3. Consider the cross section of an ideally banked turn. An ideally banked turn doesn’t require any friction for a vehicle to complete a turn of radius R when the vehicle is traveling at the ideal speed v. (A bowling ball could execute an ideally banked turn if traveling at the ideal speed.) Apply the 3 Step Plan to work your way through this problem to find the ideal banking angle θ. Step 1: Draw all the forces on the truck. Only write down real forces*! Step 2: To find add the forces graphically in a write down from the trig. Be Fnet, Fnet right triangle…and careful in adding the forces: which direction should Fnet point? Hint: Fnet will point in the direction the truck is accelerating: this direction is not parallel and down the incline! Can you see that Fnet will point horizontal and to the left? After making a beautiful right triangle, use trig to find and then apply Law. Fnet, Newt’s 2nd Step 3: Solve for in terms of v and R. Find numerically for v = 30 m/s and R = 402 m. θ θ Does depend on m? If it did, banked turns would need signs with different speeds for different vehicles. θ
3. Consider the cross section of an ideally banked turn. An ideally banked turn doesn’t require any friction for a vehicle to complete a turn of radius R when the vehicle is traveling at the ideal speed v. (A bowling ball could execute an ideally banked turn if traveling at the ideal speed.) Apply the 3 Step Plan to work your way through this problem to find the ideal banking angle θ. Step 1: Draw all the forces on the truck. Only write down real forces*! Step 2: To find Fnet, add the forces graphically in a right triangle…and write down Fnet from the trig. Be careful in adding the forces: which direction should Fnet point? Hint: Fnet will point in the direction the truck is accelerating: this direction is not parallel and down the incline! Can you see that Fnet will point horizontal and to the left? After making a beautiful right triangle, use trig to find Fnet, and then apply Newt’s 2nd Law. Step 3: Solve for θ in terms of v and R. Find θ numerically for v = 30 m/s and R = 402 m. Does θ depend on m? If it did, banked turns would need signs with different speeds for different vehicles.
AdvForcesMidtermPractice2.docx