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Ch 08: Dynamics II: Motion in a Plane
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 8, Problema 6

A 1500 kg car takes a 50-m-radius unbanked curve at 15 m/s. What is the size of the friction force on the car?

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Step 1: Identify the forces acting on the car. Since the car is taking an unbanked curve, the frictional force provides the centripetal force required to keep the car moving in a circular path.
Step 2: Write the formula for centripetal force: Fc = mv2/r, where m is the mass of the car, v is its velocity, and r is the radius of the curve.
Step 3: Substitute the given values into the formula. The mass of the car is 1500 kg, the velocity is 15 m/s, and the radius of the curve is 50 m.
Step 4: Calculate the centripetal force using the substituted values. This force is equal to the frictional force because friction is the only force providing the centripetal acceleration in this scenario.
Step 5: Ensure the units are consistent throughout the calculation. The result will be in newtons (N), as the formula involves mass in kilograms, velocity in meters per second, and radius in meters.

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Centripetal Force

Centripetal force is the net force required to keep an object moving in a circular path, directed towards the center of the circle. For an object moving at a constant speed in a circle, this force is provided by the friction between the tires and the road. The formula for centripetal force (Fc) is Fc = (mv^2)/r, where m is mass, v is velocity, and r is the radius of the curve.
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Intro to Centripetal Forces

Friction Force

Friction force is the resistance that one surface or object encounters when moving over another. In the context of a car taking a curve, static friction provides the necessary centripetal force to prevent the car from sliding outwards. The maximum friction force can be calculated using the equation F_friction = μN, where μ is the coefficient of friction and N is the normal force.
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Static Friction & Equilibrium

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, expressed as F = ma. In the case of the car on the curve, the net force acting towards the center of the circle (centripetal force) is what keeps the car in circular motion, and it can be calculated using the car's mass and the required acceleration for circular motion.
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Intro to Forces & Newton's Second Law
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