Objective Notes Summay An object moving in unifom cicula motion has constant speed but not constant velocity because the diection is changing. The velocity vecto in tangent to the cicle, the acceleation is along a adius of the cicle, and the centipetal foce is along a adius of the cicle. The velocity vecto and the acceleation vecto ae always pependicula to each othe. The acceleation vecto changes only the diection of the velocity vecto not the magnitude of it. 1. State both vebally and mathematically the conditions fo unifom cicula motion.. Distinguish between the acceleation in the equation, v a, that esults fom the change of motion and acceleation that esults fom a change in linea speed of the object involved. A V The velocity and acceleation vecto ae always to each othe when an object is moving in cicula motion. Since they ae pependicula to each othe, the speed stays the same and only the changes. Is the velocity of an object moving in hoizontal motion constant? Is the speed of an object moving in hoizontal motion constant? 3. Apply Newton s second law to detemine the The velocity and acceleation vecto ae always to each othe when an object is moving in cicula motion. Since they ae pependicula to each othe, the speed stays the same and only the changes. Is the velocity of an object moving in hoizontal motion constant? Is the speed of an object moving in hoizontal motion constant? V t tangential speed (m/s) adius of cicle (m) T peiod o time fo one evolution (sec)
foce equied to constain an object to move in a cicula path. f fequency o evolutions pe second (Hz o sec -1 ) a c centipetal acceleation (m/s ) F c centipetal foce (N) m mass (kg) seconds v avg T 1 T evolutions f d t f evolutions second a c vt F net ma A mey-goound makes 6 evolutions in 10 seconds. What is its fequency? A mey-go-ound makes 6 evolutions in 10 seconds. What is its fequency? A little gil is swinging he 5 kg puse in hoizontal cicles using the stap that allows the puse to swing 0 cm fom he hand. The gil is able to get the puse to make 10 evolutions in 8 seconds. What was the speed of the puse? What is the centipetal acceleation of the puse? How much tension is in the puse sting? A little gil is swinging he 5 kg puse in hoizontal cicles using the stap that allows the puse to swing 0 cm fom he hand. The gil is able to get the puse to make 10 evolutions in 8 seconds. What was the speed of the puse? What is the centipetal acceleation of the puse? How much tension is in the puse sting?
A 100-kg ca is tuning a cone at 8.0 m/s, and it tavels along an ac of a cicle in the pocess. If the adius of the cicle is 9.0 m, how lage a hoizontal foce must the pavement exet on the ties to hold the ca in the cicula path? In an ultacentifuge, a solution is otated with a fequency of 4.00 x 10 3 ev/s at a adius of 10.0 cm. How lage is the centipetal acceleation of each paticle in the solution? An amusement pak ide consists of a tuntable of.0 m adius tuning at 0.70 ev/s about a vetical axis. If a 70.0-kg child sits at the oute edge of the tuntable, what foce is necessay to keep the child fom sliding off? A 90.0-kg peson spinning aound on the equato of A 100-kg ca is tuning a cone at 8.0 m/s, and it tavels along an ac of a cicle in the pocess. If the adius of the cicle is 9.0 m, how lage a hoizontal foce must the pavement exet on the ties to hold the ca in the cicula path? In an ultacentifuge, a solution is otated with a fequency of 4.00 x 10 3 ev/s at a adius of 10.0 cm. How lage is the centipetal acceleation of each paticle in the solution? An amusement pak ide consists of a tuntable of.0 m adius tuning at 0.70 ev/s about a vetical axis. If a 70.0-kg child sits at the oute edge of the tuntable, what foce is necessay to keep the child fom sliding off? A 90.0-kg peson spinning aound on the equato of planet X, which is otating at 3,00 km/h. The centipetal foce holding the peson in place is 6.0
planet X, which is otating at 3,00 km/h. The centipetal foce holding the peson in place is 6.0 N. What is the adius of planet X? 4. Explain what is meant by a fame of efeence and descibe the motion of an object fom diffeent fames of efeence. 5. Distinguish between centipetal foce and centifugal foce. A peson sitting in the passenge seat of the family mini van as it goes aound a cone is in a(n) fame of efeence and will expeience a foce which is eally and move towad the (inside / outside) of the cuve. 6. Descibe how the motion of an object moving in a vetical cicle diffes fom an object moving in a hoizontal cicle. N. What is the adius of planet X? A fame of efeence is a system fo descibing the locations of objects. It is used to specify the positions and elative motions of objects. Inetial fame of efeence (non acceleating)- Newton s fist law holds tue. i.e. watching an Indy ace fom the gand stands. Acceleating fame of efeence - Newton s fist law does not hold tue. i.e. watching an Indy ace fom the point of view of the dive. Centipetal foces ae those seen by an obseve in an inetial fame of efeence. Centifugal foces ae those felt by an obseve in an acceleating fame of efeence. As a ca goes aound a cone, the passenges think they feel a foce towads the outside of the cuve, in eality this is inetia. A peson sitting in the passenge seat of the family mini van as it goes aound a cone is in a(n) fame of efeence and will expeience a foce which is eally and move towad the (inside / outside) of the cuve. Unlike object moving in hoizontal cicles, an object moving in a vetical cicle is affected by weight. In vetical cicles, the speed is not constant and neithe is the tension in the sting.
