How High Can a Dog Jump by Exerting Maximum Force?

[emily081715]

Homework Statement

A 11-kg dog jumps up in the air to catch a ball. The dog's center of mass is normally 0.20 m above the ground, and he is 0.50 m long. The lowest he can get his center of mass is 0.10 m above the ground, and the highest he can get it before he can no longer push against the ground is 0.40 m .If the maximum force the dog can exert on the ground in pushing off is 2.1 times the gravitational force Earth exerts on him, how high can he jump?

Homework Equations

Change in gravitational potential energy = mgΔx
Work = Force * Force Displacement

The Attempt at a Solution

Dog pushes itself to 0.6 m, then from that point the change in position is given by:
0.5*(2.1mg - mg) = mgΔx
0.5(2.1(11)(9.8)- (11)(9.8))/(11)(9.8)= Δx
0.55 m = Δx

Δx + 0.6 m = 1.15 m

 

[Simon Bridge]

Is there a question there?

Comments:
You have the dog lifting itself 0.6m - how does it do this?
Does the dog exert it's maximum force all the time it is pushing on the ground?
Why didn't you just cancel out the terms of "mg" instead of calculating them?

 

[emily081715]

if the maximum force the dog can exert on the ground in pushing off is 2.1 times the gravitational force Earth exerts on him, how high can he jump?

 

[emily081715]

if the maximum force the dog can exert on the ground in pushing off is 2.1 times the gravitational force Earth exerts on him, how high can he jump?

thats the question
i could've canceled out the mg but calculating them doesn't change anything, they cancel out on their own

 

[Simon Bridge]

Yes OK - I mean what is your question?
Please answer the rest of my questions too.

Note: calculating things out adds to the chance of making a mistake, and also adds rounding errors.
If you cancel them out, then you don't need to round them off. This is why it is best practise to derive the equation first, then plug in the numbers.

 

[emily081715]

Yes OK - I mean what is your question?
Please answer the rest of my questions too.

i'm asking where my error is because i believed that was the right way to do it

 

[emily081715]

0.6 comes from the highest point of the centre of mass added to the lowest point ( 0.5 +0.1)
i'm assuming it does exert the max force at all time during the push

 

[haruspex]

0.6 comes from the highest point of the centre of mass added to the lowest point ( 0.5 +0.1)
i'm assuming it does exert the max force at all time during the push

Over what vertical displacement is the dog able to exert a push against the ground? What work is done in the process?