Ch 08: Dynamics II: Motion in a Plane

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 08: Dynamics II: Motion in a Plane

Problem 6

Chapter 8, Problem 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?

Verified step by step guidance

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:

F

_c = 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

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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.

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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Textbook Question

A 500 g model rocket is on a cart that is rolling to the right at a speed of. The rocket engine, when it is fired, exerts an 8.0 N vertical thrust on the rocket. Your goal is to have the rocket pass through a small horizontal hoop that is 20 m above the ground. At what horizontal distance left of the hoop should you launch?

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Textbook Question

A 200 g block on a 50-cm-long string swings in a circle on a horizontal, frictionless table at 75 rpm. What is the tension in the string?

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Textbook Question

A 200 g block on a 50-cm-long string swings in a circle on a horizontal, frictionless table at 75 rpm. What is the speed of the block?

Textbook Question

In the Bohr model of the hydrogen atom, an electron (mass m = 9.1 x 10^-31 kg) orbits a proton at a distance of 5.3 x 10^-11 m. The proton pulls on the electron with an electric force of 8.2 x 10^-8 N. How many revolutions per second does the electron make?

Textbook Question

A 4.0 x 10¹⁰ kg asteroid is heading directly toward the center of the earth at a steady 20 km/s. To save the planet, astronauts strap a giant rocket to the asteroid perpendicular to its direction of travel. The rocket generates 5.0 x 10⁹ N of thrust. The rocket is fired when the asteroid is 4.0 x 10⁶ km away from earth. You can ignore the earth's gravitational force on the asteroid and their rotation about the sun.The radius of the earth is 6400 km. By what minimum angle must the asteroid be deflected to just miss the earth?

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