Respuesta :
Answer:
564.04Nm
Explanation:
Work is said to be dome when an applied force on an object cause the object to move through a distance. Mathematically;
Work done = Force × Distance in the direction of the force
Given the displacement
r = (3.29 m)^ ı + (2.67 m ) ^ ȷ
Force F = ( 281 N ) ^ ı − ( 135 N ) ^ ȷ
Vectorially, i.i = j.j = 1 and i.j = 0(dot product of different components gives 0)
Work done F = {(281 N) ^ ı − (135N)^ȷ} × {(3.29 m)^ı + (2.67 m )^ȷ}
Multiplying both vectors will give;
= 281i(3.29i) + 281i(2.67j) - 135j(3.29i) - 135j(2.67j)
Since i.j= 0 and i.I = j.j = 1, the answer becomes;
= 924.49(i.i)-360.45(j.j)
= 924.49-360.45
= 564.04Nm
The total work done is 564.04Nm
The dot product of two vector quantities, is given by the sum of the product of the corresponding or parallel components
The total work done on the boat by the wind is 564.04 Joules
The reason the value given for the total work is correct is as follows
The given parameters are:
The displacement the boat undergoes is [tex]\overset \rightarrow {\Delta r} = \left( 3.29 \, m\right ) \hat i + \left( 2.67\, m\right ) \hat j[/tex]
The constant force exerted by the wind, [tex]\overset \rightarrow {F} = \left( 281 \, N\right ) \hat i - \left( 135 \, N\right ) \hat j[/tex]
The required parameter:
The total work done on the boat by the wind over this period of time
Solution:
The work done by a force (vector) over a distance (vector) is given by the dot product of the two vectors as follows;
[tex]\overset \rightarrow {A} \cdot \overset \rightarrow {B}= A_x \cdot B_x + A_y \cdot B_y + A_z \cdot B_z[/tex], therefore;
The total work done on the boat by the wind, [tex]\overset \rightarrow {F} \cdot \overset \rightarrow {\Delta r}[/tex], is given as follows;
[tex]\overset \rightarrow {F} \cdot \overset \rightarrow {\Delta r}[/tex] = (281 N × 3.29 m + (-135 N) × 2.67 m) = 564.04 J
The total work done on the boat by the wind, [tex]\overset \rightarrow {F} \cdot \overset \rightarrow {\Delta r}[/tex] = 564.04 Joules
Learn more about the work done by a force here:
https://brainly.com/question/13185749
