Question

1. 1- A 300 ? mass is attached to a solid 40 ?? long string the other end of which is secured to the ceiling. The mass is given an initial speed which makes it swing around a circular path in the horizontal plane without changing its speed and without changing its height. The object completes 2 revolutions in 2 seconds.

   A) What is the magnitude of the angular velocity of this circular motion? B) Find the tension in the string.
   C) What is the radius of the circular path?

   Hint: There is no motion in vertical direction.

2. 2- A constant horizontal force is exerted on an object on an inclined surface so that it moves with a constant speed upward.

   1. A) Draw the free body force diagram for the object.

   2. B) Find an expression for the magnitude of the force ? as a function of mass of the

      object (?), gravitational acceleration (?), angle of the incline (?) and the coefficient of friction (??).

3. 3- Imagine an asteroid starting to move toward the Earth from an infinitely far distance and from rest. The speed of the asteroid when it reaches to a distance ? from the center of the Earth is ?1. It will have a speed of ?2 after it travels more and reaches to a distance ?/2from the center of the Earth. What is the ratio of ?2 and ?1? Prove your answer.

   Hint: Use work-kinetic energy theorem

1. 2- A constant horizontal force is exerted on an object on an inclined surface so that it moves with a constant speed upward.

   1. A) Draw the free body force diagram for the object.

   2. B) Find an expression for the magnitude of the force ? as a function of mass of the

      object (?), gravitational acceleration (?), angle of the incline (?) and the coefficient of friction (??).

2. 3- Imagine an asteroid starting to move toward the Earth from an infinitely far distance and from rest. The speed of the asteroid when it reaches to a distance ? from the center of the Earth is ?1. It will have a speed of ?2 after it travels more and reaches to a distance ?/2from the center of the Earth. What is the ratio of ?2 and ?1? Prove your answer.

   Hint: Use work-kinetic energy theorem

Answer 1

Griven That Giiven r:LSine since speect is chan no chanyc So,o ia constaor From fgua Sinca r Lsino Coke ー:0.6216 13 xsin( 5.51) 0.3/33