imported>Patrick at 03:07, 13 June 2011

2011-06-13T03:07:47Z

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'''(a)''' We choose the horizontal x-axis since we have a free choice (a = 0). We assume that the retarding force is really the force of friction. There are four forces acting on the lawn mower: '''<math>F_G</math>''', '''<math>F_N</math>''', '''<math>F_f</math>''' and '''<math>F</math>''' which is exerted by the man. 

We draw a free body diagram. 

[[image:N_APP_EX_7_SOLN.png|TOP]] 

Then we compute the components of all forces. 

{| border="1" cellpadding="2" style="text-align:center"
!width="50"|Forces
!x-comp
!y-comp
|-

| '''<math>F_G</math>''' || 0 || -200 N

|-

| '''<math>F_N</math>''' || 0 || <math>F_N</math>

|-

| '''<math>F_f</math>''' || <math>-F_f</math> || 0

|-

| '''<math>F</math>''' || 80 cos(- 30°) = 69 N || 80 sin(- 30°) = - 40 N

|-

| '''<math>\sum{F}</math>''' || 0 || 0

|-

|}

We do not need to solve for <math>F_N</math> 

<math>69 - F_f = 0</math> 

<math>F_f = 69 N</math> 

'''(b)''' We can still use the same diagram as above. The only difference is that we do not know the force Fx but we know that the object has the acceleration <math>a = 1 m/s^2</math>. 

We can directly compute the components.

{| border="1" cellpadding="2" style="text-align:center"
!width="50"|Forces
!x-comp
!y-comp
|-

| '''<math>F_G</math>''' || 0 || -200 N

|-

| '''<math>F_N</math>''' || 0 || <math>F_N</math>

|-

| '''<math>F_f</math>''' || - 69 N || 0

|-

| '''<math>F</math>''' || F cos(- 30°) = 0.87 F|| F sin(- 30°) = - 0.5 F

|-

| '''<math>\sum{F}</math>''' || 20 a = 20 x 1 = 20 N || 0

|-

|}

We do not need to solve for <math>F_N</math> 

<math>0.87 F - 69 = 20</math> 

<math>F = 89 / 0.87 = 103 N</math>

Newtons Laws EX 7 - Revision history

imported>Patrick at 03:07, 13 June 2011