A hammer weighing 1 kg moving with a speed of 10m/s strikes the head of a nail driving it 10cm into a wall Neglecting the mass of the nail calculate 1) ?The acceleration 2) time interval 3) impulse?

Question

Answer

1) The acceleration:
To calculate the acceleration, we can use the equation:
Acceleration (a) = Change in velocity (Δv) / Time taken (Δt)

Given that the hammer is initially at rest and then moves with a speed of 10 m/s, the change in velocity is:
Δv = 10 m/s

However, we need to find the time interval first.

2) The time interval:
To find the time interval, we can use the equation:
Distance (d) = Initial velocity (u) × Time (t) + (1/2) × Acceleration (a) × Time (t)^2

In this case, the hammer strikes the nail and drives it 10 cm into the wall, which is equivalent to a distance of 0.1 m. The initial velocity is zero since the hammer is at rest initially. We can rearrange the equation to solve for time:
0.1 m = 0 × t + (1/2) × a × t^2
0.1 m = (1/2) × a × t^2

Now we have two equations with two unknowns: a and t. We can substitute the value of acceleration (Δv / Δt) into the second equation and solve for time.

3) The impulse:
Impulse is defined as the change in momentum. Momentum (p) is calculated by multiplying mass (m) by velocity (v):
Momentum (p) = mass (m) × velocity (v)

Since the nail's mass is neglected, the momentum before and after the strike will be the same. Therefore, the impulse is zero.

To summarize:
1) The acceleration can be calculated using the equation a = Δv / Δt.
2) The time interval can be found by solving the equation 0.1 m = (1/2) × a × t^2.
3) The impulse is zero, as there is no change in momentum.

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