A. statement of fact meant to explain an action
The coefficient of friction is 0.39
Explanation:
The equation of the forces along the direction parallel to the incline is the following:
(1)
where
is the component of the weight parallel to the incline (acting downward), with
m = 50 kg being the mass of the couch
(acceleration of gravity)
is the angle of the ramp
is the force of friction, acting up along the plane, with
being the coefficient of friction
N is the normal force
is the acceleration
The equation of the forces along the direction perpendicular to the plane is
(2)
where is the component of the weight perpendicular to the plane
From (2) we find
And substituting into (1)
And solving for , we find
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Symbol is f° and c° units is degrees
Answer:
when the mug is heated thus its temperature rises increasing the kinetic energy of the molecules , the oscillations around the rest position in the mug(solid) increases which increase the spaces between molecules and the mug expands. what cause the cracking is that outside of the mug expands before the inside and the mug cracks
Answer:
A = 0.22 m
Explanation:
The spring with the block and the pebble forms an oscillatory system, this system is described by the expression
x = A cos (wt + φ)
w = √ (k / m).
The data they give us is the amplitude of the movement (A = 10 cm), the oscillation mass is equal to the block mass plus the mass of the pebble
m = m + M
m = 0.031 + 0.108
m = 0. 139 kg
To find the spring constant let's use Hooke's law
F = k X
The force is the weight of the pebble and the additional elongation is x = 4.9 cm, let's calculate
k = F / x
k = mg / x
k = 0.031 9.8 / 0.049
k = 6.2 N / m
Let's look for angular velocity
w = √ (6.2 / 0.139)
w = 6,670 rad / s
Let's write the oscillation equation with this data
x = 0.10 cos (6,670 t)
For the pebble to remain in contact with the block, the acceleration of the spring system plus block with pebble must be less than the acceleration of gravity in the descending oscillation
Let's look for system acceleration
a = d²x / dt²
dx / dt = - A w sin (wt + Ф)
d²x / dt² = - A w² cos (wt+Ф)
To find the maximum value cos (wt) = ±1
g = A w²
A = g / w²
A = 9.8 / 6.67²
A = 0.22 m
When the amplitude of the oscillation exceeds this value the pebble is delayed with respect to the block