The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and the square of its speed and inversely as the radius of the curve.

Question

The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and the square of its speed and inversely as the radius of the curve.

If 182lb of force keep a 1800lb car from skidding on a curve of radius 600ft at 30 mph, what force would keep the same car from skidding on a curve of radius 650ft at 45 mph? 378

Answer 1

F = k(w)(v^2)/r , where k is a constant

182 = k(1800)(30^2)/600
k = 182(600)/((1800)(900)) = 91/1350

so for the given question,
F = (91/1350) (1800)(45^2)/650
= 378 lb

check my arithmetic

Answer 2

To find the force needed to keep the car from skidding on a curve of radius 650ft at 45 mph, we use the concept of joint variation.

Given:
Force (F1) = 182 lb
Weight of the car (W) = 1800 lb
Radius of the curve (r1) = 600 ft
Speed (s1) = 30 mph

We can set up the equation of joint variation as follows:

F1 = k * W * s1^2 / r1

Now, let's solve for the constant of variation (k):

k = F1 * r1 / (W * s1^2)
= 182 lb * 600 ft / (1800 lb * (30 mph)^2)
= 0.04044 lb ft^3 / (mph^2)

We can use this constant of variation (k) to find the force (F2) for the new situation:

Weight of the car (W) = 1800 lb
Radius of the curve (r2) = 650 ft
Speed (s2) = 45 mph

F2 = k * W * s2^2 / r2
= 0.04044 lb ft^3 / (mph^2) * 1800 lb * (45 mph)^2 / 650 ft
≈ 377.9 lb (rounded to the nearest whole number)

Therefore, the force that would keep the same car from skidding on a curve of radius 650ft at 45 mph is approximately 378 lb.

Answer 3

To solve this problem, we can use the joint variation formula:

force = k * (weight) * (speed^2) / (radius)

First, let's find the value of the constant of variation, k. We will use the given information from the first scenario to solve for k:

182 = k * 1800 * (30^2) / 600

First, simplify the equation:

182 = k * 1800 * 900 / 600

Next, cancel out the common factors:

182 = 3k * 1800

Now, divide both sides by 3 * 1800:

182 / (3 * 1800) = k

0.0333 = k

Now that we have the value of k, we can use it to solve the second scenario. We want to find the force required to keep the car from skidding on a curve of radius 650ft at 45 mph. Plug the values into the formula:

force = 0.0333 * 1800 * (45^2) / 650

Simplify the equation:

force = 0.0333 * 1800 * 2025 / 650

force = 112.77

Therefore, the force required to keep the same car from skidding on a curve of radius 650ft at 45 mph is approximately 112.77 lb.