A 4.3 "kilo" bag of sugar is on a counter. How much work is required to put the bag on a shelf a distance of 0.43 m above the counter?
There are only two pieces of information given here: mass and distance. So, look in your text for problems involving work, mass, and distance.
Hooray! We find that work is the same as the change in energy. Hmmm. Now what. Potential energy is just force times distance.
So, we have mass and distance. We want force and distance. So, what are we doing? Moving mass upwards against gravity. Aha! In such an instance, F = ma = 9.8*m
Good old formula: W = mgh
Now we have the work is just the potential energy gained moving a 4.3kg mass for 0.43 in a gravity field.
W = mgh = 9.8 * m * 0.43 = 4.2 Nm = 4.2J
Well, to be honest, sugar bags aren't really known for their incredible work ethic. They tend to just sit there, being all granulated and sweet. So, in terms of work, you just need to summon enough strength to lift that 4.3 "kilo" bag, and move it a measly 0.43 meters to the shelf. Just think of it as a mini workout (with a sweet reward at the end)!
To calculate the work required to lift the bag of sugar onto the shelf, you need to multiply the force required to lift it by the distance it is lifted.
Step 1: Convert the weight of the bag of sugar from kilograms to newtons.
1 kilogram (kg) is equivalent to 9.8 newtons (N) on Earth's surface.
Given that the bag weighs 4.3 kilograms (kg):
Weight = mass × gravitational acceleration
Weight = 4.3 kg × 9.8 N/kg
Weight = 42.14 N
Step 2: Calculate the work done.
Work (W) = force(F) × distance(d)
Given:
Force (F) = weight = 42.14 N
Distance (d) = 0.43 m
Work (W) = 42.14 N × 0.43 m
Work (W) ≈ 18.14 joules (J)
Therefore, approximately 18.14 joules (J) of work is required to put the 4.3 kg bag of sugar on a shelf that is 0.43 m above the counter.
To calculate the work required to lift the bag of sugar onto the shelf, we can use the formula for work:
Work = Force × Distance × cos(θ)
Where:
- Force is the force applied to lift the bag
- Distance is the vertical distance the bag must be lifted (0.43 m)
- θ is the angle between the applied force and the direction of motion. In this case, as we're lifting the bag straight up, the angle θ is 0 degrees, and the cos(0°) is equal to 1.
To find the force applied, we need to consider the weight of the bag. Weight is the force exerted by an object under the influence of gravity, and it is calculated by multiplying the mass of the object by the acceleration due to gravity (9.8 m/s^2).
Given that the bag weighs 4.3 kilograms, the weight of the bag can be calculated as follows:
Weight = Mass × Gravity
Weight = 4.3 kg × 9.8 m/s^2
Now that we have the weight, we can substitute it into the formula for work:
Work = Weight × Distance × cos(θ)
Work = (4.3 kg × 9.8 m/s^2) × 0.43 m × cos(0°)
Since cos(0°) equals 1, the formula simplifies to:
Work = (4.3 kg × 9.8 m/s^2) × 0.43 m
Now we can calculate the work:
Work = 4.3 kg × 9.8 m/s^2 × 0.43 m
Calculating this expression gives the answer for the work required to lift the bag of sugar onto the shelf.