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What is the ideal banking angle (in degrees) for a gentle turn of 2.00 km radius on a highway with a 125 km/h speed limit (about

nikitadnepr [17]

An "ideal" banking angle assumes no friction is required to keep a car on the road as it turns. Let θ denote the banking angle, and consult the attached free-body diagram for a car making the turn. There are only 2 relevant forces acting on the car,

• the normal force with magnitude n

• the car's weight with magnitude w

and the net force points toward the center of the circle made by the turn, with centripetal acceleration

a = (125 km/h)² / (2.00 km) = 7812.5 km/h² ≈ 0.603 m/s²

Split up the forces into components acting perpendicular (⟂) and parallel (//) to the banked curve, so that by Newton's second law,

∑ F (⟂) = N + W (⟂) = m a (⟂)

and

∑ F (//) = W (//) = m a (//)

Let the direction of N be the positive perpendicular axis, and down the incline and toward the center of the circle the positive parallel axis. The net force vector and acceleration both make an angle θ with the banked curve, and W makes the same angle with the negative perpendicular axis, so that the equations above reduce to

N - m g cos(θ) = m a sin(θ)

and

m g sin(θ) = m a cos(θ)

The second equation is all we need at this point to find the ideal θ. The mass m cancels out, and we can solve for θ to get

tan(θ) = a/g ≈ (0.603 m/s²) / (9.80 m/s²) ≈ 0.0615

→ θ ≈ 3.52°

8 0

3 years ago

A force of 20 N acts on a smaller piston of a hydraulic press with an area of 10 dm2. How much force does the liquid act on a

ivann1987 [24]

Answer:

166.67 N

Explanation:

Applying Pascal's principle,

Presure in the smaller piston(P') = Pressure in the bigger piston(P)

But,

Pressure = Force/Area

Pressure in the smaller piston(P') = Force applied to the smaller piston(F')/Area of the smaller piston(A')

Pressure in the bigger piston(P) = Force applied to the bigger piston(F)/Area of the bigger piston(A)

F'/A' = F/A.................. Equation 1

Make F the subject of the equation

F = F'A/A'.............. Equation 2

From the question,

Given: F' = 20 N, A = 120 cm², A' = 10 dm² = (10×100) = 1000 cm²

Substitute these values into equation 2

F = 20(1000)/120

F = 166.67 N

3 0

3 years ago

1200 meters is less than 1 kilometer

SashulF [63]

1200 meters is less than 1 kilometer
is false

4 0

4 years ago

Read 2 more answers

The handle of a metal spoon warms up when it is placed in a hot bowl of soup because of

blagie [28]

conduction because energy is being conducted throughout the spoon

8 0

3 years ago

train with a mass of 485000 kg. suppose the train is traveling northwest along a straight track at a speed of 20m/s. what force

Sergeu [11.5K]

Answer:

Force = 485000 Newton.

Explanation:

Given the following data;

Mass = 485000 kg

Initial velocity = 20m/s

Final velocity = 25m/s

Time, t = 5 seconds

To find the force;

First of all, we would calculate the acceleration of the train i.e the rate of change of the velocity of the train with respect to time.

Mathematically, acceleration is given by the equation;

$Acceleration (a) = \frac{final \; velocity - initial \; velocity}{time}$

$a = \frac{v - u}{t}$

Where;

a is acceleration measured in $ms^{-2}$

v and u is final and initial velocity respectively, measured in $ms^{-1}$

t is time measured in seconds.

Substituting into the equation, we have;

Acceleration = (25 - 20)/5

Acceleration = 5/5

Acceleration = 1m/s²

Force is given by the multiplication of mass and acceleration.

Mathematically, Force is;

Force = mass * acceleration

Force = 485000 * 1

Force = 485000 Newton.

4 0

3 years ago