# Lesson Worksheet: Connected Particles Mathematics

In this worksheet, we will practice solving problems with systems of multiple connected particles

**Q1: **

Two particles, A and B, are connected by a light and inextensible string and are lying on a flat rough surface. The masses of A and B are, respectively, 10 kg and 20 kg. A constant horizontal force of 300 N is acting on particle A away from particle B, causing both particles to move on the rough flat surface. During this motion, friction forces of magnitudes 50 N and 80 N are acting on particles A and B respectively. Find the magnitude of the acceleration of particle B, rounded to the nearest tenth of a meter per second squared.

**Q2: **

Two particles, A and B, are connected by a light inextensible string and are lying on a flat rough surface. The masses of A and B are 10 kg and 20 kg respectively. A constant horizontal force of 300 N is acting on particle A away from particle B, causing both particles to move on the rough flat surface. During this motion, friction forces of magnitudes 50 N and 80 N are acting on particles A and B respectively. Find the magnitude of tension exerted by the string, rounded to the nearest tenth of a newton.

**Q3: **

Two particles, A and B, are connected by a light inextensible rod and are moving on a flat surface; their motion is caused by a constant horizontal force acting on particle A.
The masses of A and B are 35 kg and 7 kg respectively.
During this motion, friction forces of magnitudes 100 N and 20 N are acting on particles A and B respectively.
Given that particle A’s acceleration is 3 m⋅s^{−2} toward particle B, find the magnitude of the constant force.

**Q4: **

Consider two particles, A and B, that are connected by a light inextensible string and are lying on a flat smooth surface.
Particle A’s mass is 25 kg, while particle B’s mass is unknown.
A constant horizontal force of 150 N is applied to particle B in the direction away from particle A,
and both particles’ acceleration is horizontal with magnitude 5 m⋅s^{−2}.
Find the magnitude of the tension exerted by the string on particle A.

**Q5: **

Two particles, A and B, are connected by a light inextensible rod and are lying on a flat smooth surface. The masses of A and B are 10 kg and 20 kg respectively. A constant horizontal force of 300 N is acting on particle A toward particle B, causing both particles to move. Find the acceleration of particle B, rounded to the nearest meter per second squared.

- A10 m⋅s
^{−2}away from particle A - B30 m⋅s
^{−2}away from particle A - C10 m⋅s
^{−2}toward particle A - D30 m⋅s
^{−2}toward particle A

**Q6: **

An engineer is designing a connector for a pickup truck to be used when the truck needs to pull a trailer behind.
To ensure the safety of the connector, the engineer needs to calculate the maximum tension that the connector must be able to handle without breaking.
The truck’s maximum mass with a driver and passengers is 1,500 kg, and the maximum mass of the trailer with a full load is assumed to be 5,000 kg.
At the maximum capacity, the truck and trailer will experience horizontal friction of magnitudes 300 N and 1,000 N respectively.
Assuming that a connector is a light inextensible string connecting the truck and the trailer, find the magnitude of the tension in the connector under maximum capacity when the truck is on a horizontal road accelerating at 0.5 m⋅s^{−2}.

**Q7: **

A
500 g
mass is resting on top of a
2 kg
mass while the bottom mass is accelerating
upward with magnitude
2 m⋅s^{−2}.
If the positive direction is upward and , find the
force that the
500 g
mass is exerting on the
2 kg
mass to the nearest tenth of a
newton.

- A3.9 N downward
- B3.9 N upward
- C5.9 N upward
- D1 N downward
- E5.9 N downward

**Q8: **

A 2,500 g mass is resting on top
of a flat surface while the surface is accelerating
downward with magnitude 2 m⋅s^{−2}.
If the positive direction is upward and , find the force that the surface is exerting
on the mass to the nearest tenth of a newton.

**Q9: **

Two boxes are stacked up vertically on a forklift truck. The mass of the box on top is 200 kg, while the mass of the box at the bottom is 600 kg. The forklift truck applies a constant upward force of 10,000 N, lifting both boxes. Find the magnitude of the force the top box exerts on the bottom box.

**Q10: **

Two particles, A and B, are connected by a light inextensible rod and are lying on a flat
rough surface. The mass of A is half the mass of B. A constant horizontal force of
300 N
is
acting on particle A away from particle B, causing an acceleration of magnitude
5.7 m⋅s^{−2}.
During this motion, friction forces of magnitudes
50 N
and
80 N
are acting on
particles A and B respectively.
Find the mass of particle A to the nearest
kilogram.