a body takes time t to reach the bottom of an inclined plane of angle theta with the horizontal.if the plane is made rough it takes time 2t. the cofficient of static friction is
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Let the length of the incline be = L. The body slides down (not roll down).
When there is no friction:
a = g sinФ . time = t. So t² = 2 L /(g sinФ) ---(1)
When there is friction (coefficient of kinetic friction = μ):
f = μ N = μ m g CosΦ
a = g SinΦ - f/m = g (SinΦ - μ CosΦ)
=> (2 t)² = 2 L / [ g (SinФ - μ CosΦ) --- (2)
(2) / (1) => SinΦ = 4 (Sin Φ - μ CosΦ)
μ = 3/4 * TanΦ
When there is no friction:
a = g sinФ . time = t. So t² = 2 L /(g sinФ) ---(1)
When there is friction (coefficient of kinetic friction = μ):
f = μ N = μ m g CosΦ
a = g SinΦ - f/m = g (SinΦ - μ CosΦ)
=> (2 t)² = 2 L / [ g (SinФ - μ CosΦ) --- (2)
(2) / (1) => SinΦ = 4 (Sin Φ - μ CosΦ)
μ = 3/4 * TanΦ
kvnmurty:
:-)
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