Basic science, A hammer of mass is dropped from thew top of a roof of the two storey building to the ground. Another hammer of equal mass fell from a coffee table to the ground. Given than the height of the two storey building and the coffee table are 10m and 5m respectively.
(A) show that a hammer dropped from two storey building roof does more work than a hammer falling from a coffee table (6)
(B) calculate the potential energy from the two heights (4)
To show that a hammer dropped from a two-story building roof does more work than a hammer falling from a coffee table, we can compare the potential energy of each hammer.
(A) Work is defined as the amount of energy transferred by a force acting through a displacement. The work done on an object is equal to the change in its potential energy.
The potential energy (PE) of an object is given by the formula: PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
1. Let's compare the potential energy of the two hammers:
Potential energy at the two-story building roof:
PE1 = m * g * h1
Potential energy at the coffee table:
PE2 = m * g * h2
Since both hammers have equal mass (m), we can ignore it to simplify the comparison.
Now, substituting the given values:
PE1 = g * h1
PE2 = g * h2
2. Compare the potential energy:
Comparing the two potential energies, we find:
PE1 / PE2 = (g * h1) / (g * h2)
Since g is the same for both cases, it cancels out:
PE1 / PE2 = h1 / h2
We are given that the height of the two-story building roof (h1) is 10 m, and the height of the coffee table (h2) is 5 m.
Substituting these values:
PE1 / PE2 = 10 / 5
PE1 / PE2 = 2
Therefore, the hammer dropped from the two-story building roof does 2 times the work compared to the hammer falling from the coffee table.
(B) To calculate the potential energy, we can use the formula mentioned earlier: PE = mgh.
Potential energy from the two-story building roof:
PE1 = m * g * h1
PE1 = 10 * g * h1
Potential energy from the coffee table:
PE2 = m * g * h2
PE2 = 5 * g * h2
Given that the height of the two-story building roof (h1) is 10 m and the height of the coffee table (h2) is 5 m:
Potential energy from the two-story building roof:
PE1 = 10 * g * 10
PE1 = 100g Joules
Potential energy from the coffee table:
PE2 = 5 * g * 5
PE2 = 25g Joules
Therefore, the potential energy from the two-story building roof is 100g Joules, and the potential energy from the coffee table is 25g Joules.
To show that a hammer dropped from a two-story building roof does more work than a hammer falling from a coffee table, we need to calculate the work done in both cases.
The work done on an object is given by the formula:
Work (W) = Force (F) × Distance (d) × cos(θ)
Let's assume that the hammer is dropped vertically downwards in both cases, so the angle (θ) between the direction of force and the direction of motion is 0 degrees.
(A) Calculating the work done:
For the hammer dropped from the two-story building roof:
Force (F) = Weight of the hammer = mass (m) × gravitational acceleration (g)
Distance (d) = Height of the two-story building = 10m
Therefore, the work done from the two-story building roof = W1 = F × d × cos(0) = m × g × d
For the hammer falling from the coffee table:
Force (F) = Weight of the hammer = mass (m) × gravitational acceleration (g)
Distance (d) = Height of the coffee table = 5m
Therefore, the work done from the coffee table = W2 = F × d × cos(0) = m × g × d
Since the mass of both hammers is equal, the factor m × g is the same for both cases. Thus, to show that W1 is greater than W2, we need to compare the distances d.
We can see that the height of the two-story building (10m) is greater than the height of the coffee table (5m), so the work done when the hammer is dropped from the two-story building roof (W1) is indeed greater than the work done when the hammer is dropped from the coffee table (W2).
Therefore, a hammer dropped from a two-story building roof does more work than a hammer falling from a coffee table.
(B) Calculating the potential energy:
The potential energy of an object is given by the formula:
Potential Energy (PE) = mass (m) × gravitational acceleration (g) × height (h)
For the two-story building:
Potential Energy (PE1) = m × g × h1 = m × g × 10m
For the coffee table:
Potential Energy (PE2) = m × g × h2 = m × g × 5m
Therefore, the potential energy from the two heights are:
PE1 = m × g × 10m
PE2 = m × g × 5m