Example 9.3 from College Physics, 9.5 Simple Machines

What is the Advantage for the Wheelbarrow?

In the wheelbarrow of Figure 9.23, the load has a perpendicular lever arm of 7.50 cm, while the hands have a perpendicular lever arm of 1.02 m. (a) What upward force must you exert to support the wheelbarrow and its load if their combined mass is 45.0 kg? (b) What force does the wheelbarrow exert on the ground?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
Here, we use the concept of mechanical advantage.
Solution
(a) In this case, $\frac{F_{o}}{F_{i}} = \frac{l_{i}}{l_{o}}$ becomes
$F_{i} = F_{o} \frac{l_{o}}{l_{i}} .$
9.33

Adding values into this equation yields

$F_{i} = (45.0 kg) (9.80 {m/s}^{2}) \frac{0.075 m}{1.02 m} = 32.4 N .$
9.34

The free-body diagram (see Figure 9.23) gives the following normal force: $F_{i} + N = W$ . Therefore, $N = (45.0 kg) (9.80 {m/s}^{2}) - 32.4 N = 409 N$ . $N$ is the normal force acting on the wheel; by Newton’s third law, the force the wheel exerts on the ground is $409 N$ .
Discussion
An even longer handle would reduce the force needed to lift the load. The MA here is $MA = 1 . 02 / 0 . 0750 = 13 . 6$ .

0 of 3 steps open

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