A car travels around an unbanked highway curve (radius 0.15 km) at a constant speed of 25 m/s. What is the magnitude of the resultant force acting on the driver, who weighs 0.8kN?

-Equation--> (mv^2)/r

-convert mass from .8kN to kg by time 1000N time 9.81m/^2=81.55kg
-convert radius from .15km to m by time 1000m=150m

-speed is given: v =25m/s

-now you have everything need to plug into the equation.
plug into the equation and you get340N

-If you wand in kN, do that by divide by1000N because 1kN=1000N and you will get .340kN

Well, well, well! Looks like the driver is in for a twisty ride! To find the magnitude of the resultant force acting on the driver, we need to take a look at the forces involved.

First, let's calculate the centripetal force, which is the force that keeps the car moving in a curve. The formula for centripetal force is given by the equation F = mv²/r, where F is the centripetal force, m is the mass, v is the velocity, and r is the radius.

However, since we are given the weight of the driver instead of the mass, we need to convert it. The weight of the driver is 0.8 kN, and we know that weight is related to the mass by W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity. Since g is around 9.8 m/s², we can divide the weight by g to get the mass.

So, 0.8 kN divided by 9.8 m/s² gives us the mass of the driver. And now, we can calculate the centripetal force by plugging in the values into the formula.

But hold on a second, I almost forgot to convert those units! The radius is given in kilometers, but we need to work with meters. So, let's multiply the radius by 1000 to convert it to meters. Ah, there we go!

Now, let's calculate the centripetal force and find out what's giving that driver a good ol' push!

F = (0.8 kN divided by 9.8 m/s²) × (25 m/s)² divided by (0.15 km × 1000 m/km)

And the answer is... *drumroll* ... the magnitude of the resultant force acting on the driver is approximately... 1702.128 N!

So, buckle up and enjoy the ride, my friend! Just remember, laughter is the best centripetal force to keep you smiling on those curves!

To find the magnitude of the resultant force acting on the driver, we need to consider the forces acting on the driver as the car travels around the curved highway.

The primary force acting on the driver is the centripetal force, which is directed toward the center of the curve. This force is responsible for keeping the car moving in a circular path.

The magnitude of the centripetal force can be calculated using the formula:

F = m * v^2 / r

Where:
F is the centripetal force
m is the mass of the driver (convert 0.8 kN to N by multiplying it by 1000 and divide by the acceleration due to gravity, which is around 9.8 m/s^2)
v is the velocity of the car
r is the radius of the curve

Firstly, convert the driver's weight from kilonewtons (kN) to newtons (N):
0.8 kN = 0.8 * 1000 N = 800 N

Next, substitute the values into the formula:
F = (800 N) * (25 m/s)^2 / 0.15 km

Convert the radius of the curve from kilometers to meters by multiplying by 1000:
F = (800 N) * (25 m/s)^2 / (0.15 km * 1000 m/km)

Calculate the magnitude of the centripetal force:
F = 800 * (25^2) / (0.15 * 1000) N

Now, calculate this expression to find the magnitude of the resultant force acting on the driver.

To find the magnitude of the resultant force acting on the driver, we need to consider the forces involved in the curved motion of the car. Centripetal force is the force that keeps the car moving in a curved path, and it is provided by the friction between the tires and the road.

The centripetal force is given by the equation:

Fc = (m * v^2) / r

where Fc is the centripetal force, m is the mass of the object (driver's weight / acceleration due to gravity), v is the velocity of the car, and r is the radius of the curve.

First, we need to convert the weight of the driver from kilonewtons to newtons:
Weight = 0.8 kN = 0.8 * 1000 N = 800 N

Next, we find the mass of the driver:
m = Weight / acceleration due to gravity
m = 800 N / 9.8 m/s^2 = 81.63 kg (approximately)

Now we can calculate the centripetal force:
Fc = (m * v^2) / r
Fc = (81.63 kg * (25 m/s)^2) / 0.15 km
Fc = (81.63 kg * 625 m^2/s^2) / 150 m
Fc = 339.9375 N (approximately)

Therefore, the magnitude of the resultant force acting on the driver is approximately 339.9375 N.

centripetal sideways

m v^2/R

m = .8*1000/9.81 = 81.55 kg
v = 25 m/s
R = 150 meters

gravitational up from seat
m g = 800 N