1. Dynamics
Connected particles
Tow bars

2. Forces: Connected Particles
KUS objectives
BAT Set up a model of two connected particles with uniform tension on an inelastic string/cable
Starter: What are Newtons three laws?
A particle will remain at rest or will continue to move with constant velocity in a straight line unless acted on by a resultant force
Every Action has an equal and opposite reaction
The Force applied to a particle is proportional to the mass of the article and the acceleration produced
F = ma

3. WB9 Connected particles moving in the same direction
Problems concerning connected particles moving in the same direction should usually be solved by considering the particles separately
Two particles P and Q, of masses 5kg and 3kg respectively, are connected by a light, inextensible string. Particle P is pulled by a horizontal force of 40N along a rough horizontal plane. The resistance forces are g and 3 5 𝑔 respectively. Q P
3 kg
5 kg
Find the acceleration of each particle and the tension in the string
For Q:
(1) + (2)
For P:
Sub in (1)

4. WB10 Tow bar
WB10 A car of mass 1000 kg tows a caravan of mass 750 kg along a straight road. The engine of the car exerts a forward force of 2.5 kN The resistances to the motion of the car and caravan are each k × their mass where k is a constant. Given that the car accelerates at 1 ms-2 find the Tension in the tow-bar.
Draw a diagram

5. WB10 Tow bar For the car, 2500 – 1000k – T = 1000 x1 (1)
750 kg
1000 kg
For the car,
2500 – 1000k – T = x1 (1)
For the caravan,
T – 750k = x1 (2)
We have two equations with two unknowns
Now solve simultaneously to get
(1) + (2) k =
k = 3/7 , T = /7

6. WB11 Tow bar at an angle
This figure shows a lorry of mass 1600 kg towing a car of mass 900 kg along a straight horizontal road. The two vehicles are joined by a light towbar which is at an angle of 15° to the road. The lorry and the car experience constant resistances to motion of magnitude 600 N and 300 N respectively. The lorry’s engine produces a constant horizontal force on the lorry of magnitude 1500 N. Find
(a) the acceleration of the lorry and the car,
the tension in the towbar.

7. WB11 Tow bar at an angle Find (b) the tension in the towbar.
(a) the acceleration of the lorry and the car,
(b) the tension in the towbar.
For the car,
For the whole system,

8. WB11 Tow bar question taken further
When the speed of the vehicles is 6 m s–1, the towbar breaks. Assuming that the resistance to the motion of the car remains of constant magnitude 300 N,
find the distance moved by the car from the moment the towbar breaks to the moment when the car comes to rest.
(d) State whether, when the towbar breaks, the normal reaction of the road on the car is increased, decreased or remains constant. Give a reason for your answer.

9. (c) find the distance moved by the car from the moment the towbar breaks to the moment when the car comes to rest.
After towbar brakes, for the car:
(d) State whether, when the towbar breaks, the normal reaction of the road on the car is increased, decreased or remains constant. Give a reason for your answer.
Before
After
The vertical component of T is no longer present, so the normal reaction increases

10. WB12 Tow bar on a slope For the whole system: For the trailer:
A lorry of mass 900 kg is towing a trailer of mass 500 kg up an inclined road, at angle α, where tan α = ¾ .The two vehicles are joined by a light towbar . The lorry and the trailer experience constant resistances to motion of magnitude 1600 N and 600 N respectively. The lorry’s engine produces a constant horizontal force on the lorry of magnitude N. Find
(a) the acceleration of the lorry and car,
the tension in the towbar.
For the whole system:
900 kg
500 kg
For the trailer:

11. WB13 Tow bar - deceleration
A lorry of mass 900 kg is towing a trailer of mass 300 kg along a straight road. The two vehicles are joined by a light towbar . Assume resistance forces are negligible. The driver sees a red light ahead and brakes causing a braking force of 2400 N. Find
(a) the tension in the towbar,
the distance travelled before stopping
For whole system:
300 kg
900 kg
For the trailer:
When decelerating, the tow bar exerts a thrust on the car and trailer

12. Skills J
HWK J

13. One thing to improve is –
KUS objectives
BAT Set up a model of two connected particles with uniform tension on an inelastic string/cable
self-assess
One thing learned is –
One thing to improve is –

14. END