I don\'t understand what I\'m doing wrong on this problem. I\'ve answered 7.715

Question

I don't understand what I'm doing wrong on this problem. I've answered 7.715 and 7.72 for part A, and 3.172 and 3.17 for part B. All of which were wrong.

A curve of radius 151 m is banked at an angle of 11o. An 802-kg car negotiates the curve at 88 km/h without skidding. Neglect the effects of air drag and rolling friction. Find the following of air drag and rlling fiction. Find the following. (a) the normal force exerted by the pavement on the tires 7.72 (b) the frictional force exerted by the pavement on the tires 3.17 XkN 0.194 Draw a free-body diagram showing the three forces acting on the car. (A head-on view of the car may be the most useful perspective.) Both the normal force and the static friction force have components which contribute to the centripetal force in the situation described in this problem. Apply Newton's second law to relate the static friction and normal forces, and then solve these equations simultaneously to determine each of these quantities. eBook

Explanation / Answer

A.

Vertical force balance

u*Fn*sin 11 deg + mg = Fn*cos 11 deg

Fn = (mg)/(cos 11 deg - u*sin 11 deg)

Fn = 802*9.81/(cos 11 deg - 0.194*sin 11 deg)

Fn = 8328.96 N = 8.33 kN

B.

Ff = u*Fn

Ff = 0.194*8.33 kN = 1.616 kN = 1.62 kN

OR (Another method)

A.

Using force balance:

Net F = m*a

Fn*sin A + Ff*cos A = m*v^2/r

In y-diretion:

Fn*cos A - Ff*sin A = m*g

Solving both equation:

Fn = (mv^2/r)*sin A + mg*cos A

Using given values:

Fn = 802*24.44^2*sin 11 deg/151 + 802*9.81*cos 11 deg

Fn = 8328.40 N = 8.33 kN

Fn*cos A - Ff*sin A = m*g

Ff = (Fn*cos A - m*g)/sin A

Ff = (8328.40*cos 11 deg - 802*9.81)/sin 11 deg = 1612.94 N

Ff = 1.612 kN

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