Question

Determine the maximum (constant) speed at which a 3.0 x 10^3 kg car can safely round a circular curve of radius 50. m on a horizontal road if the friction between the tires and the road is 20600 N. Sketch a picture and show all of your work.

Answer 1

PLEASE SOMEONE HELPP

Answer 2

3x10^3=3000kg Ff=Fc Ff=20600N R=50

20600=m(v^2/r)

20600=3000 (v^2/50)
-3000 -3000

17600=(v^2/50)

17600/50=(v^2/50)
352=(v^2)

now we square 352 to get rid of the power
v=18.76
(if multiple choice answer to nearest number)

Answer 3

[AI-generated answer — Explain Bot]

To determine the maximum constant speed at which a car can safely round a circular curve, we need to consider the forces acting on the car.

Here's how we can approach the problem step by step:

Step 1: Identify the forces on the car:
When a car is moving in a circular path, there are two primary forces acting on it: the centripetal force (Fc) and the force of friction (Ff).

The centripetal force (Fc) is the force that keeps the car moving in a circular path and is given by the equation:
Fc = (mass of the car) x (velocity of the car)^2 / (radius of the curve)

The force of friction (Ff) opposes the motion of the car and is given by the equation:
Ff = (coefficient of friction) x (normal force)
In this case, the force of friction is equal to the maximum possible friction, which is obtained when the tires are at the verge of slipping.

Step 2: Calculate the normal force:
The normal force (Fn) is the force exerted by the surface (road) on the car and is equal to the weight of the car. Mathematically, it can be written as:
Fn = (mass of the car) x (acceleration due to gravity)

Step 3: Substitute the values and solve for the maximum speed:
Given:
Mass of the car (m) = 3.0 x 10^3 kg
Radius of the curve (r) = 50.0 m
Coefficient of friction (µ) = maximum friction = 20600 N
Acceleration due to gravity (g) = 9.8 m/s^2

First, calculate the normal force:
Fn = m x g = (3.0 x 10^3 kg) x (9.8 m/s^2)

Next, substitute the values into the equation for the force of friction:
Ff = µ x Fn = 20600 N

Finally, substitute the values for mass, velocity, and radius into the equation for the centripetal force:
Fc = m x v^2 / r

Rearrange the equation to solve for the maximum velocity (v):
v = sqrt((Fc x r) / m)

Now, plug in the values for the centripetal force and solve for the maximum velocity.

Step 4: Sketch a picture:
Unfortunately, as an AI text-based bot, I cannot draw pictures. However, you can imagine a car moving in a circular path on a horizontal road with a radius of 50.0 m.

Step 5: Calculate the maximum velocity:
Using the equation v = sqrt((Fc x r) / m), substitute the values we calculated earlier and solve for v.

Once you have solved the equation, you will have the maximum constant speed at which the car can safely round the circular curve.

Remember to be cautious and check your calculations to ensure accuracy.