The force needed to keep a car from skidding on a curve varies inversely as the radius of the curve and jointly as the weight of the car and the square of the car's speed.Suppose that 400 pounds of force keeps a 1600-pound car from skidding on a curve of radius 800ft
at 50mph. What force would keep the same car from skidding on a curve of radius 600ft at 60mph?
F = k m g v^2/R
(actually k g = 1 because v^2/R is centripetal acceleration)
anyway
400 = k (1600) 50^2/800
so k(1600) = 800 * 400 /2500
F = k (1600) 60^2 /600
F = 800*400 *3600 /{2500*600)
= (8/6)(36/25)*400
= (4/3)(36)(16) = 768 pounds
Ah, the force required to keep a car from skidding on a curve. Let me crunch some numbers while trying not to skid on a clever banana peel!
We know that the force varies inversely with the radius, and jointly with the weight and the square of the car's speed. So, let's set up the equation:
Force = k * (Weight * Speed^2) / Radius
where k is some constant.
Now, we can plug in the values from the first scenario:
400 = k * (1600 * (50^2)) / 800
Solving this equation, we can find the value of k. *drumroll, please!*
k ≈ 1/10
Alright, now let's use our newfound knowledge to calculate the force required in the second scenario. We have:
Force = (1/10) * (1600 * (60^2)) / 600
After doing the math, the force needed to keep the same car from skidding on a curve of radius 600ft at 60mph is approximately... *cue the hilarious suspense...*
480 pounds! Time to bring out the car wax and prevent some skids!
To solve this problem, we can use the formula for inverse variation:
Force = k / (radius * weight * speed^2)
First, let's find the value of k using the given information. We know that when the force is 400 pounds, the radius is 800 ft, the weight is 1600 pounds, and the speed is 50 mph.
400 = k / (800 * 1600 * 50^2)
Next, let's calculate the value of k:
400 * 800 * 1600 * 50^2 = k
k = 256,000,000,000
Now we can substitute the known values into the formula to solve for the force required on a curve of radius 600 ft and speed 60 mph:
Force = 256,000,000,000 / (600 * 1600 * 60^2)
Calculating this expression gives us:
Force ≈ 94.53 pounds
Therefore, approximately 94.53 pounds of force would be needed to keep the same car from skidding on a curve of radius 600 ft at 60 mph.
To find the force that would keep the same car from skidding on a curve of radius 600 ft at 60 mph, we need to use the given information and apply the inverse variation and joint variation concepts.
Let's break down the given information:
Force = k * (1 / radius) * (weight) * (speed^2)
We are given:
Force1 = 400 pounds
Weight = 1600 pounds
Radius1 = 800 ft
Speed1 = 50 mph
We need to find:
Force2 (the force that would keep the car from skidding on a curve of radius 600 ft at 60 mph)
First, let's find the constant of variation (k) by plugging in the values of the first scenario:
400 = k * (1 / 800) * 1600 * (50^2)
Simplifying:
400 = k * (1/800) * 1600 * 2500
Now, solve for k:
400 = 500,000 * k
k = 400 / 500,000
k = 0.0008
Now, we can use this value of k to find Force2:
Force2 = k * (1 / radius2) * weight * (speed2^2)
Plugging in the values of the second scenario:
Force2 = 0.0008 * (1/600) * 1600 * (60^2)
Simplifying and calculating:
Force2 = 0.0008 * (1/600) * 1600 * 3600
Force2 ≈ 30.72 pounds (rounded to two decimal places)
Therefore, the force that would keep the same car from skidding on a curve of radius 600 ft at 60 mph is approximately 30.72 pounds.