What Is the Final Vertical Velocity Component of the Ball?

[scbeturner]

1. A 0.20kg ball with an initial velocity of (26i-1.6j)m/s collides with a vertical wall. The wall exerts a constant force of -175i N on the ball and the ball's final horizontal velocity component is -15i m/s. Find the final vertical velocity component of the ball.



2. I know how to find the total change in momentum of the ball and how long the ball was in contact with the wall, but i don't know how to find the vertical velocity component.



3.

 

[ehild]

What vertical force acts on the ball? ehild

 

[scbeturner]

I am guessing gravity maybe?

 

[ehild]

Yes, it is gravity. Gravity causes a vertical acceleration. You know the time of interaction with the wall. How much does the vertical velocity component change during that time? ehild

 

[scbeturner]

I thought I had to know the final velocity in order to find the interaction time with the wall and would find it using the formula: FΔt=m(v2-v1)...is that right?

 

[ehild]

It is true for each components separately. The wall exerts horizontal force so it changes the horizontal velocity component. You know both the initial and final horizontal velocity components and you know that the wall exerts a horizontal force of -175i N. How long does this force act on the ball?
Gravity exerts vertical force: it changes the vertical velocity component. You need the time Δt to calculate the vertical change of velocity during the interaction with the wall.

ehild

 

[scbeturner]

so would the time be:
-175Δt=.2(-15i-26i)
-175Δt=.2(-41)
-175Δt=-8.2
t=.047?

 

[ehild]

It is OK, but use one more digits as you will use this number for further calculation. So Δt=0.0469 s.

(And either omit the i-s everywhere or use them everywhere, and do not change Δt to t.)

Now calculate the change of the vertical velocity component because of gravity.

ehild

 

[scbeturner]

9.81(.0469)=.2(v2+1.6)
.460089=.2v2+.32
.140089=.2v2
v2=.7004m/s
is that right?

 

[ehild]

No, it is wrong.

The change of velocity is aΔt.

ehild

 

[scbeturner]

I'm confused...what formula do I need to find the final vertical velocity component?

 

[ehild]

I'm confused...what formula do I need to find the final vertical velocity component?

How do you get the velocity of a falling body?

ehild

 

[scbeturner]

The motion equation: v(t)=v0+at?

 

[ehild]

Yes.

ehild

 

[scbeturner]

-1.6+(9.81)(.0460)=-1.14
Is that right?

 

[ehild]

Gravity points downward. Your result is correct if the vertical axis of the coordinate system also points downward. I guess the problem meant upward y axis. Then g=-9.81 m/s^2.

ehild

 

[scbeturner]

In my answer key, it says that the final vertical velocity component is -1.6j, which is the same as the initial vertical velocity component. what am I doing wrong?

 

[ehild]

I think you are correct. If that wall were in the free space, the answer key would be correct: The force of the wall in the x direction changes only the x component of the velocity. But we are on the Earth and everything is exposed to gravity, and it changes the vertical velocity during the time while the wall and ball are in contact.

ehild

 

[scbeturner]

In my answer key for this problem it says that the final vertical velocity component is the same as the initial vertical velocity component...is that right?

 

[ehild]

It depends on the problem, if gravity is supposed to exist or not. Ask your teacher about it. In my opinion, talking about horizontal and vertical, and ignoring gravity at the same time is not correct.

ehild

 

[scbeturner]

Alright thanks for all the help!:)

 

[ehild]

You are welcome. ehild

 

[rl.bhat]

It depends on the problem, if gravity is supposed to exist or not. Ask your teacher about it. In my opinion, talking about horizontal and vertical, and ignoring gravity at the same time is not correct.

ehild

Suppose the particle is moving in the x-y plane and g is along the z axis, then?

 

[ehild]

rl.bhat, have you read the problem? It asks the vertical velocity component after collision. Gravity is vertical. Do you mean that gravity does not act if the ball moves horizontally at the instant of collision? The vertical velocity component will change any way.

ehild

 

[rl.bhat]

In the given velocity if 'i' component is horizontal component, what is 'j' component?

 

[ehild]

In the given velocity if 'i' component is horizontal component, what is 'j' component?

I do not know. It can be anything. The problem is badly worded. I do not think it has any sense trying to read the mind of the person who wrote this problem.

ehild