Answer:
The bin moves 0.87 m before it stops.
Explanation:
If we analyze the situation and apply the law of conservation of energy to this case, we get:
Energy Dissipated through Friction = Change in Kinetic Energy of Bin (Loss)
F d = (0.5)(m)(Vi² - Vf²)
where,
F = Frictional Force = μR
but, R = Normal Reaction = Weight of Bin = mg
Therefore, F = μmg
Hence, the equation becomes:
μmg d = (0.5)(m)(Vi² - Vf²)
μg d = (0.5)(Vi² - Vf²)
d = (0.5)(Vi² - Vf²)/μg
where,
Vf = Final Velocity = 0 m/s (Since, bin finally stops)
Vi = Initial Velocity = 1.6 m/s
μ = coefficient of kinetic friction = 0.15
g = 9.8 m/s²
d = distance moved by bin before coming to stop = ?
Therefore,
d = (0.5)[(1.6 m/s)² - (0 m/s)²]/(0.15)(9.8 m/s²)
<u>d = 0.87 m</u>
