Answer:
F = - 2 A x - B
Explanation:
The force and potential energy are related by the expression
F = - dU / dx i ^ -dU / dy j ^ - dU / dz k ^
Where i ^, j ^, k ^ are the unit vectors on the x and z axis
The potential they give us is
U (x) = A x² + B x + C
Let's calculate the derivatives
dU / dx = A 2x + B + 0
The other derivatives are zero because the potential does not depend on these variables.
Let's calculate the strength
F = - 2 A x - B
Answer:
Approximately
(assuming that the melting point of ice is
.)
Explanation:
Convert the unit of mass to kilograms, so as to match the unit of the specific heat capacity of ice and of water.

The energy required comes in three parts:
- Energy required to raise the temperature of that
of ice from
to
(the melting point of ice.) - Energy required to turn
of ice into water while temperature stayed constant. - Energy required to raise the temperature of that newly-formed
of water from
to
.
The following equation gives the amount of energy
required to raise the temperature of a sample of mass
and specific heat capacity
by
:
,
where
is the specific heat capacity of the material,
is the mass of the sample, and
is the change in the temperature of this sample.
For the first part of energy input,
whereas
. Calculate the change in the temperature:
.
Calculate the energy required to achieve that temperature change:
.
Similarly, for the third part of energy input,
whereas
. Calculate the change in the temperature:
.
Calculate the energy required to achieve that temperature change:
.
The second part of energy input requires a different equation. The energy
required to melt a sample of mass
and latent heat of fusion
is:
.
Apply this equation to find the size of the second part of energy input:
.
Find the sum of these three parts of energy:
.
Answer:
M₀ = 5i - 4j - k
Explanation:
Using the cross product method, the moment vector(M₀) of a force (F) is about a given point is equal to cross product of the vector A from the point (r) to anywhere on the line of action of the force itself. i.e
M₀ = r x F
From the question,
r = i + j + k
F = 1i + 0j + 5k
Therefore,
M₀ = (i + j + k) x (1i + 0j + 5k)
M₀ = ![\left[\begin{array}{ccc}i&j&k\\1&1&1\\1&0&5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5C1%261%261%5C%5C1%260%265%5Cend%7Barray%7D%5Cright%5D)
M₀ = i(5 - 0) -j(5 - 1) + k(0 - 1)
M₀ = i(5) - j(4) + k(-1)
M₀ = 5i - 4j - k
Therefore, the moment about the origin O of the force F is
M₀ = 5i - 4j - k