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Lesson Worksheet: Newton’s Second Law: Variable Mass Mathematics
In this worksheet, we will practice using differentiation for Newton’s second law of motion of a particle with variable mass.
Q8:
A metallic ball moves in a straight line with a constant velocity of magnitude 1 m/s. It enters a dusty medium. If the force acting on the ball at any instant is 10 dynes, find the rate of change of the mass of the ball due to the dust adherence to its surface.
- A0.01 g/s
- B10 g/s
- C0 g/s
- D0.1 g/s
- E1 g/s
Q9:
Complete the following: An object of mass 10 g is moving in a two-dimensional plane with varying mass that increases with a rate of 5 g/s. The velocity vector for the object is given by . Horizontal component of the force acting on the object to keep the object moving at this velocity is dynes.
- A
- B
- C
- D
- E
Q10:
A ball of mass 5 g was moving in a straight line through a medium loaded with dust. The dust was accumulating on its surface at a rate of 1 g/s. Find the magnitude of the force acting on the ball at time , given that the displacement of the ball is expressed by the relation , where is a unit vector in the direction of the motion and the displacement is measured in centimeters.