# Desperately need help in work, energy and power question?

## A heavy haulage truck is carrying a full load on a horizontal road at a speed of $23.3 k m {h}^{-} 1$. The truck and load have a total mass of 8.79 tonnes. Total friction acting against the motion is $2.10 \cdot {10}^{4} N$. What power must the truck's engine develop?

Jul 1, 2018

The power is $= 135.9 k W$

#### Explanation:

The speed is constant $v = 23.3 \cdot \frac{1000}{3600} = 6.472 m {s}^{-} 1$

The acceleration is $a = 0 m {s}^{-} 1$

Mass of the truck plus load is $m = 8.79 \cdot {10}^{3} k g$

The total frictional force is

${F}_{r} = 2.1 \cdot {10}^{4} N$

According to Newton's Second Law

$F - {F}_{r} = m \cdot a = 0$

$F = {F}_{r}$

The power is

$P = F v = 2.1 \cdot {10}^{4} \cdot 6.472 = 13.59 \cdot {10}^{4} W = 135.9 k W$

Jul 1, 2018

$P \approx 136 \setminus k W$

#### Explanation:

The mass of the truck and load is irrelevant. If it is travelling at constant velocity, it is not accelerating, so the force required is the force to overcome friction.

You may know that work, $W$, is:

• $W = F \cdot x$

And power $P$ is:

• $P = \frac{W}{t} = \frac{F \cdot x}{t} = F \cdot v$

So, being careful with the units:

$P = 2.1 \times {10}^{4} \cdot \frac{23.3 \times {10}^{3}}{3600} \approx 136 \setminus k W$