Q2. Compare the two different scenarios of getting a heavy bag of cement to a height of 1 meter.

(a) Lifting the bag vertically upwards.
(b) Walking up a long ramp to get the bag up to a height of 1 meter.
What is the work done by gravity in either scenario? What is your work done in either scenario? Why do people use long ramps?

In both scenarios, the goal is to get a heavy bag of cement to a height of 1 meter. Let's analyze each scenario:

(a) Lifting the bag vertically upwards:

In this case, the work done by gravity is negative because it is acting against the direction of the displacement.

Work done by gravity = -mgh

where
m = mass of the bag,
g = acceleration due to gravity (approximately 9.81 m/s²),
h = height (1 meter).

The work done by you is positive because you are applying force in the direction of the displacement.

Your work done = mgh

(b) Walking up a long ramp to get the bag up to a height of 1 meter:

In this case, the work done by gravity is still negative, but its magnitude is less as compared to the previous scenario. The work done by gravity is now the component of the gravitational force acting along the ramp which is given by mg * sin(theta) (where theta is the angle of inclination of the ramp).

Work done by gravity along the ramp (negative) = -mgh (sin(theta))

The work done by you is now spread out over a longer distance. While the component of gravitational force acting against you is reduced by the sin(theta) factor, the overall force to be applied by you is still the same due to the increase in distance over which the force is applied.

Your work done = mgh (sin(theta))

People prefer using long ramps because the force needed to push or pull the heavy load is reduced. This is because the gravitational force acting against the direction of motion is reduced, making it easier to lift the heavy load along the ramp. In addition, the work is spread over a longer distance, which allows the person to use a lower force to achieve the same height over a longer period, making it less strenuous on the body.

(a) Lifting the bag vertically upwards:

Work done by gravity: In this scenario, the work done by gravity is zero because the bag is not moving vertically against gravity. Gravity is not doing any work to lift the bag.

My work done: Well, let me be clear, as a bot, I don't have any muscles or limbs, so I can't lift anything. Therefore, my work done is also zero. But if I were to lift the bag, well, let's just say it wouldn't be a pretty sight.

(b) Walking up a long ramp:

Work done by gravity: In this scenario, the work done by gravity is still zero. The bag is being pushed upwards by the force you apply, not gravity itself.

My work done: Again, no work done by me here, unless you count making jokes to lighten the load. But if I were to help push the bag up the ramp, I'd probably just end up tripping and rolling down the ramp with the bag. Not very helpful, I know.

Why do people use long ramps: People use long ramps because it allows them to reduce the amount of force they need to apply to lift heavy objects. By increasing the distance over which the force is applied, they can decrease the amount of force needed. It's a clever way of making the task easier and more manageable. Plus, it's a great opportunity to practice your roller skating skills if things go wrong!

In both scenarios, the work done by gravity can be calculated using the formula:

Work done by gravity = force of gravity × distance

However, since the force of gravity is constant and acts vertically downward, the work done by gravity will be the same in both scenarios. The force of gravity can be calculated using the formula:

Force of gravity = mass × acceleration due to gravity

Now let's analyze the work done by the person in each scenario.

(a) Lifting the bag vertically upwards:
In this scenario, the person applies a force to lift the bag directly against the force of gravity. The work done by the person can be calculated using the formula:

Work done by the person = force applied by the person × distance

Here, the distance is the height the bag is lifted, i.e., 1 meter. The force applied by the person needs to be at least equal to the force of gravity acting on the bag to lift it upward. So, the work done by the person will be greater than the work done by gravity.

(b) Walking up a long ramp:
In this scenario, the person pushes the bag up a long ramp inclined at an angle to the horizontal. Although the vertical distance covered is still 1 meter, the actual distance traveled along the ramp will be greater than 1 meter due to the inclined pathway. The work done by the person can still be calculated using the formula:

Work done by the person = force applied by the person × distance

Here, the distance is the total distance traveled along the ramp. The force applied by the person does not need to be equal to the force of gravity acting on the bag since some of the force is used to overcome the horizontal component of the bag's weight. As a result, the work done by the person will likely be less than the work done by gravity.

People use long ramps because it reduces the amount of work they need to do to lift heavy objects. By using a ramp, the force required to move the object vertically against gravity decreases since a portion of the force can be utilized to overcome the horizontal component. This allows for an easier and more efficient method of moving heavy objects to a certain height.

To compare the two different scenarios of getting a heavy bag of cement to a height of 1 meter, we will examine the work done by gravity and your work in each scenario.

(a) Lifting the bag vertically upwards:
In this scenario, you would lift the bag of cement directly upwards to a height of 1 meter. To calculate the work done by gravity, we need to know the mass of the bag of cement. Let's assume it is 50 kg.

The work done by gravity can be calculated using the formula:
Work = Force × Distance × cos(θ)
In this case, θ is the angle between the force of gravity and the direction of motion. Since the motion is vertical, θ is 0 degrees.

The force of gravity acting on the bag of cement can be calculated by multiplying its mass (m = 50 kg) by the acceleration due to gravity (g = 9.8 m/s²):
Force = m × g = 50 kg × 9.8 m/s² = 490 N

The distance lifted vertically is 1 meter.

Therefore, the work done by gravity in this scenario is:
Work = 490 N × 1 m × cos(0°) = 490 N × 1 m = 490 Joules (J)

Your work in this scenario is also 490 Joules because you are exerting a force equal to the force of gravity and lifting the bag vertically.

(b) Walking up a long ramp:
In this scenario, instead of lifting the bag vertically, you walk up a long ramp to bring the bag to a height of 1 meter. The ramp provides an inclined plane that reduces the force required to lift the bag vertically.

To calculate the work done by gravity in this scenario, we again need to know the mass of the bag of cement (50 kg) and the distance traveled along the ramp. Let's assume the ramp is 10 meters long.

The force of gravity acting on the bag of cement remains the same as in the previous scenario (490 N), since the mass and acceleration due to gravity are constant.

The distance traveled along the ramp is 10 meters. Since the ramp is inclined, a portion of the weight of the bag of cement is supported by the ramp, reducing the required effort.

Therefore, the work done by gravity in this scenario is:
Work = 490 N × 10 m × cos(θ)
θ is the angle between the ramp and the horizontal direction. The cosine of this angle represents the ratio of the vertical distance traveled to the total distance along the ramp.

The exact value of cos(θ) depends on the specific angle of the ramp. Let's assume it is a gentle slope, so cos(θ) = 0.98.

Work = 490 N × 10 m × cos(θ) = 490 N × 10 m × 0.98 = 4,804 Joules (J)

Your work in this scenario is different from the previous one. Since the ramp reduces the amount of force required to lift the bag, you need to exert a lesser force over a larger distance. Your work can be calculated using the same formula as before:

Work = Force × Distance × cos(θ)

Assuming you exert half the force you would need when lifting vertically, and the distance traveled is 10 meters, your work would be:
Work = (490 N / 2) × 10 m × cos(θ) = 2,450 Joules (J)

Many people use long ramps in scenarios like this because it reduces the amount of force needed to lift heavy objects. By distributing the effort over a longer distance, the work required becomes more manageable. Ramps allow for easier transportation and provide mechanical advantage, making it easier to move heavy objects vertically.