A Hammer weighing 3kg strikes the head of a nail with a speed of 2m/s and drives it by 1cm into the wall. find the impulse?
1cm = 0.01m
0.01m= 1/2(10.0)t
t= 0.01m/2.0m s^-1
= 0.002s
Accelaration = -10.0m/s/0.002s
= -5000m/s^2
Impulse =change in momentum
=M(v-u)
=3kg (0-2m/s)
=-6kg m/s
Impulse = M*V = 3 * 2 = 6
A hammer weighing 3kg strikes the head of A nail with a speed of 2mper sec drives by 1cm into the wall the impulse imparted to the wall is
To find the impulse, we can use the formula:
Impulse = Force × Time
We can calculate the force using Newton's second law:
Force = Mass × Acceleration
First, let's calculate the acceleration of the nail. Given that the nail moves 1cm into the wall, we can convert it to meters: 1cm = 0.01m.
We can use the kinematic equation to calculate the acceleration:
v^2 = u^2 + 2as
Where:
v = final velocity (0m/s since the nail comes to a stop)
u = initial velocity (2m/s)
a = acceleration
s = displacement (0.01m)
Rearranging the equation:
a = (v^2 - u^2) / (2s)
a = (0 - (2^2)) / (2 * 0.01)
a = -4 / 0.02
a = -200 m/s^2
Since the acceleration is negative, it indicates that the hammer is slowing down the nail.
Now we have the acceleration, we can calculate the force:
Force = Mass × Acceleration
Given that the hammer has a mass of 3kg, we can substitute the values:
Force = 3kg × (-200 m/s^2)
Force = -600 N
The negative sign indicates that the force acts in the opposite direction of the hammer's motion.
So the force applied to the nail is -600 Newtons.
Next, we need to calculate the time taken for the nail to come to a stop. Since no time is provided in the question, we need to use another equation:
v = u + at
Where:
v = final velocity (0m/s)
u = initial velocity (2m/s)
a = acceleration (-200 m/s^2)
t = time (unknown)
0 = 2 + (-200) × t
-2 = -200t
t = (-2) / (-200)
t = 0.01s
Therefore, the time taken for the nail to come to a stop is 0.01 seconds.
Now we can calculate the impulse:
Impulse = Force × Time
Substituting the values we obtained:
Impulse = -600 N × 0.01 s
Impulse = -6 N·s
Therefore, the impulse applied to the nail is -6 Newton-seconds.