Is there an error in the answer for Impulse Momentum Linear Homework?

[freshbox]

Homework Statement

Hi guys, just want to check is there any problem with the answer for part c and d of the question? I would really appreciate if you can help me double check, thank you.

 

[NascentOxygen]

Do you get their answers for (a) and (b)?

 

[freshbox]

yes but not for c and d

 

[NascentOxygen]

yes but not for c and d

I don't get anywhere near their answers for (a) or (b).

I get their answers only if I change the force to 120 MN.

 

[ehild]

For c) : Count gravity to the force that acts on the hammer+pile.

ehild

 

[ehild]

I don't get anywhere near their answers for (a) or (b).

I get their answers only if I change the force to 120 MN.

Have you used 8000 kg as mass of the hammer? (Mg = 10³ kg)


ehild

 

[NascentOxygen]

Have you used 8000 kg as mass of the hammer? (Mg = 10³ kg)

Ah, with that correction all of my answers now are the same as those given alongside the question.

 

[freshbox]

Part C

M₁=mv
=(9000)(8.82)
=79380

M₂=mv
=0

I_1-2=Force x Time
=(F)(0.1)
=0.1F

M₁+I_1-2=M₂

79380-0.1F=0
79380=0.1F
F=793800 Ans Wrong


Counting gravity force into working

I_1-2= Force x Time
=(9.81F)(0.1)
=0.981F

79380=0.981F
F=80917.43 Ans Wrong

 

[Doc Al]

Part C

M₁=mv
=(9000)(8.82)
=79380

M₂=mv
=0

I_1-2=Force x Time
=(F)(0.1)
=0.1F

M₁+I_1-2=M₂

79380-0.1F=0
79380=0.1F
F=793800 Ans Wrong

That's the net force acting. Use that to find the resistive force.

 

[freshbox]

Is I_1-2= Force x Time this force always the net force?

 

[Doc Al]

Is I_1-2= Force x Time this force always the net force?

I'd say so.

 

[freshbox]

Can you guide me on how to use the net force to find the resistive force? Is there a formula to it?

 

[Doc Al]

Can you guide me on how to use the net force to find the resistive force? Is there a formula to it?

Draw a free body diagram and analyze the forces acting on the hammer+pile system.

 

[freshbox]

There is an action and reaction force. Action :+793800 Reaction-793800

 

[Doc Al]

There is an action and reaction force. Action :+793800 Reaction-793800

For one thing, action and reaction forces act on different bodies. What you want are the forces acting on the hammer+pile.

Second, that 793800 N force is a net force, not an individual force. So even talking about it as an "action" is meaningless.

What forces act on the hammer+pile? Hint: Only two forces act.

 

[NascentOxygen]

Part C

M₁=mv
=(9000)(8.82)
=79380

M₂=mv
=0

I_1-2=Force x Time
=(F)(0.1)
=0.1F

M₁+I_1-2=M₂

79380-0.1F=0
79380=0.1F
F=793800 Ans Wrong

That's the opposing force to bring about the deceleration. In addition, you also have to oppose their weights, as well.

 

[freshbox]

Gravity and the 120kN external force?

 

[NascentOxygen]

The specs indicate that the 120kN force is turned off by the time the soil opposes the moving pile.

 

[freshbox]

I just can't think of any other forces besides gravity.. and the FBD i drew looks abit weird to me too haha..

 

[NascentOxygen]

How many Newtons force UP must be exerted to balance their weights acting DOWNWARD?

 

[Doc Al]

I just can't think of any other forces besides gravity..

What about the force you are asked to find?

 

[freshbox]

Yes the 2 forces are gravity and resistive force, sorry.

How many Newtons force UP must be exerted to balance their weights acting DOWNWARD? -793800N? What are you trying to tell me, action/reaction ?

Urgggh... so confusing I don't know how to use the net force to solve :(

 

[Doc Al]

Yes the 2 forces are gravity and resistive force, sorry.

So, what's the gravitational force? Set the sum equal to the net force.

How many Newtons force UP must be exerted to balance their weights acting DOWNWARD? -793800N? What are you trying to tell me, action/reaction ?

Forget about 'balancing' anything.

There are two forces, one unknown. And you already know the net force, so set up an equation to solve for the resistive force.

 

[ehild]

There is the system the hammer and pile together. You have two forces: their weight, G and the resistive force Fr from the ground. Their resultant F=Fr-G will change the linear momentum during the given time . FΔt=ΔI. Calculate Fr.

ehild

 

[freshbox]

793800=Fr-88290
Fr=793800+88290
Fr= 882090

Ok this is the answer but I still don't understand the concept behind it.

Doc AL said, So, what's the gravitational force? Set the sum equal to the net force. I assume G Force = Net Force -> can you explain why G force is equal to net force?

From this equation F=Fr-G, how do you determine G force is -ve, Fr and F is both +ve because at first I tried setting it as G=F-Fr because I thought all should be positive except Fr since it is "resist"


Please explain, thank you guys so much

 

[NascentOxygen]

If the hammer were acting horizontally, say driving a pile horizontally into a rock face, then gravity would not enter into the calculations for such horizontal motion. But in your problem where motion is in the same direction as gravity, to restrict the pile to moving downwards according to the equation of motion the ground must in addition oppose the weights of the hammer and pile.

 

[ehild]

The hammer and pile move together into the material. They have initial linear momentum I and mass of 9000 kg, which means 9000g weight. The weight pulls downward the pile+hammer, and the resistive force acts upward. The net force is opposite to the momentum, and equals with ΔI/Δt in magnitude.

ehild

 

[Doc Al]

793800=Fr-88290
Fr=793800+88290
Fr= 882090

OK.

Ok this is the answer but I still don't understand the concept behind it.

Doc AL said, So, what's the gravitational force? Set the sum equal to the net force. I assume G Force = Net Force -> can you explain why G force is equal to net force?

The "G force" is just the weight of the system, which acts down. It's one of the two forces acting. It's not the net force.

From this equation F=Fr-G, how do you determine G force is -ve, Fr and F is both +ve because at first I tried setting it as G=F-Fr because I thought all should be positive except Fr since it is "resist"

The resistive force is upward (the ground pushes up), the gravitational force is downward; the net force is upward. So, taking up as positive, the gravitational force would be negative.

What you did above, which is correct, is to set the net force equal to the sum of the individual forces:

ƩF = [Resistive Force] + [Gravity] (think of this as a vector equation)

Using up as positive:
793800 = Fr - mg

So Fr = 793800 + mg

 

[freshbox]

Can I ask how come the net force is upward? I thought is moving down together with the G force to produce the resistive force (upward)

 

[ehild]

The pile moves downward with decreasing speed. So the acceleration points upward. So should be the net force.

ehild