Mechanics- connected particles

• MHB
• Shah 72
In summary, the car tows a caravan down a hill. The slope of the hill makes an angle theta with the horizontal, where sin theta = 0.05. The force from the car's engine is a braking force (a negative driving force). The car has mass 1800 kg and the caravan has mass 600kg. The resistance on the car is 20N and that on the caravan is 80N. The force in the tow bar is a thrust of 50N.
Shah 72
MHB
A car tows a caravan down a hill. The slope of the hill makes an angle theta with the horizontal, where sin theta = 0.05. The force from the car's engine is a braking force ( a negative driving force). The car has mass 1800 kg and the caravan has mass 600kg. The resistance on the car is 20N and that on the caravan is 80N. The force in the tow bar is a thrust of 50N. Show that the force from the car's engine is -420N.
I don't get the ans.

forces acting on the caravan down the incline …
$mg\sin{\theta}$
up the incline …
80N resistive force + 50N thrust force from the tow bar

forces acting on the car down the incline …
$Mg\sin{\theta} +$ 50N thrust force from the tow bar
up the incline …
20N resistive force + $F_B$, the braking force

both the car & caravan have the same acceleration

try again

skeeter said:
forces acting on the caravan down the incline …
$mg\sin{\theta}$
up the incline …
80N resistive force + 50N thrust force from the tow bar

forces acting on the car down the incline …
$Mg\sin{\theta} +$ 50N thrust force from the tow bar
up the incline …
20N resistive force + $F_B$, the braking force

both the car & caravan have the same acceleration

try again
Using Newtons law
F= m×a
18000sintheta+ 6000sintheta-20-50-80=2400a
a=0.438m/s^2
Again using F=m×a
18000×0.05-50-20-braking force= 1800×0.438
I don't get the ans

for the car …

$$\displaystyle F_{net} = 900+50-F_B-20$$

$$\displaystyle a = \dfrac{F_{net}}{M} = \dfrac{930-F_B}{1800}$$

for the caravan …

$$\displaystyle F_{net} = 300 -80-50$$

$$\displaystyle a = \dfrac{F_{net}}{m} = \dfrac{170}{600} = \dfrac{17}{60}$$

set the accelerations equal & solve for $F_B$

skeeter said:
for the car …

$$\displaystyle F_{net} = 900+50-F_B-20$$

$$\displaystyle a = \dfrac{F_{net}}{M} = \dfrac{930-F_B}{1800}$$

for the caravan …

$$\displaystyle F_{net} = 300 -80-50$$

$$\displaystyle a = \dfrac{F_{net}}{m} = \dfrac{170}{600} = \dfrac{17}{60}$$

set the accelerations equal & solve for $F_B$
Thank you so so much!

skeeter said:
for the car …

$$\displaystyle F_{net} = 900+50-F_B-20$$

$$\displaystyle a = \dfrac{F_{net}}{M} = \dfrac{930-F_B}{1800}$$

for the caravan …

$$\displaystyle F_{net} = 300 -80-50$$

$$\displaystyle a = \dfrac{F_{net}}{m} = \dfrac{170}{600} = \dfrac{17}{60}$$

set the accelerations equal & solve for $F_B$
Where did you get the 900?

Where did you get the 900?

$mg\sin{\theta} = 900 \, N$ for $g \approx 10 \, m/s^2$

1. What is the difference between connected and disconnected particles in mechanics?

Connected particles are those that are physically connected to each other, either by a rigid rod or a flexible string. Disconnected particles, on the other hand, are not physically connected and can move independently of each other.

2. How do I calculate the velocity of connected particles?

The velocity of connected particles can be calculated by using the principle of conservation of momentum. This states that the total momentum of a system remains constant, so the sum of the momenta of all the particles before and after the interaction must be equal.

3. Can connected particles have different masses?

Yes, connected particles can have different masses. The mass of each particle will affect its individual velocity, but the total momentum of the system will still be conserved.

4. What is the significance of the center of mass in connected particle systems?

The center of mass is the point at which the entire mass of a system can be considered to be concentrated. In connected particle systems, the center of mass can be used to simplify calculations and determine the overall motion of the system.

5. How does the tension in a string affect the motion of connected particles?

The tension in a string can affect the motion of connected particles by providing a force that can accelerate or decelerate the particles. The magnitude and direction of the tension will depend on the mass and velocity of the particles, as well as the angle at which the string is pulled.

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