Question

Suppose that you can lift no more than 650 N (around 150 lb ) unaided.

(a) How much can you lift using a 1.4-m-long wheelbarrow that weighs and whose center of gravity is 0.50 m from the center of the wheel (Fig. E11.16)? The center of gravity of the load carried in the wheelbarrow is also 0.50 m from the center of the wheel.

(b) Where does the force come from to enable you to lift more than 650N using the wheelbarrow?

Short answer

(a) The load lifted using the wheelbarrow is 1740 N.

(b) The force that enables to lift more than 650 N is the normal reaction acting on the wheel of the wheelbarrow.

Step-by-step solution

Given information

The maximum weight that can be lifted unaided is F = 650 N.

The length of the wheelbarrow is L = 1.4 m.

The weight of the wheelbarrow is W = 80 N.

The distance of the center of gravity of the wheelbarrow from the center of the wheel is a = 0.50 m.

The distance of the center of gravity of load from the center of the wheel is a = 0.50 m.

Normal Reaction

When a body having a certain weight rests on the ground, then a reaction force equal to the body’s weight acts on it, and this force is described as ‘normal reaction force’.

The direction of the reaction force is always normal to the ground.

(a) Load lifted using the wheelbarrow

$W_1$The free-body diagram of the wheelbarrow is given by,

Here, N is the normal reaction on the wheel of the wheelbarrow and is the load carried by the wheelbarrow.

Taking moment about the right end of the wheelbarrow, and we get,

$F\times L-\left(W+W_1\right)\times a=0$

Substituting the values in the above expression and we get:

$$\begin{gathered} 650\text{N}\times \text{1.4}\text{m}-\left(80\text{N}+W_1\right)\times 0.50\text{m}=0 \\ 910\text{N}·\text{m}-40\text{N}·\text{m}-0.50W_1\text{m}=0 \end{gathered}$$

Solving further as:

$$\begin{gathered} 0.50W_1\text{m}=870\text{N}·\text{m} \\ {W}_1=\frac{870\text{N}·\text{m}}{0.50\text{m}} \\ {W}_1=1740\text{N} \end{gathered}$$

Hence, the load lifted using the wheelbarrow is 1740 N.

(b) The force required to lift more

By using the wheelbarrow, the value of the load lifted is 1740 N which is greater than the load lifted unaided.

The normal reaction on the wheel of the wheelbarrow acting upwards is given by:

$N=\left(W+W_1\right)-F$

Substituting the values in the above expression and we get:

$$\begin{gathered} N=\left(80\text{N}+1740\text{N}\right)-650\text{N} \\ N=1820\text{N}-650\text{N} \\ N=1170\text{N} \end{gathered}$$

Here, the force that enables to lift more than 650 N using the wheelbarrow is because of the normal reaction acting on the wheel of the wheelbarrow in the upward direction.

Hence, the force that enables to lift more than 650 N is the normal reaction acting on the wheel of the wheelbarrow.