a body weighing 40N drops freely from a hieght of 50m and penetrates into the ground by 100cm.find the average resistance to penetration and the time of penetration.
Change in K E = work done
1/2m(v2^2-v1^2) =FS
Here v1 is the initial velocity and v2 ia the final velocity
V1=√2gh= √2×9.8×50=31.3 m/s( dropped from cliff)
V2=P*x= 0×1=0(pentration velocity)
1/2*(40/9.8)*(0-31.3^2) =mgx-Px
-1999. 36=40*9.8*1-P*1
P=2039.88 N
Average resistance (force) * (penetration distance) = (kinetic energy at impact)
F = M g H/X = 40*50/1 = 2000 N
Avg velocity during penetration *(Time) = (Penetration distance)
Time = X/(15.7 m/s) = 0.064 s
1960J
To find the average resistance to penetration and the time of penetration, we can use the equations of motion.
First, let's calculate the velocity at impact.
The initial velocity (u) of the body is 0 since it is dropped freely.
Using the equation of motion:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance.
Plugging in the values:
v^2 = 0^2 + 2 * 9.8 * 50
v^2 = 980
v = √980
v ≈ 31.3 m/s
Next, let's find the time of penetration.
Using the equation of motion:
v = u + at
Since the final velocity is 31.3 m/s, the initial velocity is 0 m/s, and the acceleration is 9.8 m/s^2 (due to gravity), we can rearrange the equation to solve for time (t).
31.3 = 0 + 9.8 * t
t = 31.3 / 9.8
t ≈ 3.20 s
Now, let's find the average resistance to penetration.
The resistance to penetration is equal to the force required to stop the body during penetration.
Using Newton's second law of motion:
Force = mass * acceleration
The mass of the body can be found by dividing the weight by the acceleration due to gravity.
Weight = mass * gravity
Given that the weight is 40 N and the acceleration due to gravity is 9.8 m/s^2:
40 = mass * 9.8
mass ≈ 4.08 kg
The resistance to penetration is the force required to stop the body. Since the body comes to rest, the net force acting in the upward direction must be equal to the weight.
Therefore, the average resistance to penetration is equal to the weight of the body, which is 40 N.
To summarize:
- The average resistance to penetration is 40 N.
- The time of penetration is approximately 3.20 seconds.