Answer:
0.084
Step-by-step explanation:
from the question we are given the following:
mass of pellet (M₁) = 1.2 g = 0.0012 kg
mass of cheese (Mc) = 120 g = 0.12 kg
total mass (M₂) = 0.1212 kg
distance (s) = 25 cm = 0.25 m
initial velocity (U₁) = 65 m/s
final velocity (U₂) =?
coefficient of friction = ?
To get the coefficient of friction we have to apply the formula below:
frictional force = coefficient of friction x total mass x acceleration due to gravity
where
frictional force = mass x acceleration (a)
so our equation becomes
mass x acceleration (a) = coefficient of friction x mass x acceleration due to gravity
and finally we have
coefficient of friction = \frac{acceleration}{acceleration due to gravity}
so we need to find the acceleration of the pellet and cheese
from the conservation of momentum we can say
M₁ x U₁ = M₂ x U₂
0.0012 x 65 = 0.1212 x U₂
U₂ = 0.64 m/s
from the equation of motion
U₂^{2} = U₁^{2} + 2as
U₂ = final velocity = 0 since the pellet and cheese come to a stop
we now have
-U₁^{2} = 2as
(-0.64)^{2} = 2 X a X 0.25
a = 0.82 m/s^{2}
now that we have a we can substitute it into coefficient of friction = \frac{acceleration}{acceleration due to gravity}
coefficient of friction = \frac{0.82}{9.8} = 0.084