- #1

AN630078

- 242

- 25

- Homework Statement
- I have a mechanics question concerning an explosion of an object which I am truly struggling with. I think perhaps I have been thinking about it for too long to reach a credible solution.

An object of mass 16 kg is moving in the x direction at 35 m/s. The object explodes and breaks into three pieces. One piece, of mass 8 kg, continues moving in the x direction at 25 m/s. Another piece, of mass 5 kg, moves on at 30 m/s in a direction at 50o to the x direction.

Using a vector diagram find the speed and direction of the third fragment.

- Relevant Equations
- p=mv

Well, I understand that according to the conservation of momentum the total momentum of a system is conserved for objects in an isolated system, that is the sum of total momenta before the collison is equal to the sum of momenta after the collision.

In this case, the momentum of the object before the collison is equal to p=mv=16*35=560 kg ms^-1

The first piece has a momentum of; P1=8*25=200kgms^-1

The second piece has a momentum of; P2=5*30= 150 kg ms^-1

Since p before = p after

560 kg ms^-1 = 200kgms^-1 + 150 kg ms^-1 + P3

Therefore, the momentum of the third piece; P3=560-350=210 kgms^1

The mass is also conserved so, 16kg = 8kg + 5g + ?

So the mass of P3=16-13= 3kg

Rearranging the equation for momentum in terms of velocity;

p=mv

v=p/m

v=210/3=70 ms^-1 (the speed of the third fragment)

What I am struggling with is actually constructing the vector diagram to show this.

I have attached a rough sketch of my preliminary approach. However, I am rather stuck on how to find the angle of the third fragement. Moreover, would the vector diagram exhibit the momentum of the pieces or rather their velocity? I have shown it with momentum but in hindesight I am uncertain.

I have not had approached a problem where I have to find the missing vector in this way before, typically if I am using a vector diagram for say three vectors I am doing so to find the resultant force and angle.

In this case, would I do so by resolving the momentum vectors into their horizontal and vertical components (given to 3.s.f);

The resultant momentum (560kgms^-1) would be equal to the square root of the total x-component squared + total y-component squared

R =√

560=√

I just cannot fathom how to find the angle of the third piece, nor am I certain whether my inital train of thought would be correct. I think I am perhaps overthinking the problem which has caused me some confusion. I would be very grateful of any help or guidance here

In this case, the momentum of the object before the collison is equal to p=mv=16*35=560 kg ms^-1

The first piece has a momentum of; P1=8*25=200kgms^-1

The second piece has a momentum of; P2=5*30= 150 kg ms^-1

Since p before = p after

560 kg ms^-1 = 200kgms^-1 + 150 kg ms^-1 + P3

Therefore, the momentum of the third piece; P3=560-350=210 kgms^1

The mass is also conserved so, 16kg = 8kg + 5g + ?

So the mass of P3=16-13= 3kg

Rearranging the equation for momentum in terms of velocity;

p=mv

v=p/m

v=210/3=70 ms^-1 (the speed of the third fragment)

What I am struggling with is actually constructing the vector diagram to show this.

I have attached a rough sketch of my preliminary approach. However, I am rather stuck on how to find the angle of the third fragement. Moreover, would the vector diagram exhibit the momentum of the pieces or rather their velocity? I have shown it with momentum but in hindesight I am uncertain.

I have not had approached a problem where I have to find the missing vector in this way before, typically if I am using a vector diagram for say three vectors I am doing so to find the resultant force and angle.

In this case, would I do so by resolving the momentum vectors into their horizontal and vertical components (given to 3.s.f);

Piece | x-component | y-component |

P1 | 200 cos 0 = 200 | 200 sin 0 = 0 |

P2 | 150 cos 50 ~ 96.4 | 150 sin 50 ~ 115 |

P3 | 210 cos θ | 210 sin θ |

Total | 200 + 96.4 + ? | 0+115 +? |

R =√

*x^2+y^2*560=√

*x^2+y^2*I just cannot fathom how to find the angle of the third piece, nor am I certain whether my inital train of thought would be correct. I think I am perhaps overthinking the problem which has caused me some confusion. I would be very grateful of any help or guidance here