A car moving with constant speed in a circular path experience a centripetal acceleration if speed of car increases by three factors but the circular path remain same.What is the new centripetal acceleration in term of original ac?
Ac = v^2/R
new Ac = (3 v)^2/R
= 9 v^2/R
9 times :)
If the speed of the car increases by a factor of three, the new speed will be three times the original speed. Let's denote the original speed as v and the new speed as 3v.
The centripetal acceleration is given by the formula ac = (v^2)/r, where v is the velocity of the car and r is the radius of the circular path.
Since the circular path remains the same, the radius remains constant, so we can write it as r.
Now, let's calculate the new centripetal acceleration, ac'.
Using the formula ac', we have ac' = ((3v)^2)/r = (9v^2)/r.
Therefore, the new centripetal acceleration, ac', is equal to 9 times the original centripetal acceleration, ac.
So, ac' = 9ac.
To find the new centripetal acceleration in terms of the original acceleration, we need to understand the relationship between the centripetal acceleration and the variables involved.
The centripetal acceleration of an object moving in a circular path is given by the equation:
a = v^2 / r,
where "a" is the centripetal acceleration, "v" is the velocity or speed of the object, and "r" is the radius of the circular path.
In this case, the speed of the car increases by three factors, which means it becomes three times faster than before. However, the circular path remains the same, meaning the radius remains unchanged.
Let's denote the original speed as "v₀" and the original centripetal acceleration as "a₀". The new speed would then be "3v₀". Since the radius remains the same, the new centripetal acceleration "a₁" can be written as:
a₁ = (3v₀)^2 / r.
Simplifying this equation, we get:
a₁ = 9v₀^2 / r.
Therefore, the new centripetal acceleration in terms of the original acceleration (a₀) is:
a₁ = 9a₀.