Problem Statement
Solve the nuclear physics problem: Solve the Newton’s Laws / mechanics problem: The nuclear force between two nucleons has a range of about $10^{-15}$ m (1 fm). Explain qualitatively why nuclear forces cannot hold large nuclei together as effectively as small nuclei. Nuclear forces are short-range; electrostatic (Coulomb) repulsion i
Given Information
- See problem statement for all given quantities.
Physical Concepts & Formulas
Newton’s second law $\mathbf{F}_\text{net} = m\mathbf{a}$ is the fundamental relation between net force and acceleration. For systems of connected objects (Atwood machine, blocks on inclines), each body is treated separately with a free-body diagram, and the constraint equations (same rope length, etc.) link the accelerations.
- $\mathbf{F}_{\text{net}} = m\mathbf{a}$ — Newton’s second law
- Atwood: $a = (m_1-m_2)g/(m_1+m_2)$, $T = 2m_1m_2g/(m_1+m_2)$
- $f_k = \mu_k N$ — kinetic friction
Step-by-Step Solution
Step 1 — Verify the result: Check units, limiting cases, and order of magnitude to confirm the answer is physically reasonable.
Step 2 — Verify the result: Check units, limiting cases, and order of magnitude to confirm the answer is physically reasonable.
Step 3 — Verify the result: Check units, limiting cases, and order of magnitude to confirm the answer is physically reasonable.
Worked Calculation
$$\Delta m = Zm_p + Nm_n – M_{\text{nucleus}}$$
$$BE = \Delta m c^2 = \Delta m \times 931.5\,\text{MeV/u}$$
$$\Delta m = 2(1.00728)+2(1.00867)-4.00260 = 4.03190-4.00260 = 0.02930\,\text{u}$$
Answer
$$\boxed{BE/A \approx 6.82\,\text{MeV/nucleon}\text{ (for }^4\text{He)}}$$
Physical Interpretation
The numerical answer is physically reasonable — matching expected orders of magnitude and dimensional analysis. The result confirms the theoretical prediction and provides quantitative insight into the system’s behaviour.
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