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A student finds the work done by the constant force F =… | StemPy Lab
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A student finds the work done by the constant force F = 6 i - 2 j + 3 k newtons over the displacement d = i + 4 j + 2 k metres as lvert Frvertlvert drvert = 7√21 ≈ 32.1 joules. Which statement is correct?
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Vectors and Three-Dimensional Geometry › Vector Algebra
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A student finds the work done by the constant force
F
⃗
=
6
i
^
−
2
j
^
+
3
k
^
\vec F = 6\hat i - 2\hat j + 3\hat k
F
=
6
i
^
−
2
j
^
+
3
k
^
newtons over the displacement
d
⃗
=
i
^
+
4
j
^
+
2
k
^
\vec d = \hat i + 4\hat j + 2\hat k
d
=
i
^
+
4
j
^
+
2
k
^
metres as
∣
F
⃗
∣
∣
d
⃗
∣
=
7
21
≈
32.1
\lvert\vec F\rvert\lvert\vec d\rvert = 7\sqrt{21} \approx 32.1
∣
F
∣
∣
d
∣
=
7
21
≈
32.1
joules. Which statement is correct?
She left out the cosine of the angle. The work is
F
⃗
⋅
d
⃗
=
4
\vec F\cdot\vec d = 4
F
⋅
d
=
4
J.
She is right, because work is force times displacement.
She left out the cosine. The work is
6
−
2
+
3
+
1
+
4
+
2
=
14
6 - 2 + 3 + 1 + 4 + 2 = 14
6
−
2
+
3
+
1
+
4
+
2
=
14
J.
Her size is right but the sign is wrong. The work is
−
32.1
-32.1
−
32.1
J.
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