Average force exerted on the ball

[nysnacc]

Homework Statement

Homework Equations

∑F_av = mv2 - mv1

The Attempt at a Solution

We have to separate v in x dir and y dir?

 

[Doc Al]

We have to separate v in x dir and y dir?

Why? (Note that it starts from rest.)

 

[nysnacc]

but are part one and part two asking the same thing?

 

[Doc Al]

but are part one and part two asking the same thing?

No. One asks for the average total force on the ball. The other part asks for just the force exerted by the foot.

 

[nysnacc]

For the average total force on the ball (1st part). what equation should i use?

For the (2nd part) force exerted by the foot, the equation is F = (mv2- mv1 ) / Δt

 

[Doc Al]

For the (2nd part) force exerted by the foot, the equation is F = (mv2- mv1 ) / Δt

No, that will give the average total force on the ball.

 

[nysnacc]

That's total force exerted on the ball?

 

[nysnacc]

For part 1,

F = 1/ Δt * ∫ F dt ?? which is (mv2- mv1 ) / Δt ??

For part 2,

F = (mv2- mv1 ) / Δt - mg (cuz the question said subtract the weight)

 

[Doc Al]

That's total force exerted on the ball?

Yep.

 

[Doc Al]

For part 1,

F = 1/ Δt * ∫ F dt ?? which is (mv2- mv1 ) / Δt ??

Yes.

For part 2,

F = (mv2- mv1 ) / Δt - mg (cuz the question said subtract the weight)

Careful. Forces are vectors, so here you need to consider the directions of each.

 

[nysnacc]

For part 2

(mv2- mv1 ) / Δt (going up)

mg (going down)

what should i do with the 60 deg which is given?

 

[Doc Al]

what should i do with the 60 deg which is given?

That's the direction of the average total force on the ball.

 

[nysnacc]

Part 1, F = 45 N
Part 2 F = 41.236 N?

 

[haruspex]

Part 1, F = 45 N
Part 2 F = 41.236 N?

I'm not sure whether the hint given in the question is simply wrong or is assuming the weight, being a downward force, will be expressed as a negative quantity. Ask yourself this: does the presence of gravity increase or reduce the force needed from the boot to achieve the given velocity?
Secondly, forces are vectors. You cannot add (or subtract) forces acting in different directions by adding their magnitudes.

 

[nysnacc]

Is #1 correct, 45 N

 

[nysnacc]

#2 i have F = F_av (cos i + sin j) + mg (-j)

= (F_av cos )i + ( F_av sin - mg ) j

 

[Doc Al]

Is #1 correct, 45 N

Yes.

 

[nysnacc]

Yes.

why is my #2 not correct?

 

[Doc Al]

why is my #2 not correct?

You made a mistake with the sign of the weight vector.

 

[nysnacc]

Fav - mg (-j) ??
so it is a plus?

 

[nysnacc]

So 48.87 N?

#2 is greater than #1

 

[Doc Al]

$\vec{F_{total}} = \vec{F_{kick}} + \vec{F_{weight}}$
To find the force of the kick you must subtract the weight vector, but the weight points down.

 

[Doc Al]

So 48.87 N?

#2 is greater than #1

Yes.