Question

a cannon has a mass 2500. it fires a cannon-Ball during a routine exercise. the cannon is 1000 times heavier than the cannon ball. the cannon ball leaves the barrel at a horizontal velocity of 160 m/s. the cannon comes to rest 2 seconds after the cannon ball was fired. calculate the magnitude of average net force that causes the cannon to rest​

Answer 1

F = 200 [N]

Step-by-step explanation:

To solve this problem we must use the principle of conservation of linear momentum, which can be calculated by means of the following equation.

`P=m*v`

where:

P = lineal momentum [kg*m/s]

m = mass [kg]

v = velocity [m/s]

Now we must understand that the momentum is conserved before and after the firing of the cannon. Before firing the cannon we have the mass of the cannon and mass of the cannonball together at rest (speed = 0). After firing the cannon the cannonball moves forward with positive speed, while the cannon moves back (negative), in this way knowing the masses of each one we can determine the speed of the cannon.

`(m_(cannon)+m_(ball))*v_(1)=-(m_(cannon)*v_(2))+(m_(ball)*v_(3))`

where:

m_cannon = 2500 [kg]

m_ball = 2.5 [kg]

v₁ = 0 (velocity of the group before firing)

v₂ = velocity of the cannon after firing [m/s]

v₃ = 160 [m/s] (velocity of the cannonball after firing)

`(2500+2.5)*0 = -(2500*v_(2))+(2.5*160)\\v_(2)=0.16[m/s]`

Now using the following equation of kinematics, we can calculate the acceleration.

`v_(f)=v_(o)-a*t`

where:

Vf = final velocity = 0 (cannon comes to rest)

Vo = initial velocity = 0.16 [m/s]

a = acceleration [m/s²]

t = time = 2 [s]

`0 = 0.16 - a*2\\2*a=0.16\\a = 0.08 [m/s^(2)]`

With the value of acceleration, we can use Newton's second law which tells us that the forces acting on a body is equal to the product of mass by acceleration.

ΣF = m*a

where:

F = force [N] (units of Newtons)

m = mass = 2500 [kg]

a = acceleration = 0.08 [m/s²]

`F = 2500*0.08\\F = 200 [N]`