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Pressure

An elephant w...

Question

An elephant weighing 40,000 N stands on one foot of area 1000 $c m^{2}$ whereas a girl weighing 400 N is standing on one 'stiletto' heel of area 1 $c m^{2}$ .

(a) Which of the two, elephant or girl, exerts a larger force on the ground and by how much ?
(b) What pressure is exerted on the ground by the elephant standing on one foot ?
(c) What pressure is exerted on the ground by the girl standing on one heel ?
(d) Which of the two exerts larger pressure on the ground : elephant or girl ?
(e) What is the ratio of pressure exerted by the girl to the pressure exerted by the elephant ?

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Solution

$w e i g h t space o f space e l e p h a n t equals 40000 N A r e a space o f space o n e space f o o t equals 1000 space c m squared equals 1000 cross times 10 to the power of negative 4 end exponent space m squared w e i g h t space o f space g i r l equals 400 N a r e a space space o f space h e e l space o f space g i r l equals 1 space c m squared equals 1 cross times 10 to the power of negative 4 end exponent space m squared a right parenthesis e l e p h a n t space h a s space a space l a r g e r space w e i g h t space o f space 40000 N comma t h e r f o r e space comma e l e p h a n t space e x e r t s space a space l a r g e r space f o r c e space o n space t h e space g r o u n d. e l e p h a n t space e x e r t s space a space l a r g e space f o r c e space o n space t h e space g r o u n d b y space 40000 N minus 400 N equals 39600 N b right parenthesis w e i g h t space o f space e l e p h a n t equals 40000 N a r e a space o f space o n e space f o o t equals 1000 space c m squared equals 1000 cross times 10 to the power of negative 4 end exponent space m squared P r e s s u r e equals fraction numerator F o r c e over denominator A r e a end fraction equals fraction numerator 40000 over denominator 1000 cross times 10 to the power of negative 4 end exponent space end fraction equals 400000 space bevelled N over m squared c right parenthesis w e i g h t space o f space t h e space g i r l equals 400 N a r e a space o f space h e l l space o f space g i r l equals 1 space c m squared equals 1 cross times 10 to the power of negative 4 end exponent space m squared P r e s s u r e equals fraction numerator F o r c e over denominator A r e a end fraction equals fraction numerator 40000 over denominator 1 cross times 10 to the power of negative 4 end exponent space end fraction equals 4000000 bevelled N over m squared d right parenthesis g i r l space e x e r t s space a space l a r g e space p r e s s r e space o n space t h e space g r o u n d e right parenthesis R a t i o equals fraction numerator P r e s s u r e space e x e r t e d space b y space t h e space g i r l over denominator P r e s s u r e space e x e r t e d space b y space t h e space e l e p h a n t end fraction space space space space space space space space space space equals 4000000 over 400000 equals 10 t h e space p r e s s u r e space e x e r t e d space b y space g i r l space 10 space t i m e s space g r e a t e r space t h a n space t h a t space e x e r t e d space b y space t h e space e l e p h a n t$

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