# Worksheet: Newton’s Second Law: Constant Mass

In this worksheet, we will practice using Newton’s second law of motion with a particle with constant mass under the action of constant force.

**Q3: **

A body of mass 37 kg was placed on a smooth horizontal surface where a force 72 N was acting on the body such that its line of action made an angle of downward from the vertical. Determine the acceleration of the body and the magnitude of the normal reaction . Round your answers to the nearest two decimal places.

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

**Q6: **

It took one minute for a van of mass 3.5 tons to accelerate from rest to a velocity of 18.9 km/h. What was the average force provided by the engine while it was accelerating? Use .

**Q7: **

The ratio between the masses of two bodies at rest is . If a force of magnitude acts on each of them, find the ratio between the resultant acceleration of each body.

- A
- B
- C
- D

**Q8: **

A train of mass 55 metric tons was accelerating at
4 cm/s^{2} along a horizontal track. Given that the driving
force generated by the engine was 4,950 kg-wt, and the acceleration due
to gravity is 9.8 m/s^{2}, find the resistance to its motion per metric ton of its
mass.

**Q9: **

A bullet of mass 45 g was fired at 53 m/s toward a fixed wooden barrier that was 40 cm thick. Calculate the exit speed of the bullet as it leaves the rear side of the wooden barrier, given that the resistance of the wood to the bulletβs movement was 4.5 kg-wt. Take .

**Q10: **

A tank of mass 41 metric tons started moving along a section of horizontal ground. The resistance to its motion was 9 N per tonne of its mass, and the magnitude of the force generated by its engine was 1,450 N. Determine the tankβs speed 472 seconds after it started moving rounding the result to the nearest two decimal places.

**Q11: **

A hot-air balloon of mass 1.5 metric tons was accelerating vertically downward at
106.2 cm/s^{2}.
Given that the acceleration due to gravity is 9.8 m/s^{2}, find the lift force generated by the hot air.

**Q12: **

A certain force acted on three distinct bodies causing each to accelerate at a different rate: the first accelerated at , the second at , and the third at . The three bodies collided and coalesced into a single body. Given that when the same force acted upon this new body, it resulted in an acceleration of magnitude , find the ratio .

- A
- B
- C
- D

**Q13: **

A balloon of mass 1,086 kg was ascending vertically at 36 cm/s. If a body of mass 181 kg fell from it, find the distance between the balloon and the body 11 seconds after the body fell. Take .

**Q14: **

A balloon of mass kg carrying a body of mass kg was moving vertically upward with an acceleration of . The body fell from the balloon, and the balloon started moving with an acceleration of . Given that the elevator force of the balloon and the resistance to its motion are constant in both cases, determine β:β. Take .

- A2β:β11
- B13β:β2
- C2β:β13
- D11β:β2

**Q15: **

A train, weighing 136 tons, was moving along a horizontal straight railway with a uniform velocity of 14.7 m/s. While the train was moving, the last carriage, weighing 17 tons, was separated and decelerated to completely stop after 80 seconds. If the resistance per ton of the trainβs mass was constant, determine how many seconds it took for the distance between the train and the separated carriage to be 42 m.

**Q16: **

A train of mass 598 metric tons was accelerating uniformly
at 19 cm/s^{2} when the last carriage of the train was released.
The resistance to the movement of the train was 4 kg-wt per tonne of the trainβs mass.
Given that the last carriage had a mass of 25 metric tons,
find the resulting acceleration of the train after the carriage was released. Take .

**Q17: **

A body of mass 45 kg fell vertically from a point 70 cm above a sandy surface. Given that the body penetrated a distance cm into the sand and that the resistance of the sand to the bodyβs motion was 150 kg-wt, find the value of . Take .

**Q18: **

A train of mass 21 metric tons was moving on a straight track at
105.84 km/h. Suddenly,
the last carriage, of mass 7 metric tons, detached from the rest of the train. The resistance to the trainβs movement at any given moment equals 50 kg-wt per tonne
of the trainβs mass. Find the time taken for the released carriage to come to rest and the
speed of the remaining part of the train at time . Consider the acceleration due
to gravity to be 9.8 m/s^{2}.

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

**Q19: **

A bullet of mass 50 g was moving horizontally at 60 m/s when it hit a target at rest. The target was formed of two adjacent layers. The bullet passed through the first layer, which was 32 cm of fibreglass, and then it penetrated 34 cm into the second layer, which was made of wood, before it stopped. If the resistance of the wood is two times that of the fibreglass, determine the resistance of the fibreglass.

**Q20: **

A body of mass 41 kg was moving along a horizontal road at 14 m/s. A force started acting on the body opposing its motion. As a result, over the next 26 m, its speed decreased uniformly to 12 m/s. Find the magnitude of the force which caused this change in the bodyβs motion.

**Q21: **

A right circular cylinder of height 40 cm, radius 18 cm, and mass 18 kg was moving at 11 m/s when it entered a dusty cloud. The action of dust on the body caused a resistance of 0.05 g-wt for every square centimeter of the area of its curved surface. Given that it passed through the dusty cloud for 25 seconds, determine its speed as it came out the other side. Take .

**Q22: **

A force of magnitude 6 N was acting on a body of 4 kg. Given that the body started moving from rest, find the distance the body covered in the first 10 seconds of its motion.

**Q23: **

A train of mass 27 metric tons started moving out of a station.
The force of its engine was 97.2 kN more than the total resistance to its movement.
It continued accelerating under this force until its speed reached 28.8 m/s,
and then it continued moving at this speed for some time. Finally, the operator applied the brakes, which in turn caused the train to decelerate
at 7.2 m/s^{2}. Given that the total distance the train traveled
was 4,377.6 m, find the total time of the trip.

**Q24: **

A body of mass 6 kg is initially at rest at a point . It starts to move under the action of a force where m is the displacement of the body from . Find the displacement of the body when its velocity is .

- A
- B
- C
- D

**Q25: **

A body of mass 2 kg moves along a straight line under the action of a force, . The force acting on the body is N, where is the displacement of the body from its initial position. Determine the velocity of the body, rounded to two decimal places, when .