A 726 kg car travels from Boone to Blowing Rock along US321. How much working is needed to keep the car traveling at a constant speed of 21.8 m/s around a curve of radius 28.4 m?
To determine the amount of work needed to keep the car traveling at a constant speed around a curve, we can use the equation for centripetal force:
F = (mv^2) / r
where:
F is the centripetal force,
m is the mass of the car,
v is the velocity of the car,
and r is the radius of the curve.
First, we need to convert the car's weight to Newtons, since the unit of force is Newtons and weight is a force. Weight can be calculated using the formula:
weight = mass * acceleration due to gravity
where the acceleration due to gravity is approximately 9.8 m/s^2.
weight = 726 kg * 9.8 m/s^2
weight ≈ 7128.8 N
Next, we need to determine the centripetal force acting on the car. The centripetal force is equal to the weight of the car, so:
F = 7128.8 N
Now, we can substitute the given values into the equation for centripetal force:
7128.8 N = (726 kg * (21.8 m/s)^2) / 28.4 m
To solve for the work done, we need to consider that work is equal to the force multiplied by the distance traveled. The distance traveled is equal to the circumference of the curve. The formula for the circumference is:
circumference = 2πr
Given the radius of 28.4 m, we can calculate the circumference:
circumference = 2 * π * 28.4 m
circumference ≈ 178.69 m
Finally, we can calculate the work done:
work = force * distance
work = 7128.8 N * 178.69 m
Therefore, the amount of work needed to keep the car traveling at a constant speed of 21.8 m/s around a curve of radius 28.4 m is approximately the product of 7128.8 N and 178.69 m.