a 20-g projectile strikes a mud bank penetrating a distance of 6 cm before stopping. find the stopping force F if the entrance velocity is 80 meter per second.
same as last one
F * d = (1/2) m v^2
D * .06 = (1/2) *.020 * 6400
Am not comfortable with the work I mean show full working thanks
To find the stopping force (F), we can use the equation of motion:
F = (mv^2) / (2d)
where:
F = stopping force
m = mass of the projectile (20 g = 0.02 kg)
v = entrance velocity (80 m/s)
d = distance penetrated (6 cm = 0.06 m)
Substituting the given values into the equation, we get:
F = (0.02 kg * (80 m/s)^2) / (2 * 0.06 m)
Calculating the equation, we have:
F = (0.02 kg * 6400 m^2/s^2) / (0.12 m)
F = 128 N
Therefore, the stopping force (F) is 128 Newtons.
To find the stopping force F, we can use the equation for impulse.
The impulse of an object can be calculated using the equation:
Impulse = Change in momentum
The change in momentum can be calculated using the equation:
Change in momentum = Final momentum - Initial momentum
In this case, the initial momentum is given by the mass of the projectile multiplied by the initial velocity:
Initial momentum = mass × initial velocity
The final momentum is given by the mass of the projectile multiplied by the final velocity, which in this case is zero since the projectile stops:
Final momentum = mass × final velocity
Since the final velocity is zero:
Final momentum = 0
The change in momentum is therefore:
Change in momentum = 0 - (mass × initial velocity)
= -mass × initial velocity
Now, let's rearrange the equation for impulse to solve for the stopping force F:
Impulse = Change in momentum
Impulse = Force × time
Rearranging the equation:
Force = Impulse / time
In this case, we need to find the stopping force F, so we rearrange the equation and solve for F:
F = Impulse / time
However, we don't know the time it takes for the projectile to stop. To find the time, we need to use the equation for average speed:
Average speed = distance / time
In this case, the average speed is the initial velocity. Therefore:
Average speed = initial velocity
Rearranging the equation:
time = distance / average speed
Now, we have all the components we need to find the stopping force F.
First, let's calculate the change in momentum using the mass and initial velocity given:
Change in momentum = -mass × initial velocity
Next, calculate the time it takes for the projectile to stop using the given distance and initial velocity:
time = distance / average speed
= 6 cm / (80 m/s)
= 0.06 m / (80 m/s)
= 0.00075 s
Finally, substitute the values into the equation to find the stopping force F:
F = Change in momentum / time
= (-mass × initial velocity) / time
Note: You need to provide the mass of the projectile to calculate the stopping force accurately.