A 74 -kg tree surgeon rides a "cherry picker" lift to reach the upper branches of a tree. What force does the lift exert on the surgeon when it's (a) at rest; (b) moving upward at a steady \(2.4 \mathrm{m} / \mathrm{s}\) (c) moving downward at a steady \(2.4 \mathrm{m} / \mathrm{s} ;\) (d) accelerating upward at \(1.7 \mathrm{m} / \mathrm{s}^{2} ;\) (e) accelerating downward at \(1.7 \mathrm{m} / \mathrm{s}^{2} ?\)

Gravitational force is akin to the invisible cord that keeps our feet grounded on Earth. It's a universal pull that every object with mass exerts on others. For us here on Earth, it's the force that our planet exerts on us due to its mass. This force is what gives us weight.

The formula for calculating gravitational force on the surface of the Earth is simple: it's the product of an object's mass (\( m \)) and the acceleration due to gravity (\( g \)), which is roughly \( 9.8 \text{m/s}^2 \) near the Earth's surface. So, if a tree surgeon has a mass of 74 kilograms, the gravitational force on him is \( F_{\text{gravity}} = 74 \text{kg} \times 9.8 \text{m/s}^2 = 724.2 \text{N} \). That's his weight, and it's the force the lift needs to counteract when it's at rest to keep him aloft.

Acceleration is the rate at which an object changes its velocity. It's a vector, meaning it has both a magnitude and a direction. When you press the gas pedal in a car and the car speeds up, that's acceleration. When you hit the brakes and the car slows down, that's also acceleration, just in the opposite direction relative to the car's movement.

In physics, acceleration (\( a \) ) is computed as the change in velocity (\( \text{Δv} \) ) over time (\( \text{Δt} \) ): \( a = \frac{\text{Δv}}{\text{Δt}} \). A constant acceleration means a steady increase or decrease in velocity. So if our cherry picker is moving upwards with a steady acceleration of \( 1.7 \text{m/s}^2 \), the tree surgeon would be getting faster in the upward direction by that rate every second.

Understanding Newton's Second Law

Newton's second law of motion is the foundation of force calculation. It states that the force (\( F \)) applied on an object is equal to the mass (\( m \) ) of the object multiplied by its acceleration (\( a \) ): \( F = m \times a \).

When considering forces, it's crucial to include all acting on the object. For example, when our lift accelerates upward, the total force exerted by the lift includes not only the force needed to overcome gravity (the person's weight) but also the force needed to accelerate the person upwards. That's why we calculate the upward force by adding the weight to the force from acceleration: \( F_{\text{total}} = m \times a + m \times g = 849.8 \text{N} \).

Steady motion, or uniform motion, is when an object moves at a constant velocity — it means there's no acceleration. If there's no acceleration, then by Newton's second law, the net force acting on the object is zero. But how can this be when gravity is pulling down on everything?

It's all about balance. The lift exerts an upward force exactly equal to the downward force of gravity on the tree surgeon. Thus, the forces cancel each other out, resulting in no acceleration and a feeling of steady motion. Whether the lift is moving upward or downward at this steady pace, the force it needs to apply is the same as when it's stationary — just enough to counteract gravity, which is the gravitational force we've calculated earlier.