A car of mass m travelling at speed v moves on a horizontal track so that the
Question:
A car of mass m travelling at speed v moves on a horizontal track so that the centre of mass describes a circle of radius r. Show that the limiting speed beyond which the car will overturn is given by
where 2a is the separation of the inner and outer wheels and h is the height of the centre of mass above the ground.
v? = gra
Step by Step Answer:
Let us assume that the car is travelling into the page and is turning towards the left It must be subject to a centripetal force mv 2 r to the left pr...View the full answer
Related Video
The area of a circle is given by the formula: A = ?r^2 Where A is the area, ? is a mathematical constant (approximately 3.14), and r is the radius of the circle. The radius is the distance from the center of the circle to the edge. So for example, if the radius of a circle is 5 units, the area would be: A = ?(5^2) = ?(25) = 78.5 square units Here three friends went out to a restaurant and decided to have pizza for lunch. While they were waiting for their order, one of them stepped out to take a call but promised to return in two minutes. The waiter came and presented them with the menu, and they decided to order two 10-inch pepperoni pizzas. The waiter took their order and left. Just then, the third friend returned and asked what they had ordered. They explained that they had ordered two small pepperoni pizzas as they were only three of them and it would be enough for them. However, the third friend suggested that for the same price, they could get a large pizza that would be much bigger than the two small ones. He asked the waiter for a pen and paper and proceeded to calculate the area of the two small pizzas and compared it to the area of one large pizza. The friends were amazed at how the circle measurements worked and decided to change their order from two small pizzas to one large pizza.
Students also viewed these Mechanics questions
-
A car of mass m is propelled by an engine that has a maximum power P. The engine produces a force , where v is the speed of the car. The motion of the car is opposed by a frictional force that is...
-
A mechanic pushes a car of mass m, doing work W in making it accelerate from rest. Neglecting friction between car and road, (a) What is the final speed of the car? During this time, the car moves a...
-
A car of mass m passes over a bump in a road that follows the arc of a circle of radius R as in Figure P6.51. (a) What force does the road exert on the car as the car passes the highest point of the...
-
The following information was drawn from the 2016 accounting records of Ozark Merchandisers: 1. Inventory that had cost $21,200 was sold for $39,900 under terms 2/20, net/30. 2. Customers returned...
-
In the aggregate, debt offerings are much more common than equity offerings and typically much larger as well. Why?
-
In a large university, the following are the ages of 20 randomly chosen employees: Assuming that the data came from a normal population, construct a 95% confidence interval for the population mean ...
-
The Harvey Corporation is considering a change in its cash-only policy. The new terms would be net one period. Based on the following information, determine if Harvey should proceed or not. The...
-
Cusick Department Store is located near the Village Shopping Mall. At the end of the company??s calendar year on December 31, 2012, the following accounts appeared in two of its trial balances....
-
This is a partial adjusted trial balance of Pharoah Company.PHAROAH COMPANY Adjusted Trial Balance January 31, 2025 SuppliesPrepaid Insurance Salaries and Wages Payable Unearned ServiceRevenue Supp 2...
-
Capital Edge Company has found that, historically, 0.5% of its current accounts receivable, 3% of accounts 1 to 30 days past due, 4.5% of accounts 31 to 60 days past due, 8% of accounts 61 to 90 days...
-
A ball of mass 0.5 kg attached to a light inextensible string rotates in a vertical circle of radius 0.75 m, such that it has a speed of 5 ms-1 when the string is horizontal. Calculate the speed of...
-
A coin of mass 10 gram rolls along a horizontal table with a velocity of 6cms-1. What is its kinetic energy?
-
Which unit is larger? 1. 1 litre or 1 centilitre 2. 1 millilitre or 1 kilolitre 3. 1 cubic millimetre or 1 cubic centimetre 4. 1 cm3 or 1 m3 5. 1 square kilometre or 1 hectare 6. 1 mm2 or 1 dm2
-
Examine the emergence of technology and electronic health systems in health care since the passage of the Health Insurance Portability and Accountability Act (HIPAA). Provide an analysis of the...
-
Quail Company builds snowboards. Assume that you have the following information about Quail Company's costs for the most recent year. Cost of fiberglass (raw material) Advertising $ 119,000 67,200...
-
Find commonalities and differences, look for patterns. Provide an analysis in the format we've established. Determine the order of morphemes within a word. 1. nimitsita 2. nikita 3. tikmaka 4....
-
The following information is available to reconcile Branch Companys book balance of cash with its bank statement cash balance as of July 3 1 . a . On July 3 1 , the companys Cash account has a $ 2 5...
-
Accenture is a very acquisitive company. As they grow their assets through acquisitions, they need to make sure they continue to have financing for these important strategic moves. Let's help...
-
Using the PSA benchmark, complete the following table: Month PSA CPR SMM 6 100 12 50 35 99 77 411
-
What are the 5 Cs of marketing channel structure?
-
Who at Pitt Fitness determines access privileges for users and enters the appropriate authorization rules in the DBMS? a. Chief security officer b. Chief information officer c. Database administrator...
-
In outer space, two identical space modules are joined together by a mass less cable. These modules are rotating about their center of mass, which is at the center of the cable because the modules...
-
A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a crystal as shown in Figure P1.1a. The atoms reside at the corners of cubes of side L = 0.200nm. One piece...
-
Use information on the endpapers of this book to calculate the average density of the Earth. Where does the value fit among those listed in Tables 1.5 and 14.1? Look up the density of a typical...
-
Swifty Journeys Music School provides private music lessons for elementary students. Its operating costs are as follows: Rent on facilities $2,000 per month Advertising $845 per month Instrument Rent...
-
Sandstorm Manufacturing Inc. makes two types of industrial component parts-the LE100 and the UL600. It annually produces 65,000 units of LE100 and 13,000 units of UL600.The company's conventional...
-
Sunland Toys' management is considering eliminating product A, which has been showing a loss for several years. The company's annual income statement, is as follows: A B C Total Sales $2,289,000...
Study smarter with the SolutionInn App