a 2500-kg car is travelling at 20 m/s around a road curve of radius 200 m. Find the central force acting on the car?
To find the central force acting on the car, we can use the formula for centripetal force:
F = (m * v^2) / r
where:
F is the centripetal force
m is the mass of the car (2500 kg)
v is the velocity of the car (20 m/s)
r is the radius of the road curve (200 m)
Plugging in the values, we have:
F = (2500 kg * (20 m/s)^2) / 200 m
Now let's calculate the centripetal force:
F = (2500 kg * 400 m^2/s^2) / 200 m
F = 500000 N
Therefore, the central force acting on the car is 500,000 Newtons.
To find the central force acting on the car, you can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
The car is moving in a curved path, so it is accelerating towards the center of the curve. This acceleration is known as the centripetal acceleration and is given by the formula:
a = v^2 / r
where:
a = centripetal acceleration
v = velocity of the car
r = radius of the curve
In this case, the velocity of the car is given as 20 m/s, and the radius of the curve is 200 m.
Substituting these values into the formula, we have:
a = (20 m/s)^2 / 200 m
a = 400 m^2/s^2 / 200 m
a = 2 m/s^2
Now, we can find the central force by multiplying the mass of the car by the centripetal acceleration:
F = m * a
Given that the mass of the car is 2500 kg and the centripetal acceleration is 2 m/s^2, we have:
F = 2500 kg * 2 m/s^2
F = 5000 kg*m/s^2
Therefore, the central force acting on the car is 5000 Newtons.