# Centripetal force problems

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos. Science Physics library Centripetal force and gravitation Centripetal forces. Centripetal force problem solving. What is a centripetal force? Yo-yo in vertical circle example. Bowling ball in vertical loop. Mass swinging in a horizontal circle.

Next lesson. Current timeTotal duration Google Classroom Facebook Twitter. Video transcript - [Instructor] There are unfortunately quite a few common misconceptions that many people have when they deal with centripetal force problems, so in this video, we're gonna go over some examples to give you some problem solving strategies that you can use as well as going over a lot of the common misconceptions that people have when they deal with these centripetal motion problems.

So, to start with, imagine this example, let's say a string is causing a ball to rotate in a circle. And to make it simple, let's say this ball is tracing out a perfect circle, and let's say it's sitting on a perfectly frictionless table so this would be the bird's eye view.

This is the view from above. What it would look like from the side would be something like this. You'd have the ball tied to the rope and then you nail some sort of stake in the middle of the table. You tie the rope to the stake, and then you give the ball a push.

And the ball's gonna take this circular path on the table when we view it from the side. But when we view it from above, you see this path traced out. So this is a bird's eye view that you would see if you were looking down from above the table, and this would be the side view. So let me ask you this question. What force is causing this ball to go in a circle? Now, a lot of people want to answer that question with the centripetal force. They'd say that it's the centripetal force that points inward that causes this ball to go in a circle, and that's not wrong.

It's the truth, but it's not the whole truth. And the reason is that when we say centripetal force, all we really mean is a force that's directed toward the center of the circle.

So saying the force that causes this ball to go in a circle is the centripetal force is a little unsatisfying.

It'd be like answering the question, what force balances the force of gravity while the ball's on the table with the answer, the upward force. I mean, yeah, we knew it had to be an upward force, but that really doesn't tell us what force it is.Free Newsletter. Sign up below to receive insightful physics related bonus material. It's sent about once a month.

Easily unsubscribe at any time. Join me on Patreon and help support this website. Centrifugal Force Fictitious Centrifugal Force In the presence of angular velocity, there can exist a fictitious centrifugal force. This force is observed from a non-inertial reference frame. Fictitious centrifugal forces are associated with centripetal acceleration due to rotation of an object about a point.

To illustrate this concept, consider a particle P that is firmly sitting on a turntable, which is rotating about point O at angular velocity w. The radius measured from point O to the location of the particle is R. The centripetal acceleration of the particle a r with respect to ground is: This acceleration is pointing towards the center O of rotation. The friction force F r between the particle and turntable is holding the particle in place.

Thus, where m is the mass of the particle. In this situation the particle would move outwards. Thus, relative to a non-inertial reference frame attached to the turntable and moving with itthe particle must move outwards, away from the center O. The particle would continue moving outwards until it falls off the outside edge of the turntable. From the point of view of an observer sitting on the turntable and moving with itthe fictitious centrifugal force is the apparent force that appears to be acting on the particle, pushing it radially outwards, away from the center O.

The line of action of this apparent force passes through the center of rotation O. But in reality, there is no actual force acting on the particle. What the observer sees is just a consequence of the particle having zero acceleration relative to ground; which means that relative to the turntable the particle must move radially outwards. The figure below illustrates the outward radial motion of the particle. Now, the particle will also move radially outwards relative to the turntable, if the friction force F r is insufficient to hold the particle in place.

In other words, An interesting problem related to this is problem 7 in Physics Questions page. It is worth mentioning that the velocity of the particle relative to the turntable gives rise to another fictitious force, known as the Coriolis-force. And if the turntable has angular acceleration, this gives rise to yet another fictitious force, known as the Euler force. Reactive Centrifugal Force The reactive centrifugal force is defined as the reaction force to a centripetal force.By Consumer Dummies.

Using physics, you can find the centripetal acceleration of objects as they move in a circle.

For example, you can calculate the acceleration of a ferry boat making a turn at a constant speed. A ferry boat makes a degree turn in 12 minutes. The radius of the turn is 0. What is its centripetal acceleration in meters per second squared during the turn?

You twirl a lasso over your head at a constant angular speed of 3. The documentation for your slot-car set says that the maximum centripetal acceleration the cars can withstand without being ejected from the track is 3. You notice that the slot cars fly off the track if they exceed 1.

What is the radius in meters of the curve in the track? First, convert the given quantities to meters and seconds. The time it takes to complete the turn is. Express the centripetal acceleration in terms of the angular speed using.

The centripetal acceleration is. Solve the equation for centripetal acceleration for the radius and insert these quantities. The result is.

Centripetal Acceleration in Physics Problems.A gram ball, attached to the end of a cord, is revolved in a horizontal circle with an angular speed of 5 rad s K nown :. Wanted : The centripetal force. Solution :. The centripetal force is the resultant force that causes the centripetal acceleration. The equation of the centripetal force :. A stone attached at the end of a cord and rotated in a horizontal circle by a student. Known :. Wanted: The centripetal force.

A curve road of radius R is designed so that a car traveling at speed 10 ms —1 Advertisement can negotiate the turn safely. What is the radius? Wanted: Radius. The only one force in the horizontal direction is the force of static friction. The equation of the static friction :. The coefficient of static friction between tire and road is 0. Wanted: maximum speed v.

Centripetal force. Centripetal force is the net force which produces centripetal accelerations. In this case, the centripetal force is the force of static friction. The equation of the force of static friction :. The maximum speed v :. The distance between the two troughs of the water surface waves is 20 m.

