Question

Do not forget your LABELS or your AXES. And please, do NOT put in numbers until the LAST STEP. Solve SYMBOLICALLY. Assign SYMBOLS to each of your variables, and write your equations USING ONLY THE SYMBOLS.

1. Block A (2.5 kg) and block B (1.3 kg) are held together with a compressed spring (of negligible mass) between them. When they are released, the spring pushes them apart, and they then move off in opposite directions, free of the spring. The coefficients of static and kinetic friction between each block and the table are 0.5 and 0.4. The energy stored in the spring was 67 J. Assume that all the spring’s stored energy is transferred to the blocks and that this happens over a negligible time and distance.

a) Draw a free body diagram of your “system”, at three instants of time. Be clear about what your “system” is, and the physical situation for each picture. Label everything. USE ENGLISH NOT JUST EQUATIONS. MAKE SURE I KNOW WHAT YOU ARE DOING. NO NUMBERS ANYWHERE IN YOUR ANSWER.

b) Write three equations for energy conservation. Be clear about which picture each applies to. NO NUMBERS ANYWHERE IN YOUR ANSWER.

c) Write an equation for momentum conservation. Again, be clear. NO NUMBERS ANYWHERE IN YOUR ANSWER.

d) What are the maximum kinetic energies of the two blocks? HERE I WANT A NUMERICAL ANSWER BUT WAIT TILL THE LAST STEP TO PUT IN NUMBERS WITH UNITS.

e) How far does each block move until it stops? HERE I WANT A NUMERICAL ANSWER BUT WAIT TILL THE LAST STEP TO PUT IN NUMBERS WITH UNITS.

Answer 1

b] 1st energy conservation equation:

Elastic Potential energy stored in the spring = sum of kinetic energies of both blocks

(1/2)kx² = (1/2)m_Au_A² + (1/2)m_Bu_B²

2nd energy conservation equation for A:

Final kinetic energy of A = initial kinetic energy - work done by friction

(1/2)m_Av_A² = (1/2)m_Au_A² - u_km_AgL

3rd energy conservation equation for B:

(1/2)m_Bv_B² = (1/2)m_Bu_B² - u'_km_BgL'

c] Initial momentum of the system = 0 kgm/s

Final momentum of the system = m_Au_A + m_Bu_B

so, momentum conservation equation is:

0 = m_Au_A + m_Bu_B

m_Au_A = - m_Bu_B

d] Using the 1st energy conservation equation:

67 = (1/2)m_Au_A² + (1/2)m_Bu_B²

67 = (1/2)(2.5)u_A² + (1/2)(1.3)[-(2.5/1.3)u_A]²

67 = 1.25u_A² + 2.4u_A²

=> u_A = 4.28 m/s

this is the maximum velocity of A

therefore, u_B = - 8.23 m/s

this is the maximum velocity of B

using this find their maximum kinetic energies.

e] Use 2nd energy conservation equation for A with v_A = 0 to obtain L.

Similarly, use 3rd energy conservation equation for B with v_B = 0 to obtain L'.