Worksheet: Newton’s Third Law of Motion

In this worksheet, we will practice solving problems on Newton’s third law.

Q1:

An elevator is accelerating vertically upward at 2.6 m/s2. A man of mass 124 kg is standing inside. Determine the reaction force of the floor on the man.

Q2:

A body of mass 87 kg was placed inside a box of mass 60 kg which was attached to a vertical string. A tension of 265 kg-wt was applied to the string causing them to rise vertically. Determine the force exerted by the body on the base of the box while they were rising upwards. Take 𝑔=9.8/ms.

Q3:

An elevator was accelerating vertically downward at 1.7 m/s2. Given that the acceleration due to gravity is 𝑔=9.8/ms, find the reaction force of the floor to a passenger of mass 103 kg.

Q4:

An elevator is moving vertically upward at a constant speed. A man of mass 150 kg is standing inside. Determine the reaction force of the floor on the man. Take 𝑔=9.8/ms.

Q5:

A body of mass 4 kg is hanging from a spring balance fixed to the ceiling of a lift. Given that the reading on the balance is 1β€Žβ€‰β€Ž042 g-wt, determine the magnitude of the acceleration of the lift to the nearest two decimal places. Take 𝑔=9.8/ms.

Q6:

A lift is ascending with an acceleration of 140 cm/s2. Given that a person standing inside the lift is exerting a force of 88 kg-wt on the floor, find his mass. Take 𝑔=9.8/ms.

Q7:

A body of mass 45 kg was placed in a spring balance fixed to the ceiling of an elevator. If the elevator was accelerating downward at 105 cm/s2, what would the apparent weight of the body be? Consider the acceleration due to gravity to be 9.8 m/s2 and round your answer to two decimal places.

Q8:

A body is suspended from a spring balance in a hot-air balloon which was accelerating vertically downward at 79 of the acceleration due to gravity. Find the ratio between the body’s apparent and actual weights.

  • A29:
  • B97:
  • C79:
  • D92:

Q9:

A body was suspended from a spring balance fixed to the ceiling of a lift. The reading on the balance was 1.4 kg-wt when the lift was accelerating upwards, whereas when it was accelerating downwards at the same rate, the reading was 0.98 kg-wt. Find the mass of the body, taking the acceleration due to gravity to be 𝑔=9.8/ms.

Q10:

A body was suspended from a spring balance fixed to the ceiling of an elevator. When the elevator was accelerating upward at a certain rate, the reading on the balance was 1.5 kg-wt. However, when the elevator was accelerating downward at the same rate, the reading was 0.6 kg-wt. Determine the acceleration of the elevator. Take 𝑔=9.8/ms.

Q11:

A body of mass 686 g was suspended to a spring balance fixed to the ceiling of a lift. When the lift started moving, the reading on the balance was 672 g. Determine whether the lift was ascending or descending, and find the speed 𝑣, 5 seconds after it started moving. Consider the acceleration due to gravity 𝑔=9.8/ms.

  • Aascending, 𝑣=1/ms
  • Bascending, 𝑣=0.51/ms
  • Cdescending, 𝑣=1/ms
  • Ddescending, 𝑣=0.51/ms

Q12:

A man was standing on a set of scales in an elevator, recording the readings as the elevator moved. His first reading was when the elevator was accelerating upward at a rate of 7π‘Ž. He made another reading when the elevator was accelerating downward at a rate of 8π‘Ž. Given that the ratio between the two readings was 41:, determine π‘Žπ‘”: where 𝑔 is the acceleration due to gravity.

  • A112:
  • B121:
  • C113:
  • D131:

Q13:

A crane is carrying a body of mass 3,920 kg. Given that the maximum tension its cables can withstand is 4,000 kg-wt, determine the maximum acceleration π‘Ž at which the crane can lift the body safely without breaking its cables. Given that it lifted the body at this rate, find the time taken 𝑑 for the crane to raise the body 32.4 m. Consider the acceleration due to gravity to be 9.8 m/s2.

  • Aπ‘Ž=8.78/ms, 𝑑=2.72s
  • Bπ‘Ž=0.2/ms, 𝑑=18s
  • Cπ‘Ž=19.8/ms, 𝑑=1.81s
  • Dπ‘Ž=10.82/ms, 𝑑=2.45s

Q14:

A body is suspended from a spring balance fixed to the ceiling of an elevator. The reading of the balance was 50 kg-wt when the elevator was accelerating upward at π‘Ž m/s2, and the reading was 10 kg-wt when the elevator was accelerating downward at 53π‘Ž m/s2. Given that the acceleration due to gravity is 𝑔=9.8/ms, determine the value of π‘Ž.

