a 2500kg car is rounding a circular turn of radius 200m at constant speed. the magnitude of its acceleration is 2m/s2.what is the speed of the car? how much is the centripetal force?how much is the centrifugal acceleration?
To find the speed of the car, we can use the equation for centripetal acceleration:
a = v^2 / r
where:
- a is the magnitude of the acceleration (2 m/s^2),
- v is the speed of the car (what we're trying to find),
- r is the radius of the circular turn (200 m).
Rearranging the equation, we get:
v^2 = a * r
Substituting the given values, we can find the speed:
v^2 = 2 m/s^2 * 200 m
v^2 = 400 m^2/s^2
Taking the square root of both sides:
v = √400 m^2/s^2
v = 20 m/s
So, the speed of the car is 20 m/s.
To calculate the centripetal force, we can use the formula:
F = m * a
where:
- F is the centripetal force (what we're trying to find),
- m is the mass of the car (2500 kg),
- a is the magnitude of the centripetal acceleration (2 m/s^2).
Substituting the given values, we can find the centripetal force:
F = 2500 kg * 2 m/s^2
F = 5000 N
Therefore, the centripetal force is 5000 Newtons.
Now, let's address the concept of centrifugal acceleration. Centrifugal acceleration is an apparent force that seems to act outward on a rotating object. However, it is not an actual force but rather a result of inertia trying to keep an object moving in a straight line. It is experienced by an observer located on the rotating object.
Centrifugal acceleration can be calculated using the formula:
ac = v^2 / r
where:
- ac is the magnitude of the centrifugal acceleration,
- v is the speed of the car (20 m/s),
- r is the radius of the circular turn (200 m).
Substituting the given values, we can calculate the centrifugal acceleration:
ac = (20 m/s)^2 / 200 m
ac = 2 m/s^2
Therefore, the centrifugal acceleration is 2 m/s^2.