5.3 Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg,

(a) Just after it is dropped from the window of a stationary train

 

(b) Just after it is dropped from the window of a train running at a constant velocity of 36 km/h

 

(c) Just after it is dropped from the window of a train accelerating with 1 m s^-2

 

(d) Lying on the floor of a train which is accelerating with 1 m s^-2, the stone being at rest relative to the train. (Neglect air resistance throughout.)

<p><strong> (a)</strong> Mass of the stone, m = 0.1 kg, Acceleration due to gravity = 10 m/s²</p><p>Net force = 0.1&nbsp;<span title="Click to copy mathml"><math><mo>*</mo></math></span> 10 N = 1.0 N. The direction of force is downwards</p><p>&nbsp;</p><p><strong> (b)</strong> Since the train is moving at a constant velocity, the acceleration imparted by the train is zero. Only acceleration acting on the stone is gravity. So the force will be 1.0 N, acting downwards</p><p>&nbsp;</p><p><strong> (c)</strong> The acceleration of the train = 1 m/s² so the force exerted by the train = 0.1 <span title="Click to copy mathml"><math><mo>*</mo><mi></mi></math></span>&nbsp;1 N = 0.1 N and it is acting in the horizontal direction. But when the stone is dropped, the force started acting on the stone is only due to gravity, the train moving force has no effect. So the net force is = 0.1&nbsp;<span title="Click to copy mathml"><math><mo>*</mo></math></span> 10 N = 1.0 N and it is acting vertically downwards</p><p><strong> (d)</strong> When the stone is lying on the train floor, the only force acting on the stone is due to the acceleration of the train. So the net force on the stone = 0.1 <span title="Click to copy mathml"><math><mo>*</mo></math></span> 1 N. The direction is horizontal along the motion of the train</p>

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