In this worksheet, we will practice solving problems on Newtonβs third law.

**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 .

**Q3: **

A lift was accelerating vertically downwards at 1.7 m/s^{2}.
Given that the acceleration due to gravity is ,
find the reaction force of the floor to a passenger of mass 103 kg.

**Q4: **

A lift is moving vertically upwards at a constant speed. A man of mass 150 kg is standing inside. Determine the reaction force of the floor on the man. Take .

**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 1β042 g-wt, determine the magnitude of the acceleration of the lift to the nearest two decimal places. Take .

**Q6: **

A lift is ascending with an acceleration of 140 cm/s^{2}. Given that a person standing inside the lift is exerting a force of 106 kg-wt on the floor, find his mass. Take .

**Q7: **

A body of mass 45 kg was placed in a spring balance fixed to the ceiling of a lift.
If the lift was accelerating at 105 cm/s^{2},
what would the apparent weight of the body be? Consider the acceleration due to gravity to be 9.8 m/s^{2}.

- A 47.25 N
- B 441 N
- C 488.25 N
- D 393.75 N

**Q8: **

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

- A
- B
- C
- D

**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 .

**Q10: **

A body was suspended from a spring balance fixed to the ceiling of a lift. When the lift was accelerating upwards at a certain rate, the reading on the balance was 1.5 kg-wt. However, when the lift was accelerating downwards at the same rate, the reading was 0.6 kg-wt. Determine the acceleration of the lift. Take .

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

- Aascending,
- Bascending,
- Cdescending,
- Ddescending,

**Q12: **

A climber of mass 85 kg is sliding down on a rope. The maximum tension the rope can exert on him is 17 kg-wt. What is the minimum acceleration with which he can descend? Given that he maintained this acceleration over 50 m, what was his speed at the end? Take .

- A
10 m/s
^{2}, 22.36 m/s - B
11.76 m/s
^{2}, 24.25 m/s - C
9.6 m/s
^{2}, 30.98 m/s - D
7.84 m/s
^{2}, 28 m/s

**Q13: **

A man was standing on a set of scales in a lift, recording the readings as the lift moved. His first reading was when the lift was accelerating upwards at a rate of . He made another reading when the lift was accelerating downwards 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

**Q14: **

A crane is carrying a body of mass 3βββ920 kg. Given that the maximum tension its cables can withstand is 4βββ000 kg-wt,
determine the maximum acceleration 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 for the crane to raise the body 32.4 m.
Consider the acceleration due to gravity to be 9.8 m/s^{2}.

- A ,
- B ,
- C ,
- D ,

**Q15: **

A body is suspended from a spring balance fixed to the ceiling of a lift. The reading of the balance was 50 kg-wt when the lift was accelerating
upwards at m/s^{2}, and the reading was 10 kg-wt when the
lift was accelerating downwards at m/s^{2}. Given that the acceleration due to gravity is , determine the value of .

**Q16: **

A body was suspended from a spring balance fixed to the ceiling of a lift. When the lift was moving upwards with an acceleration of magnitude , the reading on the balance was 23 kg-wt. When it was accelerating downwards at , the balance read 6 kg-wt. What would the reading on the balance be if, while the lift was descending, it decelerated at ? Take .

**Q17: **

A body that weighs 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/s^{2}. Calculate the tension in the string. If the string snapped, what would the force 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/s^{2}.

- A ,
- B ,
- C ,
- D ,

**Q18: **

A lift of mass 556 kg
was moving downwards at
420 cm/s.
If the tension in the liftβs cable
should not exceed 834 kg-wt,
determine the minimum safe
stopping distance for the lift moving at this speed. Consider the acceleration due to
gravity to be 9.8 m/s^{2}.

**Q19: **

A body of mass 75 kg
was attached to a string fixed to the ceiling of a lift. Starting from rest,
the lift began accelerating vertically upwards at 44 cm/s^{2}.
During this time the tension in the string was .
After accelerating, the lift continued moving at the speed it had gained, at which point the tension in the string was .
Finally, the lift decelerated at 24 cm/s^{2},
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/s^{2}.

- A , ,
- B , ,
- C , ,
- D , ,

**Q20: **

A body of mass 130 kg was placed on the floor of a lift of mass 761 kg. The lift 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 liftβs motor when the lift was accelerating upwards and the magnitude of the reaction exerted on the body by the floor of the lift during the third stage of the motion. Take .

- A ,
- B ,
- C ,
- D ,

**Q21: **

A person of mass 82 kg was inside a lift. The lift started moving upwards 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 lift covered was 18 m, find the action of the manβs weight on the floor of the lift during each time interval: during the first interval, let the forces be , in the second interval , and in the last interval . Take .

- A , ,
- B , ,
- C , ,
- D , ,

**Q22: **

A body of mass 19 kg was placed on the floor of a lift. Find, to the nearest two decimal places, the force this body exerts on the floor of the lift when the lift is accelerating downwards at 143 cm/s^{2}. Consider the acceleration due to gravity to be 9.8 m/s^{2}.

**Q23: **

Determine the force that a body of mass 14 kg exerts on the floor of a lift when it is accelerating upwards at 84 cm/s^{2}. Take .

**Q24: **

A body of mass 32 kg
was suspended from a spring balance fixed to the ceiling of a lift. Given that the lift was accelerating upwards at
405 cm/s^{2}, find the apparent weight of
the body. Take .

- A 129.6 N
- B 313.6 N
- C 184 N
- D 443.2 N

**Q25: **

A body was suspended from a spring balance fixed to the ceiling of a lift. The balance
reading was 17 kg-wt when the lift was
accelerating upwards at , whereas when it was accelerating upwards at
, the reading was 11 kg-wt. Find the mass of the body,
given that the acceleration due to gravity is
9.8 m/s^{2}.

- A 5.8 kg
- B 9.67 kg
- C 73 kg
- D 29 kg