A car of mass M = 1000kg traveling at 40.0km/hour enters a banked turn covered w

Question

A car of mass M = 1000kg traveling at 40.0km/hour enters a banked turn covered with ice. The road is banked at an angle ?, and there is no friction between the road and the car's tires. (Figure 1) . Use g = 9.80m/s2 throughout this problem.

Part A

What is the radius r of the turn if ? = 20.0? (assuming the car continues in uniform circular motion around the turn)?

Express your answer in meters.

A car of mass M = 1000kg traveling at 40.0km/hour enters a banked turn covered with ice. The road is banked at an angle ?, and there is no friction between the road and the car's tires. (Figure 1) . Use g = 9.80m/s2 throughout this problem. What is the radius r of the turn if ? = 20.0? (assuming the car continues in uniform circular motion around the turn)? Express your answer in meters.

Explanation / Answer

V= 40 km/ hour = 11.11 m/s

So make a free body diagram with the angla in it

and Ncos(theta)= mg

So the total force left is Nsin(theta)

so ma= Nsin(theta)

You practically divide the two equations and you get

tan(theta)= a/g

a= V^2/r

tan(theta)= V^2/rg

we're looking for r

switch the equation around

rg= V^2/ tan(theta)

r= V^2/ gtan(theta)

r= (11.11)^2 / (9.8)(tan(20))

r= 123.46/ 3.57

r= 34.6 meters

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