Answer:
(A) the angular acceleration of the blades is 13.33 m/s.
Explanation:
Given;
moment of inertia of a blade, I = 0.2 kgm²
net torque exerted on fan blades, ∑τ = 8Nm
Torque is given as product of moment of inertia and angular acceleration;
τ = Iα
where;
α is the angular acceleration
Since there are three blades of the ceiling fan, the net torque is given as;
∑τ = (3I)α
∑τ = 3Iα
α = ∑τ / 3I
α = (8) / (3 x 0.2)
α = 13.33 m/s
Therefore, the angular acceleration of the blades is 13.33 m/s.
Answer:
3.0 x 10¹ Nm
Explanation:
Torque = F x r
Where F is force applied and r is perpendicular distance from pivot point . r
is also called lever arm
Here F = 15 N and r = 2.0 m
Torque
= 15 N X 2.0 m
= 3.0 10¹ Nm.
Answer:
a.
b.
c.
d. The angular acceleration when sitting in the middle is larger.
Explanation:
a. The magnitude of the torque is given by
, being r the radius, F the force aplied and
the angle between the vector force and the vector radius. Since
and so
.
b. Since the relation
hols, being I the moment of inertia, the angular acceleration can be calculated by
. Since we have already calculated the torque, all left is calculate the moment of inertia. The moment of inertia of a solid disk rotating about an axis that passes through its center is
, being M the mass of the disk. If we assume that a person has a punctual mass, the moment of inertia of a person would be given by
, being
the mass of the person and
the distance from the person to the center. Given all of this, we have
.
c. Similar equation to b, but changing
, so
.
d. The angular acceleration when sitting in the middle is larger because the moment of inertia of the person is smaller, meaning that the person has less inertia to rotate.
Answer:
The minimum speed required is 5.7395km/s.
Explanation:
To escape earth, the kinetic energy of the asteroid must be greater or equal to its gravitational potential energy:

or

where
is the mass of the asteroid,
is its distance form earth's center,
is the mass of the earth, and
is the gravitational constant.
Solving for
we get:

putting in numerical values gives


in kilometers this is

Hence, the minimum speed required is 5.7395km/s.
Answer:
η = 58.8%
Explanation:
Work is defined as the force applied by the distance traveled by the body.

where:
W = work [J] (units of joules)
F = force = 294 [N]
d = distance = 5 [m]
![W = 294*5\\W = 1470 [J]\\](https://tex.z-dn.net/?f=W%20%3D%20294%2A5%5C%5CW%20%3D%201470%20%5BJ%5D%5C%5C)
Efficiency is defined as the energy required to perform an activity in relation to the energy actually added to perform some activity. This can be better understood by means of the following equation.
