
Since we are given the mass and speed of the hammer, we can calculate its momentum using the formula:
Momentum = Mass * Velocity
First, let's calculate the momentum of the hammer. Given:
Mass (m) = 1 kg
Velocity (v) = 10 m/s
Momentum = Mass * Velocity
Momentum = 1 kg * 10 m/s
Momentum = 10 kg⋅m/s
Now, we need to determine the force applied to the nail to drive it into the wall. We can use Newton's second law of motion, which states that force is equal to the rate of change of momentum.
The force required to drive the nail into the wall is equivalent to the impulse applied. Therefore:
Impulse = Force * Time
Since the mass of the nail is neglected, we can consider the interaction to be an elastic collision. This means that the hammer will exert its full momentum to the nail in a very short amount of time. We can assume the time is Δt = 0.
Therefore, the impulse is equal to the momentum of the hammer:
Impulse = Momentum
Impulse = 10 kg⋅m/s
The impulse experienced by the hammer when striking the nail is 10 kg⋅m/s.