Question

A woman is pushing a load in a wheelbarrow, as in (Figure1). The combined mass of the wheelbarrow and the loadis 100kg, with a center of gravity at d =0.35m behind the axle. The woman supports the wheelbarrow atthe handles, 1.1 m behind the axle.Part A: What is the force required to support the wheelbarrow?Part B:What fraction of the weight of theThis problem has been solved!You'll get a detailed solution from a subject matter expert that helps you learn core concepts.A woman is pushing a load in a wheelbarrow, as in (Figure1). The combined mass of the wheelbarrow and the loadis 100kg, with a center of gravity at d =0.35m behind the axle. The woman supports the wheelbarrow atthe handles, 1.1 m behind the axle.Part A: What is the force required to support the wheelbarrow?Part B:What fraction of the weight of the wheelbarrow and the load doesthis force represent?

Answer 1

The force required represents about 24.1% of the total weight of the wheelbarrow and the load.

To determine the force required to support the wheelbarrow and the load and the fraction of the weight it represents, we can use the principles of torque and equilibrium.

Let's start by calculating the torque exerted by the combined mass of the wheelbarrow and the load about the axle:

Torque = Force × Distance

The torque due to the combined mass acting at the center of gravity (0.35m behind the axle) must be balanced by the torque applied by the woman at the handles.

Given:

Combined mass (wheelbarrow + load) = 100 kg

Distance from the axle to the center of gravity = 0.35 m

Distance from the handles to the axle = 1.1 m

First, let's find the torque exerted by the combined mass:

Torque due to the load = Force_due_to_load × Distance

Since the entire load is acting at the center of gravity:

Torque_due_to_load = Weight × Distance_from_axle_to_CG

Weight = mass × gravity

Weight = 100 kg × 9.81 m/s² ≈ 981 N

Torque_due_to_load = 981 N × 0.35 m ≈ 343.35 N·m

Now, let's find the force required to support the wheelbarrow at the handles:

Torque_due_to_force = Force_required × Distance_from_axle_to_handles

The system is in equilibrium, so the torque exerted by the woman equals the torque due to the load:

Force_required × 1.1 m = 343.35 N·m

Now, solve for Force_required:

Force_required = 343.35 N·m / 1.1 m ≈ 312.14 N

So, the force required to support the wheelbarrow and the load is approximately 312.14 Newtons.

To find the fraction of the weight of the wheelbarrow and the load represented by this force:

Total weight of the wheelbarrow and load = 981 N (weight of the load) + 312.14 N (force required)

Total weight = 1293.14 N

Fraction represented by the force required:

Fraction = Force_required / Total_weight

Fraction ≈ 312.14 N / 1293.14 N ≈ 0.241 or approximately 24.1%

Answer 2

A. The force required to support the wheelbarrow is 312N

2. This force represents 31.8% of the weight of the wheelbarrow and the load

How to determine the required force and fraction of the weight of the wheelbarrow and the load the force represent?

Using the principle of moments, which states that the sum of clockwise moments equals the sum of anticlockwise moments about any point for the system to be in equilibrium, we can solve this problem.

Given:

`\(W` represents the combined mass (load + wheelbarrow) acting downward
`(\(W = 981 \, \text{N}\))`

`\(F\)` is the force required to support the wheelbarrow

`\(d_1\)` is the distance between the point where the woman supports the wheelbarrow and the axle
`(\(d_1 = 1.1 \, \text{m}\))`

`\(d_2\)` is the distance between the center of gravity of the system and the axle
`(\(d_2 = 0.35 \, \text{m}\))`

Part A:

The equation for the equilibrium of moments is:
`\(Fd_1 = Wd_2\)`

Therefore,
`\(F = (Wd_2)/(d_1)\)`

Substituting the given values:

`\(F = \frac{981 \, \text{N} * 0.35 \, \text{m}}{1.1 \, \text{m}}\)`

`\(F = 312.45 \, \text{N}\)`

Hence, the force required to support the wheelbarrow is approximately \(312.45 \, \text{N}\).

Part B:

To determine the fraction of the weight of the wheelbarrow and the load that this force represents:

`\(\text{Fraction} = \frac{\text{Force}}{\text{Weight}}\)`

Given:

`\(Weight = 981 \, \text{N}\)`

`\(\text{Fraction} = \frac{312.45 \, \text{N}}{981 \, \text{N}}\)`

`\(\text{Fraction} = 0.318\)`

Therefore, the force required to support the wheelbarrow represents approximately
`\(31.8\%\)` of the weight of the wheelbarrow and the load.