A particle moves along a straight path through displacement i = (2.2 m) + c while force = (3.2 N) - (3.8 N) acts on it. (Other forces also act on the particle.) What is the value of c if the work done by on the particle is (a) zero, (b) 3.2 J, and (c) -7.3 J?
I assume you have vector displacement andforces.
work=force dot displacement=3.2*2.2-3.8*c
solve for c.I will do one. If work 7.3J
7.3=7.04-3.8c
.26=3.8c
c=14.6
To find the value of c in each of the given scenarios, we need to use the work-energy principle. The work done by a force on an object is equal to the change in its kinetic energy. Mathematically, it can be expressed as:
Work = ΔKE
Now, let's calculate the work done using the given displacement and force vectors:
Work = F · d
To find the dot product of two vectors, we multiply their corresponding components and add them up:
Work = (3.2 N - 3.8 N) · (2.2 m + c)
Simplifying the equation:
Work = (3.2 N - 3.8 N) · 2.2 m + (3.2 N - 3.8 N) · c
= (-0.6 N) · 2.2 m + (-0.6 N) · c
= -1.32 Nm - 0.6 Nc
Now we can find the value of c for each scenario:
(a) Work = 0 J
Setting the work to zero:
-1.32 Nm - 0.6 Nc = 0
Rearranging the equation:
-0.6 Nc = 1.32 Nm
Dividing both sides by -0.6 N:
c = -1.32 Nm / -0.6 N
c = 2.2 m
The value of c when the work done is zero is 2.2 m.
(b) Work = 3.2 J
Setting the work to 3.2 J:
-1.32 Nm - 0.6 Nc = 3.2 J
(c) Work = -7.3 J
Setting the work to -7.3 J:
-1.32 Nm - 0.6 Nc = -7.3 J
Now, to solve for c in both (b) and (c) scenarios, we need more information about the relationship between work and displacement. Specifically, we need to know how the force changes with respect to displacement or have additional information about the system.