# Lesson Worksheet: Newton’s Third Law of Motion Mathematics

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

Q1:

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 .

Q2:

Fill in the blank with , , , , or : When a body of mass is suspended from a spring scale fixed at the ceiling of an elevator and the elevator descends with uniform acceleration, then the apparent weight the real weight.

• A
• B
• C
• D
• E

Q3:

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.

Q4:

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

Q5:

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.

Q6:

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 . After accelerating, the elevator continued moving at the speed it had gained, at which point the tension in the string was . Finally, the elevator decelerated at 24 cm/s2, at which point the tension in the string was . Determine the magnitudes of , , and . Consider the acceleration due to gravity to be 9.8 m/s2.

• A, ,
• B, ,
• C, ,
• D, ,

Q7:

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 .

Q8:

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 1‎ ‎042 g-wt, determine the magnitude of the acceleration of the lift to the nearest two decimal places. Take .

Q9:

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 . He made another reading when the elevator was accelerating downward at a rate of . Given that the ratio between the two readings was , determine where is the acceleration due to gravity.

• A
• B
• C
• D

Q10:

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 , 5 seconds after it started moving. Consider the acceleration due to gravity .

• Aascending,
• Bascending,
• Cdescending,
• Ddescending,

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