Question

You are in charge of a cannon that exerts a force 11500 N on a cannon ball while the ball is in the barrel of the cannon. The length of the cannon barrel is 1.7 m and the cannon is aimed at a 49.3 ◦ angle from the ground. The acceleration of gravity is 9.8 m/s 2 . If you want the ball to leave the cannon with speed v0 = 72.3 m/s, what mass cannon ball must you use? Answer in units of kg.

Answer 1

Answer:

m = 7.48 kg

Explanation:

force (f) = 11,500 N

length of barrel (s) = 1.7 m

angle above the ground = 49.3 degrees

acceleration due to gravity (g) = 9.8 m/s^{2}

initial velocity (u) = 0 m/s

final velocity (v) = 72.3 m/s

mass (m) = ?

force = mass (m) x acceleration (a)

acceleration (a) = force / mass (m)

acceleration (a) = 11500 / m

applying the equation of motion $v^{2} = u^{2} + 2as$ , we can get the mass

$72.3^{2} = 0^{2} + (2 x \frac{11500}{m} x 1.7 )$

5227.3 = 0 + $\frac{39100}{m}$

m =  $\frac{39100}{5227.3}$

m = 7.48 kg