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Exp. 6: Centripetal Force: Find the centripetal force (N) of a 1.0 kg mass that takes 2.0 seconds to make 10 turns in a radius of 15.0 cm. Select one: 1.48 N 14804 ...

Question

Exp. 6: Centripetal Force: Find the centripetal force (N) of a 1.0 kg mass that takes 2.0 seconds to make 10 turns in a radius of 15.0 cm. Select one: 1.48 N 14804 N 148 N 31 N None of the alternativesExp. 8: Rotational Motion and Moment of Inertia: Determine the moment of inertia (kgm2) of a 1.0 kg mass turning in a radius of 15.0 cm. Select one: 56.25 kgm2 0.0225 kgm2 225 kgm2 0.005625 kgm2 None of the alternatives

Exp. 6: Centripetal Force: Find the centripetal force (N) of a 1.0 kg mass that takes 2.0 seconds to make 10 turns in a radius of 15.0 cm. Select one: 1.48 N 14804 N 148 N 31 N None of the alternatives Exp. 8: Rotational Motion and Moment of Inertia: Determine the moment of inertia (kgm2) of a 1.0 kg mass turning in a radius of 15.0 cm. Select one: 56.25 kgm2 0.0225 kgm2 225 kgm2 0.005625 kgm2 None of the alternatives



Answers

Find the centripetal force on an object of mass 10 kg with the given position function (in units of meters and seconds). $$\mathbf{r}(t)=(6 \cos 4 t, 6 \sin 4 t)$$

So in this question uh car which is moving along the card room, which is unfair and there was a bit of the cars and let's say to radius is high. So the centrifugal fools have seen, which is responsible for the significant uh for the surplus motion is the boss of the car. M can do in spite of the magnitude of velocity upon us. And now if you draw a free body diagram for the car, except this is the car and the forces acting on the carbs debate takes multiple download. It is F. G. And a normal reaction force. Listen. And affection for selecting on uh lives. That is miller stein, that's it. And this friction folds which is acting readily in world so that is responsible for the centripetal force. So we can see uh static frictional fools is providing to center the cell phones and the magnitude of this false it is the friction force is security. The mass of the car that is uh huh. 1500 kg into the square. Up to speed that is 15 10 m. was a green square Upon that areas and then it is is 400 weeks. So the man food at the frictional forces 844 Yeah.

You're given the centripetal force of an object with mass m. This is fubar close. Many times we squared. Those are our where the is the speed of rotation and R is the distance from the center. In part, a were has to find the rate of change of centripetal force. First type distance, innocent station. Other words. We want to find a crime of art. This is simple. You take the derivative This is negative and times the square over our spring. Then in part B, we're asked to find the rate of change of centripetal force of an object with a mass of 1000 kg The velocity of 13.89 m per second in a distance from the center of rotation uh, 200 m. So the mass and it was 1000 kg. V is 13.89 m per second and our is 200 years now. We're looking for the rate of change of centripetal force. We use f crime of our they found the part A. This is negative 1000 times 13.89 weird over 200 squared If you put this into a calculator, this is approximately negative 4.8 the three now ordinarily, Forces and Newton's. But this is the rate of change, of course, with respect to distance. So the units are going to Newton's with respect to the distance here.

Okay for this question. They want us to find these centripetal force again from the position function. Three co sign or five t and three sign of five teams. And, well, let's see it to compete that force, we're going to find the acceleration function. The velocity is given by negative 15 Sign on five team and 15 co sign of five teams. Now the acceleration take. The second derivative will be given by Negative. Let's see a 15 times science well, at 75 negative 75 co sign a five teen on negative 75 Sign five team That seems right. Well, if there were kind of have a computer velocity, they better give us the mess, huh? I mean, excellent her force. And they do give us the mess they get with 10 kilogram. So we know that our centripetal force will be given by Might see 10 times all that. So negative 750 co sign. Fine. Empty A negative 750 sign of five t

Hello. Mhm. We have a merry go around on the force of £20. £20 is being applied to the outside. Off a stationary radius is five. Food on the time is more 0.5 seconds. The moment off inertia is equal to send on. We need the resulting change in angular velocity, The angular velocity change off the merry go round. Okay, Since we start with angular velocity zero, we just want to find omega. The formula for the angular Momenta. Um, a formula for the angular momentum. The a circular Ah, emotion is we have the ah, in the expression for torque we have, the turkey is equal to be angular. The moment of inertia, times the angular acceleration. All right. Now, the angular acceleration is the derivative off the angular speed on that You the ah, the second derivative off the position function. Depending on the off the angle fu, we will find that the, uh, angular acceleration is ah, offer equals the tour tour divided by the ah moment of inertia. The Turk is equal to dark is equal to 5 ft times 5 ft times £20 times the sine of the angle says This is right angle. So times one mhm uh, the amount of turkey is 100 foot pounds. Be compounds. Ah, which means the we had this angular acceleration acceleration for the period when? For the period, while the while the forces being applied in torque was being generated. So we have for tea between not 0.5 on zero. So we have that this is 100 over can Ah which is thin. So Alfa is equal. 10 for T between zero and 0.5 a sick. So from this from this relation, we will find that the change in the mega that is the angle speed is going to be the integral off Alfa Off T. When he goes from 0 to 0.5, they Okay, so this is the integral of 0.5 10 80 which is 10 c calculate 0.5. So we have look for five times 25 Martin zero five mm radio hurt sick. And is the change in the the change in the angle speed? So, to Rekha, we have a stationary merry go around. So the first, the initial and you will speak zero. We apply force to the outside of America around, which means at an angle of 90 degrees to the radio, knowing the Turk is three victor product off the position on the force. The yeah magnitude of the torque is going to be the radius times the force times the sign off the angle for eight times Be the magnitude off eight times. Be easy from the magnitude of a times the magnitude of the times sine of the angle between A and B. So sign off the angle between the radius on the fourth sign, 90 therefore amount of Turkey's 100 ft. How were given that the moment of inertia is 10. However, we know the relation between the moment of inertia on for is the one given here. From this, we calculate what is the angular acceleration we have that we have 10 radiance per second per second change in. You'll speed Andi from this relation here, that angular acceleration is the derivative off the angular, off the angular speed. Then it you The way that we find speed from angular acceleration is that speed is the integral off function off the angular acceleration. Now the angular acceleration is constant on Lee for the not 0.5 seconds off. Duration off. Applying this force here. So we are looking at a function. Uh huh. Alfa t on the interval off T being from 0 to 0.5 on finding integral, we find that the angular speed change waas five brilliant per second. I hope it helps, but


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