(A) Draw a free-body diagram which shows the forces acting on the car and the radius of the curve. Assume rolling friction and air drag are negligible (and that no propulsion force is required to maintain a constant speed). Include your coordinate axes. (B) Use Newton's second law to write an equation for the resulting centripetal force. Solve this equation for centripetal force in terms of: the mass of the car m, the radius of the curve r, time to make the curve t, and any needed constants of proportionality. Simplify as possible. (C) If the car makes the turn in 3.80 seconds and the right hand turn in the road has a radius of 45.7m, would a coefficient of static friction between the tires and the road is 0.90 be sufficient to keep the car on the road? Justify your result.
(A) Draw a free-body diagram which shows the forces acting on the car and the radius of the curve. Assume rolling friction and air drag are negligible (and that no propulsion force is required to maintain a constant speed). Include your coordinate axes. (B) Use Newton's second law to write an equation for the resulting centripetal force. Solve this equation for centripetal force in terms of: the mass of the car m, the radius of the curve r, time to make the curve t, and any needed constants of proportionality. Simplify as possible. (C) If the car makes the turn in 3.80 seconds and the right hand turn in the road has a radius of 45.7m, would a coefficient of static friction between the tires and the road is 0.90 be sufficient to keep the car on the road? Justify your result.
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Transcribed Image Text:**Physics Problem: Car Negotiating a Turn**
A car of mass \( m \) negotiates a right-hand 90º turn at constant speed \( v \) on a flat road such that the radius of the turn is given by \( r \). The time the car takes to go around the turn is \( t \). There is friction \( f \) between the tires and the road. The car makes the turn at high speed without skidding (sliding). After the turn, the car continues down the road at constant speed.
**(A)** Draw a free-body diagram showing the forces acting on the car and the radius of the curve. Assume rolling friction and air drag are negligible (and that no propulsion force is required to maintain a constant speed). Include your coordinate axes.
**(B)** Use Newton's second law to write an equation for the resulting centripetal force. Solve this equation for centripetal force in terms of: the mass of the car \( m \), the radius of the curve \( r \), time to make the curve \( t \), and any needed constants of proportionality. Simplify as possible.
**(C)** If the car makes the turn in 3.80 seconds and the right-hand turn in the road has a radius of 45.7 m, would a coefficient of static friction between the tires and the road is 0.90 be sufficient to keep the car on the road? Justify your result.
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