A car has a mass of 2000 kg. While it is traveling along a perfectly flat road, it goes around an unbanked turn that has a radius of 40.0 m. The coefficient of static friction between the car tires and the road is 0.500. The car travels successfully around the turn at a constant speed of 10.0 m/s. Calculate the magnitude of the car's acceleration as it goes around the turn. _______ m/s^2

Answers

Answer 1

Answer:

2.5 m/s²

Explanation:

The given parameters are;

The mass of the car, m = 2,000 kg

The radius of the car, r = 40.0 m

The coefficient of friction between the car tires and the road, μ = 0.500

The constant speed with which the car moves, v = 10.0 m/s

The normal reaction of the road on the car, N = The weight of the car;

∴ N = m × g

Where;

g = The acceleration due to gravity ≈ 9.81 m/s²

N ≈ 2,000 kg × 9.81 m/s² = 19,620 N

The frictional force, [tex]F_f[/tex] = μ × N

The centripetal force, [tex]F_c[/tex] = m·v²/r

The car moves without slipping when [tex]F_f[/tex] = [tex]F_c[/tex]

Therefore, [tex]F_f[/tex] = 0.500 × 19,620 N = 2,000 kg × [tex]v_{max}[/tex]²/40.0 m

∴ [tex]v_{max}[/tex] = √(0.500 × 19,620 N × 40.0 m/2,000 kg) ≈ 14.007 m/s

Therefore, the velocity with which the car moves, v < [tex]v_{max}[/tex]

The cars centripetal acceleration, [tex]a_c[/tex] = v²/r

∴ [tex]a_c[/tex] = (10.0 m/s)²/40.0 m = 2.5 m/s²

The cars centripetal acceleration as it goes round the turn, [tex]a_c[/tex] = 2.5 m/s².


Related Questions

derive an expression for resistivity of conductor of length l and area of cross section A​

Answers

Answer

Resistivity R = K * L / A    where resistivity is constant for material, L the length of the material and A the area of the material

K = R * A / L     where R is the resistance of the material

Saul is testing an installation and discovers a short circuit what’s causing this
A.high current

B.high voltage

C.low resistance

D.low voltage

Answers

Answer:
C. Low resistance

Answer:

im pretty sure that it's (A.) High current

Explanation:

pf

not 100% sure, tho

Other Questions
What are the advantages of Radio waves over micro waves? Write the fraction or mixed number as a decimal. A company like Motorola might establish a goal of reducing its inventory by 50 percent over the next year. To ensure that it reaches this goal, the company could monitor its progress on a quarterly or monthly basis. If the managers at Motorola discover that there is a danger of not achieving this goal, they can take corrective action to adjust for the deficiency. This is a description of the managers' ____ function. Needed in 2 minutes ASAP HELP PLZ!!!!!!!!!!!!!!!!! How does aerobic capacity relate to cardiorespiratory endurance? Consider the reaction: NaNO3(s) + H2SO4(l) NaHSO4(s) + HNO3(g) H = 21.2 kJ How much heat must absorbed by the reaction system to convert 100g of NaNO3 into NaHSO4(s)? The Crusades had which effect on Muslims in Europe?A. Muslims became powerful nobles in European kingdomsB. Muslims were pushed out of many parts of Europe.C. Muslims were killed in pogroms across Europe.D. Most Muslims in Europe became Christian. The Rybczynski theorem asserts that in a two-good world, and assuming that product prices stay constant, growth in the endowment of one factor of production, with the other factor unchanged, will lead to: A. An equal percentage increase in the output of both goods. B. An increase in the output of the good that uses the growing factor intensively and a decrease in the output of the other good. C. An increase in the output of both goods but a greater percentage increase in the output of the good that uses the growing factor intensively. D. An increase in the output of the good that uses the growing factor intensively and no change in the output of the other good. . A ball of mass 0.50 kg is rolling across a table top with a speed of 5.0 m/s. When the ball reaches the edge of the table, it rolls down an incline onto the floor 1.0 meter below (without bouncing). What is the speed of the ball when it reaches the floor? The triangle below is isosceles. Find the length of side x in simplest radical form witha rational denominator.V10Answer: 2==Submit Answer At year-end (December 31), Chan Company estimates its bad debts as 0.30% of its annual credit sales of $896,000. Chan records its Bad Debts Expense for that estimate. On the following February 1, Chan decides that the $448 account of P. Park is uncollectible and writes it off as a bad debt. On June 5, Park unexpectedly pays the amount previously written off. Prepare Chan's journal entries for the transactions. 1 atm is equal toO 1 mmHg 14.7 mmHg 76 mmHg 760 mmHg Read the following paragraph:"Brownies made from a mix are vastly underrated and can be baked to suit any taste. As with those made from scratch, the texture of browniesfrom a box is dependent on the amount of eggs added to the batter. A single egg produces a denser brownie than one made with two eggs. Brownietexture can also be varied through the choice of pan because glass heats more slowly than metal."Which sentence uses subjective language?O Brownie texture can also be varied through the choice of pan because glass heats more slowly than metal.As with those made from scratch, the texture of brownies from a box is dependent on the amount of eggs added to the batter.O Brownies made from a mix are vastly underrated and can be baked to suit any taste.A single egg produces a denser brownie than two eggs. Standish Company manufactures consumer products and provided the following information for the month of February: Units produced 131,000 Standard direct labor hours per unit 0.20 Standard fixed overhead rate (per direct labor hour) $2.50 Budgeted fixed overhead $65,000 Actual fixed overhead costs $68,300 Actual hours worked 26,350Required:a. Calculate the fixed overhead spending variance using the formula approach.b. Calculate the volume variance using the formula approach. hi, please solve these three questions for me, i have to shoe solving steps. PLEASE HELP DUE!!!WILL GIVE BRAINLIEST!!can someone help me please? The sum of two numbers is 83 if one of the number is 7 more than the other find the two numbers? Dollar bills are legal tender in the U.S.True False A storeowner orders 25 calculators that cost $38 each. The storeowner can sell each calculator for $42. The storeowner sold 22 calculators to customers. He had to return 3 calculators that were never sold and pay a $2 charge for each returned calculator (although the initial cost is refunded). What is the storeowner's profit?