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Lesson Worksheet: Newton’s Second Law: Variable Mass Mathematics

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In this worksheet, we will practice using differentiation for Newton’s second law of motion of a particle with variable mass.

Q1:

Fill in the blank: The force acting on a mass varying according to the function 𝑚(𝑡)=(5+2𝑡)kg and moving with a constant velocity of 4 m/s is .

Q2:

Complete the following equation: 𝐹=𝑡(×)ddmass.

  • Amomentum
  • Bweight
  • Ctime
  • Dvelocity
  • Eacceleration

Q3:

Complete the following: The rate of change in with respect to time is equal to the acting force.

  • Amomentum
  • Bmass
  • Cvelocity
  • Dforce
  • Eacceleration

Q4:

A body moves in a straight line. At time 𝑡 seconds, its displacement from a fixed point is given by 𝑠=6𝑡+9𝑡m. Its mass varies with time such that 𝑚=(8𝑡+9)kg. Write an expression for the force acting on the body at time 𝑡.

  • A(384𝑡+180) N
  • B(96𝑡+108) N
  • C(192𝑡+180) N
  • D(96𝑡+180) N

Q5:

A body moves in a straight line. At time 𝑡 seconds, its displacement from a fixed point is given by 𝑠=2𝑡+5𝑡+4m. Its mass varies with time such that 𝑚=(6𝑡+5)kg. Determine the force acting upon the body when 𝑡=3s.

Q6:

The mass of a body at time 𝑡 is given by 𝑚(𝑡)=(2𝑡+12)kg, whereas its position vector is rc(𝑡)=2𝑡+3𝑡+15, where c is a constant unit vector, r is measured in meters, and 𝑡 is measured in seconds. Find the magnitude of the force acting on the body at 𝑡=2seconds.

Q7:

An object moves in a straight line. At time 𝑡 seconds, its velocity is given by 𝑡+2 m/s. Its mass varies with time as (3𝑡+1) kg. Find the magnitude of the force acting on the body at time 𝑡=3seconds.

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 vij=2𝑡+12𝑡/cms. Horizontal component of the force acting on the object to keep the object moving at this velocity is dynes.

  • A30𝑡
  • B40𝑡+30𝑡
  • C40𝑡+24𝑡ij
  • D40𝑡
  • E24𝑡

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 𝑡=5seconds, given that the displacement of the ball is expressed by the relation sc(𝑡)=23𝑡+𝑡+7𝑡+1, where c is a unit vector in the direction of the motion and the displacement is measured in centimeters.

This lesson includes 41 additional questions and 207 additional question variations for subscribers.

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