Problem1 h\' A small block of mass M is projected upward with a speed v. A massl

Question

Problem1 h' A small block of mass M is projected upward with a speed v. A massless spring of stiffne hangs from the ceiling Its bottom is a height h 'above the ground. Let M- 3.5 kg. a) 2800 1, b) 1840J, c)I125J d) 625 J a) 27.5 m/s, b) 20.7 m/s, c) 12.4 m/s, d) 33.6 m/s a) 2.20 m, b) 1.15m, c) 4.28 m,d) 3.22 m a) 22.7 m, b) 19.4 m, c)21.6 m, ) 20.5 m -40 m/s, k 200 N/m and h- 24m. A) Find the total mechanical energy in the system when the block hits the spring B) Find the speed of the block when the block hits the spring C) The block sticks to the spring. Find the maximum compression of the spring, s. D) When the mass reaches its lowest point find the height above the ground, h" E) If it didn't stick to the spring find the speed v" of the mass just before it lands. a) 35 m/s, b) 25 m/s, c) 40 m/s, d 30 m/s

Explanation / Answer

A) total mechanical energy will be equal to the energy of block only which will be equal to it kinetic energy in the beginning, so energy E = 1/2Mv2 = 1/2 x 3.5 x 402 = 2800J

option (a)

B) potential energy at 24 m is U = mgh = 3.5 x 9.8 x 24 = 823.2J

hence kinetic energy remaining = 2800 - 823.2 = 1976.8J

hence 1/2Mv'2 = 1976.8, solving it we get, speed when block touches the spring = 33.6 m/s

option (d)

C) suppose x is the maximum compression,

elastic potential energy in spring + gravitational potential energy stored in block upto height x = kinetic energy of block at 24m

1/2kx2 + mgx = 1976.8

solving it by quadratic equation, we get x = 4.28m

Option (c)

D) now energy stored is 1976.8J, when it will come down, it will be stored in elastic potential energy

1/2kx2 - mgx = 1976.8, solving it x = 4.62m, hence height above the ground is 24 - 4.44 = 19.4m

E) same speed 40m/s

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