block A: mass = 100·g, spring stretched 10·cm
block B: mass = 400·g, spring stretched 20·cm
block C: mass = 200·g, spring stretched 20·cm
block D: mass = 200·g, spring stretched 20·cm
Rank the blocks, from largest to smallest, based on the potential energy stored in the spring attached to each block (largest to smallest)
To rank the blocks from largest to smallest based on potential energy stored in the spring, we need to calculate the potential energy for each block using the formula:
Potential energy (PE) = 1/2 * k * x^2
where:
- PE is the potential energy
- k is the spring constant
- x is the displacement of the spring from its equilibrium position
In this case, the spring displacement (x) is given as 10 cm for Block A, and 20 cm for Blocks B, C, and D.
The spring constant (k) is not given, but we can assume it is the same for all blocks since they all have the same spring attached.
1. Calculate the potential energies for each block using the given data:
- Block A:
Spring displacement (x) = 10 cm = 0.1 m
Mass (m) = 100 g = 0.1 kg
Potential energy (PE) = 1/2 * k * x^2 = 1/2 * k * (0.1)^2
- Block B, C, and D:
Spring displacement (x) = 20 cm = 0.2 m
Mass (m) = 400 g = 0.4 kg (for Block B)
Mass (m) = 200 g = 0.2 kg (for Blocks C and D)
Potential energy (PE) = 1/2 * k * x^2 = 1/2 * k * (0.2)^2
2. Since the spring constant (k) is assumed to be the same for all blocks, we can compare the potential energies by comparing the masses and the square of the displacement.
The potential energy increases with both the mass and the square of the displacement. Therefore, to rank the blocks from largest to smallest potential energy, we consider the product of mass and the square of the displacement.
Calculating the products for each block:
- Block A: Mass (m) * (spring displacement (x))^2 = 0.1 * (0.1)^2
- Block B: Mass (m) * (spring displacement (x))^2 = 0.4 * (0.2)^2
- Block C: Mass (m) * (spring displacement (x))^2 = 0.2 * (0.2)^2
- Block D: Mass (m) * (spring displacement (x))^2 = 0.2 * (0.2)^2
3. Comparing the products, we can see that the ranking from largest to smallest potential energy is:
1. Block B
2. Block C
3. Block D
4. Block A
Therefore, the ranking of the blocks from largest to smallest potential energy stored in the spring is: Block B, Block C, Block D, and Block A.