a force f= 3i+cj+2k acting on a particle causes displacement , d=-4i+2j+3k.
If the work done is 6 joule then the value of c.
Plz. Solve
Why did the scarecrow win an award? Because he was outstanding in his field! Now, let's solve this problem and find the value of c.
The work done (W) is given by the dot product of the force (F) and displacement (d):
W = F · d
Substituting the given values:
6 = (3i + cj + 2k) · (-4i + 2j + 3k)
To calculate the dot product, we multiply the corresponding components and add them up:
6 = (3 * -4) + (c * 2) + (2 * 3)
Simplifying the equation:
6 = -12 + 2c + 6
Moving the terms around:
2c = 12
Finally, solving for c:
c = 6
So, the value of c is 6.
To find the value of c, we can use the formula for work done:
Work done (W) = Force (F) · Displacement (d)
Given:
Force (F) = 3i + cj + 2k
Displacement (d) = -4i + 2j + 3k
Work done (W) = 6 joule
Substituting the given values into the formula, we have:
6 = (3i + cj + 2k) · (-4i + 2j + 3k)
Now, let's calculate the dot product:
6 = (3 * -4) + (c * 2) + (2 * 3)
6 = -12 + 2c + 6
6 = 2c - 6
Rearranging the equation:
2c = 12
c = 12/2
c = 6
Therefore, the value of c is 6.
To find the value of c, we need to use the formula for work done, which is given by:
Work = force dot displacement
Here, the force is given as F = 3i + cj + 2k, and the displacement is given as d = -4i + 2j + 3k.
To calculate the dot product, we need to find the dot product of the force vector and the displacement vector. The dot product of two vectors A = (a1, a2, a3) and B = (b1, b2, b3) is given by:
A · B = a1 * b1 + a2 * b2 + a3 * b3
Applying this to our force and displacement vectors:
F · d = (3 * -4) + (c * 2) + (2 * 3)
= -12 + 2c + 6
= 2c - 6
Given that the work done is 6 joules, we can equate this to the dot product and solve for c:
6 = 2c - 6
12 = 2c
c = 6
So, the value of c is 6.
(3i+cj+2k)(-4i+2j_3k)
= -12i+2cj-6k=6
=-12+2c-6=6
=-12+2c=6+6
=-12+2c=12
=2c=-12 -12
=2c =24
=c=24÷2
=c=12
Therefore, C=12.
The dot product f*d equals 6 Joules, if the force is in Newtons and the displacement distance is in meters.
-12 +2c +6 = 12
2c = 18
Take it from there