Answer:
The question is incomplete, below is the complete question "A particle moves through an xyz coordinate system while a force acts on it. When the particle has the position vector r with arrow = (2.00 m)i hat − (3.00 m)j + (2.00 m)k, the force is F with arrow = Fxi hat + (7.00 N)j − (5.00 N)k and the corresponding torque about the origin is vector tau = (4 N · m)i hat + (10 N · m)j + (11N · m)k.
Determine Fx."
Explanation:
We asked to determine the "x" component of the applied force. To do this, we need to write out the expression for the torque in the in vector representation.
torque=cross product of force and position . mathematically this can be express as
Where
and the position vector
using the determinant method to expand the cross product in order to determine the torque we have
![\left[\begin{array}{ccc}i&j&k\\2&-3&2\\ F_{x} &7&-5\end{array}\right]\\\\](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5C2%26-3%262%5C%5C%20F_%7Bx%7D%20%267%26-5%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C)
by expanding we arrive at
since we have determine the vector value of the toque, we now compare with the torque value given in the question
if we directly compare the j coordinate we have
#1
As we know that
now plug in all data into this
now from the formula of strain
#2
As we know that
pressure * area = Force
here we know that
now force is given as
#3
As we know that density of water will vary with the height as given below
here we know that
now density is given as
#4
as we know that pressure changes with depth as per following equation
here we know that
now we will have
here we will have
so it is 20.1 m below the surface
#5
Here net buoyancy force due to water and oil will balance the weight of the block
so here we will have
so it is 3.48 cm below the interface
Explanation:
a. moving a 145 kg aluminum sculpture across a horizontal steel platform
b. pulling a 15 kg steel sword across a horizontal steel shield
c. pushing a 250 kg wood bed on a horizontal wood floor
d. sliding a 0.55 kg glass amulet on a horizontal glass display case
Answer:
5.38 m/s
Explanation:
Given (in the x direction):
Δx = 2.45 m
v₀ = v cos 42.5°
a = 0 m/s²
Δx = v₀ t + ½ at²
(2.45 m) = (v cos 42.5°) t + ½ (0 m/s²) t²
2.45 = (v cos 42.5°) t
t = 3.32 / v
Given (in the y direction):
Δy = 0.373 m
v₀ = v sin 42.5°
a = -9.8 m/s²
Δx = v₀ t + ½ at²
(0.373 m) = (v sin 42.5°) t + ½ (-9.81 m/s²) t²
0.373 = (v sin 42.5°) t − 4.905 t²
0.373 = (v sin 42.5°) (3.32 / v) − 4.905 (3.32 / v)²
0.373 = 2.25 − 54.2 / v²
v = 5.38
Graph:
desmos.com/calculator/5n30oxqmuu