An object floats on the surface of The tension force of the rope is An object vibrates with a frequency of 5 Hz to rightward and leftward.

The object moves from equilibrium point to the Centripetal force — problems and solutions 1. Related Posts Force of gravity and gravitational field — problems and solutions 1. Two objects m1 and m2 each with a mass of 6 kg and 9 kg separated by a distance of Parabolic motion, work and kinetic energy, linear momentum, linear and angular motion — problems and solutions 1. Transverse waves — problems and solutions 1.

Speed of the mechanical waves — problems and solutions 1. Simple harmonic motion — problems and solutions 1. By continuing to use the site, you agree to the use of cookies.To create playlists you must logged in.

If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list not that we recommend cramming, but when in Rome Science Chemistry Physics. Search for:. Add to playlist. Centripetal Force Problem - Car Doesn't Lose Contact With Ground This classic centripetal force problem describes a small hill in a road as "approximately circular", and then asks the maximum speed that a car can go over that hump without "loosing contact with the road", or some other description that translates to "set the normal force equal to zero.

Maximum G-Force At Bottom of Plane Loop-to-Loop When a military jet does a vertical loop, the pilot is "pulling g's", getting squished down into her seat. In this problem or similar ones involving roller coastersthey ask you to calculate the minimum radius such that the pilot doesn't pull more than a certain number of g's that would make her pass out.

## Centripetal Force in Physics Problems

Jet Speed At Top of Loop To Experience Weightlessness This problem is just like the previous one about a car going over a hump in the road: calculate the speed such that the pilot feels weightless. Once again you're setting normal force equal to zero, except this time it's normal force of air on the wings or the seat on the pilot's butt rather than the force of the tires on the road. Roller Coaster Speed at Top of Loop To Maintain Contact With Track Once again we're setting normal force equal to zero, except this time it's to find the speed at which a roller coaster car "loses contact with the track" or "passengers don't leave their seats".

Centripetal Force - Minimum Coefficient of Friction To Prevent Car Skidding In the first of a few problems about cars going around turns, in this case the road is level - not banked - and we'll calculate the minimum coefficient of static friction to prevent the car from skidding. Centripetal Force - Bank Angle For Road To Prevent Car Sliding no friction This is another classic car problem, in which they tell you that the road is so slippery that there is no friction at all, and then they ask you to calculate the angle that the road should be banked to keep the car going nicely through the turn without sliding to the outside or inside of the turn.

It's not impossible, but it does make for some juicy algebra and trig as you attempt to solve a system of two equations and two unknowns, one of which is stuck inside trig functions!

All rights reserved. Start your trial!Any force or combination of forces can cause a centripetal or radial acceleration. Any net force causing uniform circular motion is called a centripetal force.

The direction of a centripetal force is toward the center of curvature, the same as the direction of centripetal acceleration. You may use whichever expression for centripetal force is more convenient. Centripetal force F c is always perpendicular to the path and pointing to the center of curvature, because a c is perpendicular to the velocity and pointing to the center of curvature.

This implies that for a given mass and velocity, a large centripetal force causes a small radius of curvature—that is, a tight curve.

Figure 1. The frictional force supplies the centripetal force and is numerically equal to it. Centripetal force is perpendicular to velocity and causes uniform circular motion.

The larger the F cthe smaller the radius of curvature r and the sharper the curve. Friction is to the left, keeping the car from slipping, and because it is the only horizontal force acting on the car, the friction is the centripetal force in this case.

Thus the centripetal force in this situation is. Now we have a relationship between centripetal force and the coefficient of friction. Using the first expression for F c from the equation. The coefficient of friction found in Part 2 is much smaller than is typically found between tires and roads. The car will still negotiate the curve if the coefficient is greater than 0.

Note that mass cancels, implying that in this example, it does not matter how heavily loaded the car is to negotiate the turn. Mass cancels because friction is assumed proportional to the normal force, which in turn is proportional to mass. If the surface of the road were banked, the normal force would be less as will be discussed below. Figure 2. This car on level ground is moving away and turning to the left. The centripetal force causing the car to turn in a circular path is due to friction between the tires and the road. A minimum coefficient of friction is needed, or the car will move in a larger-radius curve and leave the roadway.

Let us now consider banked curveswhere the slope of the road helps you negotiate the curve. See Figure 3. Race tracks for bikes as well as cars, for example, often have steeply banked curves. For ideal bankingthe net external force equals the horizontal centripetal force in the absence of friction.

The components of the normal force N in the horizontal and vertical directions must equal the centripetal force and the weight of the car, respectively. In cases in which forces are not parallel, it is most convenient to consider components along perpendicular axes—in this case, the vertical and horizontal directions. The only two external forces acting on the car are its weight w and the normal force of the road N. A frictionless surface can only exert a force perpendicular to the surface—that is, a normal force.

Because this is the crucial force and it is horizontal, we use a coordinate system with vertical and horizontal axes. Only the normal force has a horizontal component, and so this must equal the centripetal force—that is. Because the car does not leave the surface of the road, the net vertical force must be zero, meaning that the vertical components of the two external forces must be equal in magnitude and opposite in direction.

That is, roads must be steeply banked for high speeds and sharp curves. Friction helps, because it allows you to take the curve at greater or lower speed than if the curve is frictionless.These 20 tips tell patients what they can do to get safer care. Glossary Our easy-to-read glossary helps patients make sense of health care the terms.

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### Centripetal force problem solving

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