# Homework Help: Max height of dog

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1. Nov 15, 2016

### emily081715

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
Change in gravitational potential energy = mgΔx
Work = Force * Force Displacement

3. 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

2. Nov 15, 2016

### Simon Bridge

Is there a question there?

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?

3. Nov 15, 2016

### 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?

4. Nov 15, 2016

### emily081715

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

5. Nov 15, 2016

### Simon Bridge

Yes OK - I mean what is your question?

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.

6. Nov 15, 2016

### emily081715

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

7. Nov 15, 2016

### 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

8. Nov 15, 2016

### haruspex

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