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My dad was driving in a highway, when we leave the highway there is a banked road. When car turning right, my body is leaning to the left. I thought my body will lean to the center due to centripetal force. Why??

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There is centripetal force on the free upper part of your body, only to the extent it is attached to the lower part of your body, which is attached to the seat by friction and by the lap part of your seat belt. On the free upper part, there is centrifugal force which is caused by the inertia of the free upper part of your body tending to continue in a straight line as the car makes a turn to the right. Thus, the upper part of your body tends to lean left as the car turns right.

If it weren't for the friction of the car seat and the lap part of the seat belt, your entire body would tend to slide left as the car turns right. But your tether to the car causes you to seek the center of the arc being made by the car as it turns. Likewise, the friction of the car's tires on the road allow it to seek the center of the arc it makes, and to avoid flying off the road. Friction provides centripetal force, which overcomes the centrifugal force acting on the car and on you.

I'm assuming there is enough play in the upper part of the seat belt to allow you to lean somewhat toward the left. If there were a sudden acceleration to the right, the seat belt probably would clinch and prevent you from leaning left.

Centrifugal force is sometimes called a fictitious force, as it exists only in a rotating (accelerating in the sense of change of direction) reference frame. In an inertial reference frame free from acceleration, such as the world outside the car, centrifugal force doesn't exist.

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Inertia.

Your body, like all mass, tries to stay where it is, according to Newton's first law. If the car turns right, your body tries to stay where it was, which is on the left.

Same reason when the car accelerates forwards, you are pushed back into your seat.

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The source of the centripetal force that forces you to go around the turn is the friction between your seat and your thighs. Your upper body doesn't feel a force and so continues in the same direction. Your lower half is pulled out from under you by seat friction to the right, leaving you leaning to the left.

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