Q15:

A body was suspended from a spring balance fixed to the ceiling of an elevator. When the elevator was moving upward with an acceleration of magnitude π‘Ž, the reading on the balance was 23 kg-wt. When it was accelerating downward at 32π‘Ž, the balance read 6 kg-wt. What would the reading on the balance be if, while the elevator was descending, it decelerated at 2π‘Ž? Take 𝑔=9.8/ms.

Q16:

A body that has a mass of 94 kg was placed inside a box of mass 66 kg. The box was lifted up by a vertical string which resulted in an upward acceleration of 220 cm/s2. Calculate the tension 𝑇 in the string. If the string snapped, what would the force 𝑃 exerted by the body on the base of the box be while they were in free fall? Consider the acceleration due to gravity to be 9.8 m/s2.

  • A𝑇=792N, 𝑃=1,842.4N
  • B𝑇=1,920N, 𝑃=0N
  • C𝑇=1,128N, 𝑃=921.2N
  • D𝑇=195.92N, 𝑃=646.8N

Q17:

An elevator of mass 556 kg was moving downward at 420 cm/s. If the tension in the elevator’s cable should not exceed 834 kg-wt, determine the minimum safe stopping distance for the elevator moving at this speed. Consider the acceleration due to gravity to be 9.8 m/s2.

Q18:

A body of mass 75 kg was attached to a string fixed to the ceiling of an elevator. Starting from rest, the elevator began accelerating vertically upward at 44 cm/s2. During this time the tension in the string was π‘‡οŠ§. After accelerating, the elevator continued moving at the speed it had gained, at which point the tension in the string was π‘‡οŠ¨. Finally, the elevator decelerated at 24 cm/s2, at which point the tension in the string was π‘‡οŠ©. Determine the magnitudes of π‘‡οŠ§, π‘‡οŠ¨, and π‘‡οŠ©. Consider the acceleration due to gravity to be 9.8 m/s2.

  • A𝑇=717N, 𝑇=735N, 𝑇=768N
  • B𝑇=73N, 𝑇=75N, 𝑇=78N
  • C𝑇=768N, 𝑇=735N, 𝑇=717N
  • D𝑇=78N, 𝑇=75N, 𝑇=73N

Q19:

A body of mass 130 kg was placed on the floor of an elevator of mass 761 kg. The elevator ascended from rest and it covered 15 m while accelerating uniformly. Following this, it continued moving at the speed it had gained for a certain distance. Finally, it decelerated uniformly for 5 seconds over a distance of 10 m until its speed became 1 m/s. Find the force of the elevator's motor 𝐹 when the elevator was accelerating upward and the magnitude of the reaction 𝑅 exerted on the body by the floor of the elevator during the third stage of the motion. Take 𝑔=9.8/ms.

  • A𝐹=8,999.1N, 𝑅=1,222N
  • B𝐹=7,686.1N, 𝑅=1,274N
  • C𝐹=7,914.4N, 𝑅=1,326N
  • D𝐹=9,266.4N, 𝑅=1,274N

Q20:

A person of mass 82 kg was inside an elevator. The elevator started moving upward from rest with a uniform acceleration for 3 seconds. Following this, it continued moving at the speed that it had gained for a further 2 seconds. Finally, it decelerated for 3 seconds until it came to rest. Given that the total distance the elevator covered was 18 m, find the action of the man’s weight on the floor of the elevator during each time interval: in the first interval, let the forces be π‘ƒοŠ§, in the second interval π‘ƒοŠ¨, and in the last interval π‘ƒοŠ©. Take 𝑔=9.8/ms.

  • A𝑃=705.2N, 𝑃=803.6N, 𝑃=705.2N
  • B𝑃=902N, 𝑃=803.6N, 𝑃=705.2N
  • C𝑃=902N, 𝑃=402N, 𝑃=902N
  • D𝑃=98.4N, 𝑃=1,607.2N, 𝑃=98.4N

Q21:

A body of mass 19 kg was placed on the floor of an elevator. Find, to the nearest two decimal places, the force this body exerts on the floor of the elevator when the elevator is accelerating downward at 143 cm/s2. Consider the acceleration due to gravity to be 9.8 m/s2.

Q22:

Determine the force that a body of mass 14 kg exerts on the floor of an elevator when it is accelerating upward at 84 cm/s2. Take 𝑔=9.8/ms.

Q23:

A body of mass 32 kg was suspended from a spring balance fixed to the ceiling of an elevator. Given that the elevator was accelerating upward at 405 cm/s2, find the apparent weight of the body. Take 𝑔=9.8/ms.

Q24:

A body was suspended from a spring balance fixed to the ceiling of an elevator. The balance reading was 17 kg-wt when the elevator was accelerating upward at π‘Ž, whereas when it was accelerating upward at 32π‘Ž, the reading was 11 kg-wt. Find the mass of the body, given that the acceleration due to gravity is 9.8 m/s2.

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