physics momentum and collision help!!?

Question

A cannon at rest with a mass of 1.2 x 10^3 kg fires a 53kg person out of it (horizontally) at a velocity of 67 m/s. What is the recoil velocity of the cannon?

Answer 1

Total Momentum Before = Total Momentum After
momentum of cannon and person = momentum of cannon + momentum of cannon
(1.2 x 10^3kg + 53kg)(0) =(1.2 x 10^3kg)Vc + 53kg(67m/s)
0 = (1.2 x 10^3 kg)Vc + 53kg(67m/s)
Vc = -53kg(67m/s)/1.2 x 10^3 kg) = -2.96 m/s ANS

teddy boy

Answer 2

The energy of the cannon in recoil does not equal the energy of the person; that is patently obvious when we work the conservation of momentum. Let V = the velocity of the person of mass m and v = the velocity of the cannon (the recoil) of mass M. The two momenta are equal, but opposite; so we have mV = Mv and v = (m/M) V, which is the recoil velocity you are looking for.

But check out the two kinetic energies...the cannon KE(M) = 1/2 Mv^2 = 1/2 M (m/M)^2 V^2 = 1/2 mV^2 = KE(m), which is the bullet KE; thus m^2/M = m or m/M = 1 and m = M when the kinetic energies are equal. Which means that v = V as well. So the only way the two energies can be equal is for the masses to be equal; a very unlikely case.

Answer 3

If each and every automobiles are traveling opposite innovations they frequently collide head on? Conservation of linear momentum. If the velocities are the equivalent, then the autos will shuttle contained in the direction of the better motor vehicle after the collision, yet at a slower velocity. The collision would be inelastic. climate or now no longer this is thoroughly inelastic relies upon. At a some distance better velocity the autos will in all probability mesh mutually contained in the supply way metallic and bring about a splendidly inelastic collision.

Answer 4

to answer this question, remember newton's first law says that every action has an equal, and opposite reaction

in this case, you fire a person out with a certain energy and the cannon must recoil with the same energy, written like this:
E of cannon = - E of person

in this case, we're talking kinetic energy, or the energy of moving objects. recall that kinetic energy is given by the equation:
E = mass * velocity^2 / 2

so, plugging kinetic energy into our first equation, you get

mass of person * velocity of person^2 / 2
=
mass of cannon * velocity of cannon^2 / 2

now you know the mass of both cannon and person, and you know the velocity of the person - all that is left for you to do is to solve this equation for the one unknown, the velocity of the person.

hope that helped!

Answer 5

Great answer Ben.. You of course meant your last word to be cannon.

Answer 6

It's often unclear whether you have all the energy terms for conservation of energy. HOWEVER, conservation of momentum is ALWAYS true.