Impulse and Momentum: Gernade Problem

In summary, the question involves calculating the velocity of the third piece, C, which has a mass of 3.0kg, after a grenade weighing 10kg explodes into three pieces. The first two pieces, A and B, weigh 5.0kg and 2.0kg respectively, and move off in the same plane. Using the equation Pt=Pt', where Pt is the total momentum before the explosion and Pt' is the total momentum after the explosion, the momentum of each piece can be calculated using vector addition. Alternatively, the momentum in the x and y directions can be treated separately and then combined using Pythagoras' theorem.
  • #1
Avis
42
0

Homework Statement


A grenade of mass 10kg explodes into three pieces in the same plane, two of which, A(5.0kg) and B(2.0kg), move off as shown. Calculate the velocity of the 3.0 kg third Piece, C
scan0001.jpg


Homework Equations


Pt=Pt'


The Attempt at a Solution


scan0002.jpg


I do not get the right answer at all. I'm not sure where I'm going wrong.
 
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  • #2
Figure momentum is going to be conserved.

Isn't it really a matter of vector addition?

Pa = Ma*(-Va*cos30 i + Va*sin30 j)
Pb = Mb*(...

These added together give you -Pc don't they?
 
  • #3
I'm not really sure what you mean. The way I did is the way my Teacher told me to. I'm my class is tough through Video Conference so its hard to ask her. I told her I wasent getting the right answer and she said to do it exactly the way i have it. Her answer is 128.93 m/s [R82°D]
 
  • #4
Avis said:
I'm not really sure what you mean. The way I did is the way my Teacher told me to. I'm my class is tough through Video Conference so its hard to ask her. I told her I wasent getting the right answer and she said to do it exactly the way i have it. Her answer is 128.93 m/s [R82°D]

I was merely treating momentum as vectors and taking the components independently.

As an alternative method, consider the momentum in x and the momentum in y, separately.

Pax + Pbx + Pcx = 0

and

Pay + Pby + Pcy = 0

Once you have determined the components of Pc then you can use Pythagoras to give you Pc.
 

FAQ: Impulse and Momentum: Gernade Problem

1. What is impulse and momentum?

Impulse and momentum are physical quantities that describe the motion of objects. Impulse is the product of force and time, while momentum is the product of mass and velocity. They both play important roles in understanding the interactions between objects in motion.

2. How are impulse and momentum related?

Impulse and momentum are related through Newton's second law of motion, which states that the change in an object's momentum is equal to the impulse applied to it. This relationship is represented mathematically as J = mΔv, where J is the impulse, m is the mass, and Δv is the change in velocity.

3. What is the conservation of momentum?

The conservation of momentum is a fundamental law of physics that states that the total momentum of a closed system remains constant. In other words, the total momentum before a collision or interaction is equal to the total momentum after the collision or interaction. This law is based on the principle of conservation of energy and is applicable to all types of collisions, including elastic and inelastic collisions.

4. How is impulse and momentum applied to a grenade problem?

In a grenade problem, impulse and momentum are used to calculate the velocity of the grenade after it explodes and to determine the distance it travels. The explosion of the grenade creates an impulse that causes a change in the grenade's momentum, and this change in momentum is used to calculate its final velocity and distance traveled.

5. What factors affect the impulse and momentum in a grenade problem?

The factors that affect impulse and momentum in a grenade problem include the mass and velocity of the grenade before and after the explosion, as well as the duration of the explosion. These factors determine the magnitude of the impulse and the resulting change in momentum, which in turn affects the final velocity and distance traveled by the grenade.

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