Data:
Centripetal Force = ? (Newton)
m (mass) = 68 Kg
s (speed) = 3.9 m/s
R (radius) = 6.5 m
Formula:

Solving:





Answer:
<span>
B.159 N</span>
Answer:
The torque on the wrench is 4.188 Nm
Explanation:
Let r = xi + yj where is the distance of the applied force to the origin.
Since x = 18 cm = 0.18 cm and y = 5.5 cm = 0.055 cm,
r = 0.18i + 0.055j
The applied force f = 88i - 23j
The torque τ = r × F
So, τ = r × F = (0.18i + 0.055j) × (88i - 23j) = 0.18i × 88i + 0.18i × -23j + 0.055j × 88i + 0.055j × -23j
= (0.18 × 88)i × i + (0.18 × -23)i × j + (0.055 × 88)j × i + (0.055 × -22)j × j
= (0.18 × 88) × 0 + (0.18 × -23) × k + (0.055 × 88) × (-k) + (0.055 × -22) × 0 since i × i = 0, j × j = 0, i × j = k and j × i = -k
= 0 - 4.14k + 0.0484(-k) + 0
= -4.14k - 0.0484k
= -4.1884k Nm
≅ -4.188k Nm
So, the torque on the wrench is 4.188 Nm
Answer: 
Explanation:
In the image attached with this answer are shown the given options from which only one is correct.
The correct expression is:

Because, if we derive velocity
with respect to time
we will have acceleration
, hence:

Where
is the mass with units of kilograms (
) and
with units of meter per square seconds
, having as a result 
The other expressions are incorrect, let’s prove it:
This result has units of
This result has units of
This result has units of
and
is a constant
This result has units of
This result has units of
This result has units of
and
is a constant
This result has units of
and
is a constant
because
is a constant in this derivation respect to
This result has units of
and
is a constant
Complete Question
The complete question is shown on the first uploaded image
Answer:
The temperature change is 
Explanation:
From the question we are told that
The velocity field with which the bird is flying is 
The temperature of the room is 
The time considered is t = 10 \ seconds
The distance that the bird flew is x = 1 m
Given that the bird is inside the room then the temperature of the room is equal to the temperature of the bird
Generally the change in the bird temperature with time is mathematically represented as
![\frac{dT}{dt} = -0.4 \frac{dy}{dt} -0.6\frac{dz}{dt} -0.2[2 * (5-x)] [-\frac{dx}{dt} ]](https://tex.z-dn.net/?f=%5Cfrac%7BdT%7D%7Bdt%7D%20%3D%20-0.4%20%5Cfrac%7Bdy%7D%7Bdt%7D%20-0.6%5Cfrac%7Bdz%7D%7Bdt%7D%20-0.2%5B2%20%2A%20%20%285-x%29%5D%20%5B-%5Cfrac%7Bdx%7D%7Bdt%7D%20%5D)
Here the negative sign in
is because of the negative sign that is attached to x in the equation
So
![\frac{dT}{dt} = -0.4v_y -0.6v_z -0.2[2 * (5-x)][ -v_x]](https://tex.z-dn.net/?f=%5Cfrac%7BdT%7D%7Bdt%7D%20%3D%20-0.4v_y%20%20-0.6v_z%20-0.2%5B2%20%2A%20%20%285-x%29%5D%5B%20-v_x%5D)
From the given equation of velocity field



So
substituting the given values of x and t
Answer:
-10.9 rad/s²
Explanation:
ω² = ω₀² + 2α(θ - θ₀)
Given:
ω = 13.5 rad/s
ω₀ = 22.0 rad/s
θ - θ₀ = 13.8 rad
(13.5)² = (22.0)² + 2α (13.8)
α = -10.9 rad/s²