PHYSICS 281 General Physics I Exam 2 Practice Problems 1. A block of mass m is s
ID: 1781968 • Letter: P
Question
PHYSICS 281 General Physics I Exam 2 Practice Problems 1. A block of mass m is suspended at a height h above a massless platform placed on a massless spring of force constant k. The block is released from rest and falls onto the platform, compress- ing the spring. (a) Find the maximum distance the block falls below the spring's neu (with the block on the platform) equilibrium position. (b) Compute block's maximmm speed. 2. A erate travels at 10.0m/s on a smooth horizontal surface before mocting a ramp inclined 36.87 above the horizontal. It slides 5.00m along the rough ramp before momentarily coming to rest. (a) What is the cocflicieut of friction between the block ajd the ramp. (b) What speed does the block acquire on its descent upon reaching the bottom of the incline? Use g 10.0m/s2
Explanation / Answer
1. (a) Applying energy conservation,
m g h + 0 = k d^2 /2 - m g d
(k/2) d^2 - (m g ) d - m g h = 0
d = m g + sqrt[ m ^2 g^2 + 2 m g h k] / k
d = m g + m g sqrt[ 1 + 2 h k /mg ]
equilibrium position, Fnet = m g - kx = 0
x = m g / k
d' = d - x = ( m g / k) sqrt[1 + 2h k / m g ]
(b) maximum speed will be at equilibrium posint,
m g h + 0 = - m g ( mg /k) + k (m g / k)^2 /2 + m v^2 /2
m v^2 / 2 = m g h + m^2 g^2 / k - m^2 g^2 /2 k
v = sqrt[ 2 g h + mg^2 / k]
v = sqrt[ 2 g h (1 + m g /2 hk)]
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