The maximum speed is 0.55 m/s
Explanation:
For an object in uniform circular motion, the force of friction between the object and the ground provides the centripetal force required to keep the body in motion. Therefore we can write:
where the term on the left is the frictional force and the term on the right is the centripetal force, and where
is the coefficient of static friction
m is the mass of the body
g is the gravitational acceleration
v is the speed of the body
r is the radius of the circular path
In this problem, we have:
r = 0.102 m
Substituting and re-arranging, we find the maximum speed v at which the salt shaker can rotate:
Learn more about circular motion:
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Answer:
Explanation:
The acceleration of the bycicle is given by:
where
v = 20 m/s is the final velocity of the bike
u = 40 m/s is the initial velocity
t = 5 s is the time interval
Substituting numbers, we find
and the acceleration is negative, which means that the bycicle is slowing down.
Answer:
Part a)
Part b)
Explanation:
As the uniform sphere is rolling down the inclined plane then the net force on the sphere is given as
also we have torque equation on it
for pure rolling
now we have
now we have
now given that
so we have
Part b)
If the inclined plane is frictionless then the acceleration is given as
The resultant force on the object is
∑ <em>F</em> = 〈0, 8〉 N + 〈6, 0〉 N = 〈6, 8〉 N
which has a magnitude of
<em>F</em> = √((6 N)² + (8 N)²) = √(100 N²) = 10 N
By Newton's second law, the acceleration has magnitude <em>a</em> such that
<em>F</em> = <em>m a</em>
10 N = (2 kg) <em>a</em>
<em>a</em> = (10 N) / (2 kg)
<em>a</em> = 5 m/s²
so the answer is B.
The cyclist who travels 20 kilometers per hour for 15 kilometers