How Does the Third Piece's Velocity Compare After the Clay Ball Shatters?

[perfectlovehe]

Homework Statement

A 6-kg clay ball is thrown directly against a perpendicular brick wall at a velocity of 22 m/s and shatters into three pieces, which all fly backward, as shown in the figure. The wall exerts a force on the ball of 2430 N for 0.1 s. One piece of mass 2 kg travels backward at a velocity of 15 m/s and an angle of 32° above the horizontal. A second piece of mass 1 kg travels at a velocity of 7 m/s and an angle of 28° below the horizontal. What is the velocity of the third piece? (Let up be the +y positive direction and to the right be the +x direction.)

Homework Equations

Initial momentum = Final momentum + impulse delvered by the wall.

The Attempt at a Solution

22 = x + 2430 ? I came out with -2408 and I believe it's incorrect.

 

[Doc Al]

Initial momentum = Final momentum + impulse delvered by the wall.

I would write it differently:
Initial momentum + impulse delvered by the wall = Final momentum

You'll use this to find the total momentum of all pieces of the ball after the ball shatters.

22 = x + 2430 ? I came out with -2408 and I believe it's incorrect.

What's the initial momentum of the ball? What's the impulse? (Be sure to give the correct signs, since momentum is a vector and direction matters.)

 

[perfectlovehe]

Initial momentum is 22m/s and force is 2430 J. So would that be 2452 J? Or is that incorrect?

Initial momentum is 22m/s and force is 2430 J. So would that be 2452 J? Or is that incorrect?

 

[Doc Al]

That's incorrect. One step at a time:
(1) What's the definition of momentum? Calculate the initial momentum of the ball. What direction is the momentum? What sign?
(2) What's the definition of impulse? Calculate the impulse given to the ball. What direction is the impulse? What sign?

 

[rwisz]

I would approach this problem by first identifying the relevant equations and principles that apply to this scenario. The equation for conservation of momentum, which states that the initial momentum of a system is equal to the final momentum of the system, is a key concept here. Additionally, the impulse-momentum theorem, which states that the change in momentum of an object is equal to the impulse delivered to the object, is also relevant.

Using these principles, we can set up the following equation:

Initial momentum = Final momentum + impulse delivered by the wall

The initial momentum of the system is the momentum of the 6-kg clay ball, which is given by its mass (6 kg) multiplied by its initial velocity (22 m/s). This can be represented as 6 kg * 22 m/s = 132 kg*m/s.

The final momentum of the system is the sum of the momenta of the three pieces of the clay ball. We can represent this as:

Final momentum = (2 kg * 15 m/s) + (1 kg * 7 m/s) + (x kg * v3)

where v3 represents the velocity of the third piece, which is what we are trying to find.

The impulse delivered by the wall is given by the force exerted by the wall (2430 N) multiplied by the time (0.1 s) over which the force is applied. This can be represented as 2430 N * 0.1 s = 243 kg*m/s.

Putting all of this together, we can now set up our equation:

132 kg*m/s = (2 kg * 15 m/s) + (1 kg * 7 m/s) + (x kg * v3) + 243 kg*m/s

Simplifying, we get:

132 kg*m/s = 30 kg*m/s + 7 kg*m/s + (x kg * v3) + 243 kg*m/s

Rearranging and solving for v3, we get:

v3 = (132 kg*m/s - 30 kg*m/s - 7 kg*m/s - 243 kg*m/s) / x kg

Substituting in the values given in the problem, we get:

v3 = (132 - 30 - 7 - 243) / x

v3 = -148 / x

Since we do not have enough information to determine the mass of the third piece (x