You are writing a physics test, and your formula sheet has a smudge on it, makin

Question

You are writing a physics test, and your formula sheet has a smudge on it, making it hard to read the exponent of one of your equations, which describes the energy stored in a spring. Your copy reads U = 1/2kx2 where ? represents the number that you can't read. Rather than asking the instructor (WHICH YOU SHOULD ALWAYS DO WHEN WRITING A TEST!), you decide to use dimensional analysis to figure out the power. You remember that the units of energy, U, are [U] = J = Nm, the units of the spring constant, k, are [k] = N/m, and the units of position, x, are [x] = m, where 1 N = 1 kg m/s2. Express the units of U( /1) and k ( /1) in terms of kg, m and s, and solve for the value of ? ( /3).

Explanation / Answer

U = Kg- m2 /s2

k= N/m = Kg /s2

x=m

we can write as

U = 0.5(N/m) * (m)n    ( where n is unknown exponent)

=> Kg- m2 /s2= 0.5 (( Kg- m /s2)/m ) *mn   (remove the constant )

=>Kg- m2/s2 =(( Kg /s2)*mn

=>m *m = mn

=> m2= mn

comparing the powers as the bases are same, we get ,

n= 2

hence ,

U=0.5 k*x2

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.