Question

3. A car is negotiating a curve of radius 250 m. If the maximum speed the car can go without slipping is 47 m/s. Find coefficient of static friction between car's tires and the road. A) 0.6 B) 0.7 C) 0.8 D) 0.9 4. A car on a roller coaster has a speed of 12 m/s at an elevation of 20 m above the ground. It coasts down a slope, and then comes to rest after climbing a hill. Find the height h of the hill. (Hint: Use conservation of mechanical energy] A) 25.2 m B) 27.3 m C) 12.5 m D) 10.3 m 20 m

Answer 1

3) mass of the car=m radius of turn=R All the forces should bein balance when the carisin equilibrium balance equtaion along vertical axis should be Fw cose= mg +u, Fn sine ...eq(1) weknow angle of banking =0 =0° andalong horizantal axis should be Kjsin8+u, . cose= m (centrifugalforce) . ..eq(2) Fy = normal force=mg if the minimum coefficient of friction is u, and speed of the car = v R = radius of curvature solving the pair of equation 1 and 2 for 0 =0° = v*cose – Rgsine v2 (Rgcose - v2 sine) Rg v=47" ; R =250 m;g=9.8 when plug the values in therelation u. = 0.90 choice is (D) => 4) the height of hill=h by the conservation of energy mgh=mgh'+ mv =>h'=initial height =20m weplug the know values in the relation gives h = 27.365 m