An engineer wants to design a circular racetrack of radius L such that cars of mass M can go around the track at speed W without the aid of friction or other forces other than the perpendicular contact force from the track surface. Find an expression for the required banking angle 0 of the track, measured from the horizontal. Express the answer in terms of M, L, W, and g. Suppose the race cars actually round the track at a speed u > W. What additional radial force F, is required to keep F, = the cars on the track at this speed? Express the answer in terms of M, L, W, u, and g. ||

An engineer wants to design a circular racetrack of radius L such that cars of mass M can go around the track at speed W without the aid of friction or other forces other than the perpendicular contact force from the track surface. Find an expression for the required banking angle 0 of the track, measured from the horizontal. Express the answer in terms of M, L, W, and g. Suppose the race cars actually round the track at a speed u > W. What additional radial force F, is required to keep F, = the cars on the track at this speed? Express the answer in terms of M, L, W, u, and g. ||

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: car is on a banked left curve with radius r = 100 m and banking angle θ = 20◦. What is the ideal…

A: Free body diagram

Q: A car of mass m travels around a flat, circular curve of radius r at the fastest possible speed, v =…

Q: Two blocks m1=5.6kg and m2= 3.7kg are sliding on a circular track with radius R=8.1m as shown in the…

Q: A roller-coaster at a theme park is designed so that a 70 kg rider in a car at the top of a circu…

A: Given: The speed of the car at the top of the loop, v=10 m/s. The radius of the loop r=20 m. Mass…

Q: A car travels at a steady 39 m/s around a horizontal curve of radius 143 m. What is the minimum…

A: The centripetal force required to move the car in the circle of radius 'r' will be provided by the…

Q: PART D

A: The formula for the orbital period is:

Q: A completely smooth table has a circular end with radius R=40.0 cm. The height of the table is h=…

Q: What is the maximum speed with which a 1200 kg car can round a turn of radius 89.0m on a flat tire…

Q: .. A small rock with mass m is attached to a light string of length L and whirled in a vertical…

A: Mass of rock = mLength of string = L

Q: The maximum static coefficient of friction between the tires of a 2000 kg car and the road is µs,max…

A: Given data The car's mass is: m = 2000 kg The friction coefficient is: μs,max=0.25 The rotation's…

Q: A roller-coaster car has a mass of 1220 kg when fully loaded with passengers. As the car passes over…

A: Given data- The mass of the roller coaster is m=1220 kg Radius of he circular hill is r=18.1 m

Q: Engineers who design roads typically “bank” (incline) curves in such a way that a car traveling at…

Q: A person of mass 60.0 kg is riding on a Ferris wheel as illustrated. Draw the free body diagram for…

A: Draw the free body diagram and then apply the Newton's second law. Also use the centripetal…

Q: A car takes a 100 m radius curve with a bank angle of 15° and a friction coefficient of 0.78.…

Q: What is the minimum coefficient of friction needed for a frightened driver to take the same curve at…

A: Given data: r = 80 mθ = 15° a) the ideal speed of car v1 The velocity v1 is given by tan θ = v12r .…

Q: A "swing" ride at a carnival consists of chairs that are swung in a circle by 18.7 m cables attached…

A: Given: Length of cable = 18.7 m Mass of chair +occupant M =294 kg

Q: 5. A truck, of mass M, that's carrying a load of mass m, is driving with constant speed v over a…

A: Solution:- A0. For object in cirecular motion;…

Q: A roller-coaster car has a mass of 510 kg when fully loaded with passengers. The path of the coaster…

Q: A motorcycle has a constant speed of 24.2 m/s as it passes over the top of a hill whose radius of…

Q: A jet flying at 112 m/s banks to make a horizontal circular turn. The radius of the turn is 3810 m,…

Q: A crate is given an initial speed of 2.2 m/s up the 24 degree plan. Assume uk= 0.12. How far up the…

A: Initial speed (u) = 2.2 m/s Angle of inclination (theta) = 24° Coefficient of kinetic friction= 0.12…

Q: A jet airplane with a mass m=8330 kg is in level fight at constant speed, around a circular path of…

A: The air generated lift force on the plane is.F=85500.055NThe banking angle is.θ=17.3oExplanation:The…

Q: Suppose the radius of the room is 3.91 m and the speed of the wall is 13.9 m/s when the floor falls…

A: Given , Radius of room , r = 3.91 m speed of wall , v = 13.9 m/s We know that centripetal force =…

Q: A race car is making a U-turn at constant speed. The coefficient of friction between the tires and…

Q: small car with mass 0.650 kg travels at constant speed on the inside of a track that is a vertical…

A: Given: Mass of car is m=0.650 kg Car is moving with constant speed in vertical circle of radius r=5…

Q: A car travels at a steady 37.4 m/s around a horizontal curve of radius 161 m. What is the minimum…

Q: Disturbed by speeding cars outside his workplace, Nobel laureate Arthur Holly Compton designed a…

A: Given : Mass of a car (m) = 1800 kg Radius (r) = 19.6 m Speed of a car (v) = 25.0 km/h =…

