Circular_Gravitation_P1 [22 marks]

Transcription

1 Circular_Gravitation_P1 [ marks] 1. An object of mass m at the end of a strin of lenth r moves in a vertical circle at a constant anular speed ω. What is the tension in the strin when the object is at the bottom of the circle? m(ωr + ) m(ωr ) m(ωr + 1) m(ωr 1). A mass at the end of a strin is swun in a horizontal circle at increasin speed until the strin breaks. The subsequent path taken by the mass is a line alon a radius of the circle. horizontal circle. curve in a horizontal plane. curve in a vertical plane.. An object of mass m moves in a horizontal circle of radius r with a constant speed v. What is the rate at which work is done by the centripetal force? mv r mv πr mv πr zero

2 . A mass attached to a strin rotates in a ravitational field with a constant period in a vertical plane. How do the tension in the strin and the kinetic enery of the mass compare at P and Q? 5. A satellite X of mass m orbits the Earth with a period T. What will be the orbital period of satellite Y of mass m occupyin the same orbit as X? T T T T 6. A horizontal disc rotates uniformly at a constant anular velocity about a central axis normal to the plane of the disc. Point X is a distance L from the centre of the disc. Point Y is a distance L from the centre of the disc. Point Y has a linear speed v and a centripetal acceleration a. What is the linear speed and centripetal acceleration of point X?

3 7. An object of constant mass is tied to the end of a rope of lenth l and made to move in a horizontal circle. The speed of the object is increased until the rope breaks at speed v. The lenth of the rope is then chaned. At what other combination of rope lenth and speed will the rope break? 8. Two satellites of mass m and m orbit a planet at the same orbit radius. If is the force exerted on the satellite of mass m by the planet and a is the centripetal acceleration of this satellite, what is the force and acceleration of the satellite with mass m? 9. The ravitational field strenth at the surface of Earth is. Another planet has double the radius of Earth and the same density as Earth. What is the ravitational field strenth at the surface of this planet? 10. A small ball of weiht W is attached to a strin and moves in a vertical circle of radius R. What is the smallest kinetic enery of the ball at position X for the ball to maintain the circular motion with radius R? W R W R W R 5W R

4 The centre of the Earth is separated from the centre of the Moon by a distance Point P lies on a line joinin the centre of the 11. Earth and the centre of the Moon, a distance X from the centre of the Earth. The ravitational field strenth at P is zero. mass of the Moon What is the ratio? mass of the Earth (D X) X (D X) X X (D X) X D X 1. On Mars, the ravitational field strenth is about radius of Earth What is? radius of Mars of that on Earth. The mass of Earth is approximately ten times that of Mars. 1. Planet X has mass M and radius R. Planet Y has mass M and radius R. The ravitational field strenth at the surface of planet X is. What is the ravitational field strenth at the surface of planet Y? What is the correct definition of ravitational field strenth? The mass per unit weiht The weiht of a small test mass The force actin on a small test mass The force per unit mass actin on a small test mass 15. An object rotates in a horizontal circle when acted on by a centripetal force. What is the centripetal force actin on the object when the radius of the circle doubles and the kinetic enery of the object halves? 16. The maximum speed with which a car can take a circular turn of radius R is v. The maximum speed with which the same car, under the same conditions, can take a circular turn of radius R is v. v. v. v.

5 17. A body moves with uniform speed around a circle of radius r. The period of the motion is T. What is the speed of the body? πr T πt r Zero πr T 18. The centres of two planets are separated by a distance R. The ravitational force between the two planets is. What will be the force between the planets when their separation increases to R? The acceleration of free fall of a mass of.0 k close to the surface of Mars is.6 ms. What is the ravitational field strenth at the surface of Mars in N k 1? A mass at point X ives rise to a ravitational field strenth at point P as shown below. An identical mass is placed at point Y as shown below. The resultant ravitational field strenth at P is now reater than. between and. between and zero. zero.

6 1. A pendulum bob is attached to a liht strin and is swinin in a vertical plane. At the lowest point of the motion, the manitude of the tension in the strin is less than the weiht of the mass of the pendulum bob. zero. reater than the weiht of the mass of the pendulum bob. equal to the weiht of the mass of the pendulum bob.. A spherical planet of uniform density has three times the mass of the Earth and twice the averae radius. The manitude of the ravitational field strenth at the surface of the Earth is. What is the ravitational field strenth at the surface of the planet? 6 International Baccalaureate Oranization 018 International Baccalaureate - Baccalauréat International - Bachillerato Internacional Printed for HAE (Psychico Collee)