Force and laws of motion Done by Akshita Saloni yadav Saloni rose

Aristotle’s fallacy:

Aristotle’s fallacy Aristotle’s law of motion An external force is required to keep a body in motion.

Conservation of momemtum:

Conservation of momemtum Linear momentum can be represented by the formula

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in an isolated system with only two objects, the change in momentum of one object must be equal and opposite to the change in momentum of the other object m 1 u 2 – m 1 u 1 = m 2 v 2 – m 2 v 1

Hooke’s law:

Hooke’s law As long as they are not stretched or compressed beyond their elastic limit, most springs obey Hooke's law, which states that the force with which the spring pushes back is linearly proportional to the distance from its equilibrium length: where x is the displacement vector – the distance and direction in which the spring is deformed F is the resulting force vector – the magnitude and direction of the restoring force the spring exerts k is the rate, spring constant or force constant of the spring, a constant that depends on the spring's material and construction.

Motion of a car on level circular road:

Motion of a car on level circular road When vehicles go through turnings, they travel along a nearly circular arc. There must be some force which will produce the required acceleration. If the vehicles go in a horizontal circular path, this resultant force is also horizontal. Consider the situation in which a car of weight mg is moving on a horizontal circular road of radius r with a constant velocity v. The external forces acting on the car are weight mg normal contact force N friction Fs The tyres have a tendency to slip outwards. Hence, the frictional forces act towards the centre. Thus, for a safe turn we must have

Motion of a car on a banked road:

Motion of a car on a banked road As opposed to a car riding along a flat circle, inclined edges add an additional force that keeps the car in its path and prevents it from being "dragged into" or "pushed out of" the circle. This force is the horizontal component of the car's normal force. In the absence of friction, the normal force is the only one acting on the car in the direction of the center of the circle. Therefore, as per Newton's second law, we can set the horizontal component of the normal force equal to mass multiplied by centripetal acceleration:

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Because there is no motion in the vertical direction, the sum of all vertical forces acting on the system must be zero. Therefore we can set the vertical component of the car's normal force equal to its weight: Ncos θ = mg Solving the above equation for the normal force and substituting this value into our previous equation, we get:

Motion of a car on a banked road with friction:

Motion of a car on a banked road with friction When considering the effects of friction on the system, once again we need to note which way the friction force is pointing. When calculating a maximum velocity for our automobile, friction will point down the incline and towards the center of the circle. Therefore we must add the horizontal component of friction to that of the normal force. The sum of these two forces is our new net force in the centripetal direction:

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Once again, there is no motion in the vertical direction, allowing us to set all opposing vertical forces equal to one another. These forces include the vertical component of the normal force pointing upwards and both the car's weight and vertical component of friction pointing downwards: Ncos θ = μsNsin θ + mg By solving the above equation for mass and substituting this value into our previous equation we get:

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