Q: horizontal circumference at a speed of 500 km / h. The wings form an angle of 35 ° to the…

A: We know that we have given that let An airplane flies in a horizontal circumference at a speed of v…

Q: Fg

A: For the given diagram, write the below mentioned notation Now write the magnitude of the normal…

Q: Banked curves are designed so that the radial component of the normal force on the car rounding the…

Question

An engineer wants to design a circular racetrack of radius L
such that cars of mass M can go around the track at speed W
without the aid of friction or other forces other than the
perpendicular contact force from the track surface.
Find an expression for the required banking angle 0 of the
track, measured from the horizontal. Express the answer in
terms of M, L, W, and g.
Suppose the race cars actually round the track at a speed
u > W. What additional radial force F, is required to keep
F, =
the cars on the track at this speed? Express the answer in
terms of M, L, W, u, and g.
||

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A pickup truck has a box sitting loose in its bed. The box has a mass of 2.5kg and the coefficient of static friction between the box and the pickup bed is 0.8. The mass of the truck is 3150 kg and its tires have a coefficient of static friction with the road of 0.9. the truck is currently going through a roundabout with a radius of 30m. How fast can the truck go and not have the box slide on the truck bed? Please answer in m/s.
A hockey puck that has a mass of 0.150 kg is tied to a light string and spun in a circle of radius 1.15 m on frictionless ice. If the string breaks under a tension that exceeds 4.00 N, what is the maximum speed vmax of the puck without breaking the Umax = m/s string?
Suppose a car rounds a curve at a constant speed of 13 m/s. The curve is a circular arc with a radius of 100 m. Ignore air friction initially. (a) What is the magnitude and direction of the horizontal force that the road must exert on the car to keep it moving along the curve? Express this magnitude as a fraction of the car’s weight. The magnitude of the horizontal force is _______∣F→g∣|. The direction is (Choose one) Horizontal and parallel to the direction the car turns to Vertical and perpendicular to the direction the car turns to vertical and parallel to the direction the car turns to horizontal and perpendicular to the direction the car turns to (b) Now suppose that air friction is not zero, but is about half the result that you calculated for part (a). Must the force that the road exerts on the car increase in magnitude compared to the no-drag case? (Choose )Yes or No Must it change its direction? (Choose) Yes Or No
A small 0.250-kg object is attached to a string (see figure), where it swings in a section of a vertical circle of radius 2.50 m. Find the magnitude of the tension in the string when θ = 28.0°, the speed of the object is 4.50 m/s
A small block with mass 0.0300 kg slides in a vertical circle of radius 0.550 m on the inside of a circular track. During one of the revolutions of the block, when the block is at the bottom of its path, point A, the magnitude of the normal force exerted on the block by the track has magnitude 3.75 N. In this same revolution, when the block reaches the top of its path, point B, the magnitude of the normal force exerted on the block has magnitude 0.685 N. Part A How much work was done on the block by friction during the motion of the block from point A to point B? Express your answer with the appropriate units. W friction = Submit μA Value Request Answer Units ?
At a circus, a stunt rider is going to do a "Loop-de-Loop". The radius of the circular part of the track is 8.13 m. The mass of the motorcycle and the rider is 318. kg. What is the minimum speed the motorcycle must have to just make it around the loop without falling?
A "swing" ride at a carnival consists of chairs that are swung in a circle by 12.4 m cables attached to a vertical rotating pole, as the drawing shows. Suppose the total mass of a chair and its occupant is 135 kg. (a) Determine the tension in the cable attached to the chair. (b) Find the speed of the chair.
A car of massm travels around a flat, circular curve of radius r at the fastest possible speed, v = 13.5 m/s without sliding off. The car and road have a coefficient of friction, between them. If the car wishes to take the turn at 2.4x the velocity, by what factor would the radius need to increase (so the car doesn't slide off) ? Give your answer to 1 decimal place.
Two banked curves have the same radius. Curve A is banked at 13.9 °, and curve B is banked at an angle of 18.1 °. A car can travel around curve A without relying on friction at a speed of 13.7 m/s. At what speed can this car travel around curve B without relying on friction?
Please Asap
The car is fully loaded with passengers and has a total mass of 575 kg. At point A, the car is at the lowest point in a circular arc of radius r1 = 12.4 m. At point B, the car is at the highest point of a circular arc of radius r2 = 17.3 m. (a) If the car has a speed of 25.0 m/s at point A, what is the magnitude of the force (in N) of the track on the car at this point? (b) What is the maximum speed (in m/s) the car can have at point B in order for the car to maintain contact with the track at all times (that is, so that it does not "jump" off the track)?
The lift force on an airplane of mass 897 kg with speed v is given by c v2 (N), where c is some constant depending on the air density and wing geometry. The lift force points perpendicular to the wings of the plane, so that if the plane banks by, say 10 degrees, then the lift force turns 10 degrees from the vertical. Now suppose that the pilot of this plane wishes to complete a flat turn of radius 931 m with speed 104 m/s. How much should they bank the plane, in degrees? (Please answer to the fourth decimal place - i.e 14.3225)