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2. A 10 Mg truck hauls a 20 Mg trailer. If the unit starts from rest on a level road with a
tractive force of 20 kN between the driving wheels of the truck and the road, calculate the
acceleration of the unit and the tension in the horizontal draw-bar.
Drawbar
20 Mg Trailer
10 Mg Truck
a=0.667 m/s2
T= 13.3 KN
Oro
W​

Respuesta :

tochjosh

Answer:

The acceleration on the unit is 0.667 m/s^2

The tension on the draw-bar is 13.34 kN

Step-by-step explanation:

The mass of the truck = 10 Mg = 10 x 10^3 kg

The mass of the trailer = 20 Mg = 20 x 10^3 kg

Tractive force from the truck = 20 kN = 20 x 10^3 N

The total mass of the unit = 10 Mg + 20 Mg = 30 Mg = 30 x 10^3 kg

The tractive force on the unit will produce an acceleration that is given as

F = ma

where

F is the tractive = 20 x 10^3 N

m is the mass of the unit = 30 x 10^3 kg

a is the acceleration of the unit = ?

substituting into the equation

20 x 10^3 = 30 x 10^3 x a

a = (20 x 10^3)/(30 x 10^3) = 0.667 m/s^2

the tension on the draw-bar T is gotten from considering only the mass that is pulled by the draw-bar which is 20 Mg

The acceleration on the unit = 0.667 m/s^2

The drawn mass = 20 Mg = 20 x 10^3 kg

The tension on the draw bar = ma = 20 x 10^3 x 0.667 = 13340 N

= 13.34 kN

MrRoyal

The acceleration is 0.00067m/s^2, while the tension on the horizontal bar is 13.4 N

The given parameters are:

[tex]\mathbf{m = 10Mg}[/tex] -- mass of the truck

[tex]\mathbf{M = 20Mg}[/tex] -- mass of the trailer

[tex]\mathbf{F_T = 20kN}[/tex] --- tractive force

Start by calculating the total mass

[tex]\mathbf{M_T = m + M}[/tex]

So, we have:

[tex]\mathbf{M_T = 10Mg + 20Mg}[/tex]

[tex]\mathbf{M_T = 30Mg}[/tex]

Convert to kilograms

[tex]\mathbf{M_T = 30 \times 10^3kg}[/tex]

[tex]\mathbf{M_T = 30000 kg}[/tex]

Force is calculated as:

[tex]\mathbf{F =ma}[/tex]

So, we have:

[tex]\mathbf{20kN =30000kg \times a}[/tex]

Divide both sides by 30000

[tex]\mathbf{a = 0.00067ms^{-2}}[/tex]

The tension on the horizontal bar (i.e. the 20 Mg trailer) is:

[tex]\mathbf{T=ma}[/tex]

So, we have:

[tex]\mathbf{T=20Mg \times 0.00067ms^{-2}}[/tex]

Rewrite as:

[tex]\mathbf{T=20 \times 10^3 kg \times 0.00067m/s}[/tex]

[tex]\mathbf{T=13.4N}[/tex]

Hence, the acceleration is 0.00067m/s^2, while the tension on the horizontal bar is 13.4 N

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