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iren2701 [21]
3 years ago
10

The constant forces F1 = 8 + 29 + 32 N and F2 = 48 - 59 - 22 N act together on a particle during a displacement from the point A

(20, 15,0)m to the point B (0,07) m. What is the work done on the particle? The work done is given by F. f, where is the resultant force (here F = Fi + F2) and is the displacement.
Physics
1 answer:
steposvetlana [31]3 years ago
3 0

Answer:

- 600 J

Explanation:

A (20, 15, 0 ) m

B (0, 0, 7) m

\overrightarrow{F_{1}}=8\widehat{i}+29\widehat{j}+32\widehat{k}

\overrightarrow{F_{2}}=48\widehat{i}-59\widehat{j}-22\widehat{k}

Net force

\overrightarrow{F}=\overrightarrow{F_{1}}+\overrightarrow{F_{2}}

\overrightarrow{F}}=\left ( 8+48 \right )\widehat{i}+\left ( 29-59 \right )\widehat{j}+\left ( 32-22 \right )\widehat{k}

\overrightarrow{F}}=56\widehat{i}-30\widehat{j}+10\widehat{k}

\overrightarrow{S}=\overrightarrow{OB}-\overrightarrow{OA}

\overrightarrow{S}=\left ( 0-20 \right )\widehat{i}+\left ( 0-15 \right )\widehat{j}+\left ( 7-0 \right )\widehat{k}

\overrightarrow{S}=-20\widehat{i}-15\widehat{j}+7\widehat{k}

Work done is defined as

W = \overrightarrow{F}.\overrightarrow{S}

W = \left ( 56\widehat{i}-30\widehat{j}+10\widehat{k} \right ).\left (-20\widehat{i}-15\widehat{j}+7\widehat{k}  \right )

W = -1120 + 450 + 70

W = - 600 J

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Answer:

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Notice that both the speed and the direction of motion of this block are constant. In other words, the velocity of this block is constant.

By Newton's Second Law, the net force on this block would be 0. External forces on this block should be balanced. Thus, the magnitude of the (downward) weight of this block should be equal to the magnitude of the (upward) force that the boy applies on this block.

Let m denote the mass of this block. It is given that m = 1\; {\rm kg}. The weight of this block would be:

\begin{aligned}\text{weight} &= m\, g \\ &= 1\; {\rm kg} \times 9.8\; {\rm N \cdot kg^{-1}} \\ &= 9.8\; {\rm N}\end{aligned}.

Hence, the force that the boy applies on this block would be upward with a magnitude of F = 9.8\; {\rm N}.

The mechanical work that a force did is equal to the product of:

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\begin{aligned}\text{work} &= F\, s \\ &= 9.8\; {\rm N} \times 1\; {\rm m} \\ &= 9.8\; {\rm J}\end{aligned}.

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