Give the magnitude and direction of …

(a) Given: The mass of the stone is 0.1 kg. Since the train is stationary, only the acceleration due to gravity acts in the downward direction. Newton’s second law of motion is given as, F=mg By substituting the given values in the above expression, we get F=( 0.1 kg )( 10 m/ s 2 ) =1 N Thus, a force of 1 N is acting in the downward direction. (b) Since the train is moving at constant velocity, the stone acquires only horizontal component of velocity. There is no acceleration in the horizontal direction. Only the acceleration due to gravity acts in the downward direction. Newton’s second law of motion is given as, F=mg By substituting the given values in the above expression, we get F=( 0.1 kg )( 10 m/ s 2 ) =1 N Thus, a force of 1 N is acting in the downward direction. (c) Given: The mass of the stone is 0.1 kg and the acceleration of the train is 1 m/ s 2 . As the stone is resting on the floor of the train, it experience the same acceleration as that of the train. The horizontal force acts on the stone as long as it is in the train. The horizontal force on the stone becomes zero as soon as it is dropped from the train. This is because the force at an instant doesn’t depend on the previous situations but only the situation present at that instant. Therefore, only gravitational force acts on the stone. Newton’s second law of motion is given as, F=mg By substituting the given values in the above expression, we get F=( 0.1 kg )( 10 m/ s 2 ) =1 N Thus, a force of 1 N is acting in the downward direction. (d) As the stone is at rest on the floor, it experiences the same acceleration as that of the train. The weight of the stone is balanced by the normal force applied by the floor. The force on the stone is given as, F=ma By substituting the given values in the above expression, we get F=( 0.1 kg )( 1 m/ s 2 ) =0.1 N Thus, the stone experiences force of 0.1 N in the direction of motion of the train.