Newtons Laws EX 7

(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: $F_{G}$, $F_{N}$, $F_{f}$ and $F$ which is exerted by the man.

We draw a free body diagram.

Then we compute the components of all forces.

Forces	x-comp	y-comp
$F_{G}$	0	-200 N
$F_{N}$	0	$F_{N}$
$F_{f}$	$-F_{f}$	0
$F$	80 cos(- 30°) = 69 N	80 sin(- 30°) = - 40 N
$\sum {F}$	0	0

We do not need to solve for $F_{N}$

$69-F_{f}=0$

$F_{f}=69N$

(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 $a=1m/s^{2}$.

We can directly compute the components.

Forces	x-comp	y-comp
$F_{G}$	0	-200 N
$F_{N}$	0	$F_{N}$
$F_{f}$	- 69 N	0
$F$	F cos(- 30°) = 0.87 F	F sin(- 30°) = - 0.5 F
$\sum {F}$	20 a = 20 x 1 = 20 N	0

We do not need to solve for $F_{N}$

$0.87F-69=20$

$F=89/0.87=103N$