Question

An object with mass 80 kg moved in outer space. When it was at location <7, -34, -7> its speed was 14.0 m/s. A single constant force <200, 460, -150> N acted on the object while the object moved to location <12, -42, -11> m. What is the speed of the object at this final location?

Answer 1

Answer:

W = -2080 J

Explanation:

initial position vector of the object is given as

$r_i = 7\hat i - 34\hat j - 7 \hat k$

similarly final position vector is given as

$r_f = 12\hat i - 42\hat j - 11\hat k$

now the displacement of the object is given as

$\vec d = \vec r_f - \vec r_i$

now we will have

$\vec d = (12\hat i - 42\hat j - 11\hat k) - (7\hat i - 34\hat j - 7 \hat k)$

$\vec d = 5\hat i - 8\hat j- 4\hat k$

now the force on the object is given as

$\vec F = (200\hat i + 460 \hat j - 150 \hat k)$

so here in order to find the work done

$W = \vec F . \vec d$

$W = (200\hat i + 460 \hat j - 150 \hat k). (5\hat i - 8\hat j- 4\hat k)$

$W = 1000 - 3680 + 600 = -2080 J$