p05 002

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2. We apply Newton’s second law (Eq. 5-1 or, equivalently, Eq. 5-2). The net force applied on the chopping

block is 

F

net

= 

F

1

+ 

F

2

, where the vector addition is done using unit-vector notation. The acceleration

ofthe block is given by a =





F

1

+ 

F

2



/m.

(a) In the first case



F

1

+ 

F

2

=



(3.0 N)ˆi + (4.0 N)ˆj



+



(

3.0 N)ˆi+ (4.0 N)ˆj



= 0

so a = 0.

(b) In the second case, the acceleration a equals



F

1

+ 

F

2

m

=



(3.0 N)ˆi + (4.0 N)ˆj



+



(

3.0 N)ˆi+ (4.0 N)ˆj



2.0 kg

= 4.0ˆj m/s

2

.

(c) In this final situation, a is



F

1

+ 

F

2

m

=



(3.0 N)ˆi + (4.0 N)ˆj



+



(3.0 N)ˆi + (

4.0 N)ˆj



2.0 kg

= 3.0ˆi m/s

2

.


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