7. Identify the foces acting on an object moving in a vetical cicle and detemine the net foce at any point. At the top of the cicula path, the speed and the tension in the sting ae at a minimum. At the bottom of the cicle, the speed and tension in the sting ae at a maximum. At the top and bottom of the cicle, F C ΣF V. Theefoe, at the top of the cicle F T Tension in sting(n) m mass (kg) mv g 9.8 m/s, down F T + mg v speed at that point (m/s) adius of cicle (m) Theefoe, at the bottom of the cicle mv mg F T The fomulas you leaned that apply to hoizontal cicles can also be used to apply to vetical cicles at cetain points. T f seconds evolutions evolutions second T 1 f T peiod o time fo one evolution (sec) f fequency o evolutions pe second (Hz o sec -1 ) a c vt F net ma a c centipetal acceleation (m/s ) adius of cicle (m) v t speed (m/s) F net centipetal foce (N) m mass (kg) Sample: A stuntman swings fom the end of a 4 m long ope along the ac A stuntman swings fom the end of a 4 m long ope along the ac of a cicle. At the bottom of his path his speed is 9 m/s. (a) What is the centipetal acceleation at this point? (b) If his mass is 70 kg, find the tension in
of a cicle. At the bottom of his path his speed is 9 m/s. (a) What is the centipetal acceleation at this point? (b) If his mass is 70 kg, find the tension in the ope at this point. the ope at this point. 8. Define citical velocity and solve poblems involving vetical cicula motion. The citical velocity is the minimum velocity an object can have and emain in a vetical cicle of constant adius. If an object does not maintain the citical velocity, the adius of the obit begins to decay (get smalle). (Pe-AP and DI ) v cit g v cit citical velocity (m/s) adius (m) g acceleation due to gavity (m/s ) Sample: A canival clown ides a motocycle down a amp and aound a loop-the-loop. If the loop has a adius of 18 m, what is the slowest speed the ide can have at the top of the loop to avoid falling? A 75-kg pilot flies a plane in a loop nea the eath s suface. At the top of the loop, whee the plane is completely upsidedown fo an instant, the pilot hangs feely in the seat and does not push against the seat belt. The aispeed indicato eads 10 m/s. What is the A canival clown ides a motocycle down a amp and aound a loop-the-loop. If the loop has a adius of 18 m, what is the slowest speed the ide can have at the top of the loop to avoid falling? A 75-kg pilot flies a plane in a loop nea the eath s suface. At the top of the loop, whee the plane is completely upside-down fo an instant, the pilot hangs feely in the seat and does not push against the seat belt. The aispeed indicato eads 10 m/s. What is the adius of the plane s loop?
adius of the plane s loop? 9. Undestand that gavitational foce is popotional to both masses and the invese squae of the distance between the centes of spheical bodies. Law of Univesal Gavitation - thee is a foce of attaction between any two objects with mass. Gm1m F g d F g Foce of attaction (N) G 6.67 * 10-11 Nm /kg m 1 mass of object one (kg) m mass of object two (kg) d distance between the centes of the two objects (m) m e mass of the Eath (5.98 *10 4 kg) e adius of the Eath (6.37 * 10 6 m) Sample What is the foce of attaction between a 0.0 kg pea and a 0.03 kg gapefuit that ae sitting 15 cm apat? 10. Recognize that the motion of satellites in cicula obits about Eath can be undestood using equations of unifom cicula motion; solve poblems involving obital velocity and peiod. What is the foce of attaction between a 0.0 kg pea and a 0.03 kg gapefuit that ae sitting 15 cm apat? Satellites actually move in elliptical obits but we will teat them as though they ae cicula obits. The weight of the satellite is actually the gavitational attaction between the satellite and the Eath. When the weight of the satellite (m s g) is set equal to the gavitational attaction between the eath and the satellite (Gm s m e /d ), the mass of the satellite will cancel out telling us that the acceleation due to gavity at any point can be calculated using the following equation. (PeAP and DI) Gm g d G 6.67 * 10-11 Nm /kg m mass of the celestial body at the cente of otation (kg) d distance between the centes of the two objects (m)
The citical speed of a satellite can be calculated using (Pe-AP and DI) Gm v d v citical velocity of a satellite (m/s) G 6.67 * 10-11 Nm /kg m mass of the celestial body at the cente of otation (kg) d distance between the centes of the two objects (m) (Pe-AP and DI) The peiod of a satellite can be calculated using T Π 3 d Gm T peiod of a satellite (sec) G 6.67 * 10-11 Nm /kg m mass of the celestial body at the cente of otation (kg) d distance between the centes of the two objects (m) 11. Undestand the use of the tem weightlessness in descibing objects in feefall and in obit. 1. Descibe gavitational fields and state that the field concept does not explain the oigin of gavity. Tue weightlessness does not exist. In ode to be tuly weightless you would have to be infinitely fa fom all othe objects with mass, since this is not possible, all objects have weight. Astonauts ae said to be weightless but in actuality they ae in feefall towad the Eath just as thei spaceship is. Hence they ae both acceleating at the same ate so you have the appeaance of weightlessness. The misnome (wong name) came about due to the fact that if you attempted to weigh them the scale would egiste a value of zeo since both ae in fee fall Theefoe, the astonauts would weigh zeo but would not have a weight of zeo. A field is a egion in which a suitable detecto expeiences a foce. A suitable detecto fo a gavitational field is an object with a vey small mass.