a) i) the direction of the centripetal force is always towards the centre of the circle
a) ii) the centripetal force is provided by the force of friction between the tires of the motorbike and the road
b) i) At higher speed, the centripetal force is larger
b) ii) At smaller radius, the centripetal force is larger
Explanation:
a) i)
When an object is moving in a circular motion, there should be a force acting on it, responsible for changing direction of motion of the object. This force is called centripetal force, and its direction is always towards the centre of the circular trajectory.
The magnitude of this centripetal force is given by
[tex]F=m\frac{v^2}{r}[/tex]
where
m is the mass of the object
v is its speed
r is the radius of the circle
If the value of the speed does not change during the motion, the motion is said to be uniform circular motion.
As we said, the direction of the centripetal force is always towards the centre of the circle.
ii)
The nature of the centripetal force is always different in every situation: this means that in different situations, the centripetal force (which is the force responsible for keeping the object in circular motion) is provided by a different force.
For instance, for a satellite orbiting around the Earth, the centripetal force is provided by the gravitational force between the Earth and the satellite, responsible for "keeping" the satellite along its circular trajectory.
In this problem, we have a motorbike driving along a circular bend: in this case, the centripetal force is provided by the force of friction between the tires of the motorbike and the road itself. Therefore, we can equate the force of friction to the centripetal force: for an unbanked road,
[tex]\mu mg = m\frac{v^2}{r}[/tex]
where [tex]\mu[/tex] is the coefficient of friction and g is the acceleration of gravity. Re-arranging, we get
[tex]v=\sqrt{\mu gr}[/tex]
which is the speed at which the motorbike can safely drive along the bend.
b) i)
We can answer this part of the problem by looking again at the formula for the centripetal force:
[tex]F=m\frac{v^2}{r}[/tex]
where
m is the mass of the object
v is its speed
r is the radius of the circle
In this problem, we are told that the motorbike is driven round the bend at a higher speed, so the new speed is larger than the previous speed:
[tex]v'>v[/tex]
So the new centripetal force is
[tex]F'=m\frac{v'^2}{r}[/tex]
We observe that the centripetal force is proportional to the square of the speed: therefore, as the speed increases, the centripetal force also increases.
b) ii)
Again, the formula to look at is
[tex]F=m\frac{v^2}{r}[/tex]
In this problem, the motorbike is driven at the same speed, however the bend has a smaller radius, so
[tex]r'<r[/tex]
This means that the new centripetal force is
[tex]F'=m\frac{v^2}{r'}[/tex]
From the equation, we observe that the centripetal force is inversely proportional to the radius of the bend: therefore, as the radius becomes smaller, the centripetal force becomes larger.
Learn more about centripetal force:
brainly.com/question/2562955
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