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Lesson Worksheet: Newton’s First Law of Motion Mathematics

In this worksheet, we will practice solving problems using Newton’s first law.

Q1:

In the given figure, the body is moving with uniform velocity under the action of a system of forces. Given that the forces are measured in newtons, find the magnitudes of 𝐹 and 𝐾.

  • A𝐹=123N, 𝐾=27N
  • B𝐹=27N, 𝐾=123N
  • C𝐹=57N, 𝐾=93N
  • D𝐹=93N, 𝐾=57N

Q2:

In the given figure, the body is subject to the action of a system of forces. Given that it is moving at a constant speed 𝑣 and that the forces are measured in newtons, find 𝐹 and 𝐾.

  • A𝐹=33N, 𝐾=7N
  • B𝐹=2N, 𝐾=7N
  • C𝐹=4N, 𝐾=7N
  • D𝐹=4N, 𝐾=56N

Q3:

In the figure, the body is moving at a constant velocity v under the action of a system of forces. Given that the forces are measured in newtons, find the magnitudes of F and K.

  • A𝐹=51N, 𝐾=79N
  • B𝐹=79N, 𝐾=51N
  • C𝐹=11N, 𝐾=79N
  • D𝐹=99N, 𝐾=31N

Q4:

An engine pulls its carriages along a horizontal track at uniform speed. Given that the engine provides a driving force of 2,080 kg-wt and combined mass of the engine and carriages is 250 metric tons, determine the resistance to their motion per tonne.

Q5:

A body was moving uniformly under the effect of three forces F, F, and F. Given that Fi=7 and Fj=8, where i and j are orthogonal unit vectors, determine F which ensures that it will move at a constant velocity.

  • A7+8ij
  • B78ij
  • C78ij
  • D7+8ij
  • E8+7ij

Q6:

A body is moving in a straight line at a constant velocity under the action of a system of forces F, F, and F. If Fijk=𝑎5, Fijk=4+𝑏3, and Fijk=+6+𝑐, find 𝑎, 𝑏, and 𝑐.

  • A𝑎=3, 𝑏=5, 𝑐=8
  • B𝑎=3, 𝑏=7, 𝑐=8
  • C𝑎=3, 𝑏=5, 𝑐=8
  • D𝑎=5, 𝑏=7, 𝑐=2

Q7:

A body moves under the effect of two forces: Fij=8+ and Fi=4, where i and j are orthogonal unit vectors. A third force F acts on the body, causing it to move uniformly. Find the angle F makes with the unit vector i rounding the result to the nearest minute.

  • A13613
  • B35650
  • C27355
  • D1942

Q8:

A body was descending vertically in a liquid such that it was covering equal distances in each consecutive time interval of equal length. Given that the weight of the body was 55 kg-wt, find the magnitude of the resistive force of the liquid acting against the motion of the body.

Q9:

A body of mass 20 kg is pulled along a horizontal plane by a rope that makes an angle 𝜃 with the plane, where tan𝜃=512. When the tension in the rope is 91 N, the body moves with uniform velocity. Find the total resistance to the motion, 𝐹, and the normal reaction, 𝑅. Use 𝑔=9.8/ms.

  • A𝐹=84N, 𝑅=20N
  • B𝐹=84N, 𝑅=161N
  • C𝐹=91N, 𝑅=112N
  • D𝐹=35N, 𝑅=112N

Q10:

A soldier jumped out of a plane with a parachute. After he had opened his parachute, the resistance to his movement was directly proportional to the cube of his speed. When his speed was 19 km/h, the resistance to his motion was 127 of the combined weight of him and his parachute. Determine the maximum speed of his descent.

This lesson includes 28 additional questions and 297 additional question variations for subscribers.

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