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The ability of an object to resist a change in its state of motion is called inertia. This concept is the key to Newton’s first law of motion.
The acceleration produced by the force is in the same direction as the force. The second law is sometimes expressed as: = m. However, to preserve the vector nature of the forces, and the fact that by “force” we mean “net force,” we write the second law as:”
TIP:
Make sure you understand all of Newton's laws. On an AP free-response problem, you should make a declaration like F = O (for equilibrium) or F = ma (for accelerated systems).
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Sample Problem
How much does a 2-kg mass weigh on the surface of Earth?
Solution
We use the formula for weight:
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The direction and length of the arrows indicate the direction and relative magnitude of the force.
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Example: An object has three forces pulling on it in the directions shown.
Choose your x- and v-axis based on the motion of the object. (One axis should be in the direction of acceleration!) Break vectors A and B into components using trigonometry. Then add up the x-components separately from the y-components.
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Centripetal force is the force that keeps an object moving in a circular path. It always points towards the center of the circle and is required to overcome the tendency of an object to move in a straight line.
The magnitude of the centripetal force required to keep an object moving in a circular path depends on the object's mass, speed, and radius of the circle.
The centripetal force is not a distinct type of force, but rather a resultant force that arises from other forces acting on the object in the circular path. For example, in the case of a car going around a curve, the centripetal force is the result of the friction force acting between the tires and the road.
If the centripetal force acting on an object is not sufficient to keep it moving in a circular path, the object will move outwards, away from the center of the circle. This is known as centrifugal force, which is not actually a force but rather a perceived force resulting from an object's inertia.
Examples of centripetal force in everyday life include the tension force acting on a swing as it moves back and forth, the gravitational force that keeps planets in orbit around the sun, and the force acting on a spinning top as it rotates.
Sample Problem
A car (mass M) takes a turn (of radius R) on a flat road without any slipping or sliding at a constant speed S. Find an expression for the minimum coefficient of friction needed between the wheels and road.
Solution
A rolling tire that is not slipping or sliding relies on static friction to accelerate the car. In this case, the required acceleration is a centripetal one (changing direction rather than speeding up or slowing down):
We can determine an expression for the minimum coefficient of static friction required to take this turn:
Since the normal force is only responsible for canceling the weight of the car in this case:
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