(mg - ma)/g = 1 - a/g

 

Reasoning

 

= (g - a)/g (because mg - ma = g - a)

 

 

= g/g - a/g = 1 - a/g

 

 

Is that correct?

(mg - ma)/g = (g - a)/g

That's wrong. Test it for m=5, g=1 and a=0, for example.

Should it be (mg - ma)/mg = 1 - a/g ?

 

If so then there's a typo in the physics book I'm reading.

The equations in the original post are obviously incorrect from a dimensional analysis perspective. The left-hand side of (mg-ma)/g=1-a/g has units of mass while the right hand side is unitless.

 

Are you sure the text doesn't have (mg-ma)/g = m(1-a/g), which is trivially correct?

The question is asking for a ratio of force to a persons weight.

 

The solution in the book states the following:-

 

F(rope) = mg - ma and the weight of person = mg

 

therefore the ratio of F(rope) to their weight = (mg - ma)/g = 1.0 - a/g

 

So my question was how do you get from (mg - ma)/g to 1.0 - a/g

The question is asking for a ratio of force to a persons weight.

 

The solution in the book states the following:-

 

F(rope) = mg - ma and the weight of person = mg

 

therefore the ratio of F(rope) to their weight = (mg - ma)/g = 1.0 - a/g

 

So my question was how do you get from (mg - ma)/g to 1.0 - a/g

 

The ratio of F(force) to their weight is :

 

(mg-ma)/mg = 1-a/g

Yes it is but in the book the 'm' is missing from the denominator so I am assuming that there is a typo in the book as without the 'm' being in the denominator the answer cannot be 1 - a/g.

 

If there was a mechanism to display an image of the page from the book then I think it would be easier to show what the problem is.

Yes it is but in the book the 'm' is missing from the denominator so I am assuming that there is a typo in the book as without the 'm' being in the denominator the answer cannot be 1 - a/g.

 

If there was a mechanism to display an image of the page from the book then I think it would be easier to show what the problem is.

 

 

Yes there is a typo in the book. No doubt about it

it should be

(mg - ma)/mg then = (1 - a)/g

it's wright anwer

 

 

 

 

 

 

 

 

 

Braun 790 Shaver

Its conditionally correct.

 

if mg-ma = g-a , m should be 1, 0

 

if m=1

(mg-ma)/g =(g-a)/g

=1 -a/g

 

if m=0

g-a =0

(mg-ma)g= 0/g

= g-a/g

= 1- a/g

 

a = g, not 0

but, considering that it is a physics equation, the terms have units.

 

0 kg does not equal 0 with no units.

 

Its conditionally correct.

 

if mg-ma = g-a , m should be 1, 0

 

if m=1

(mg-ma)/g =(g-a)/g

=1 -a/g

 

if m=0

g-a =0

(mg-ma)g= 0/g

= g-a/g

= 1- a/g

 

a = g, not 0

I think (based on your initial post),

 

equation: (mg - ma)/g = m(g/g) - m(a/g) = m - m(a/g)

 

given: mg-ma = g-a, m = 1 OR 0

 

for m=0: m - m(a/g) = 0

 

for m=1: m - m(a/g) = 1 - (a/g)

Edited January 19, 201114 yr by khaled