In a shuffleboard game, the puck slides a total of 12 m before coming to rest. If the coefficient ofkinetic friction between the
1 answer:
Answer:
puck decelerates due to the kinetic frictional force μk mg
Explanation:
given data
total distance = 12 m
coefficient of kinetic friction = 0.28
solution
we will apply equation of motion that is
v² - u² = 2 × a × s ................1
we know acceleration will be
a =
Then we have
Force = mass × acceleration .................2
m × = -μk mg
The puck decelerates due to the kinetic frictional force μk mg
and frictional force is negative as it opposes the motion.
so we get initial velocity of the puck which is strike.
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1) The car overtakes the truck at a distance of 160 m far from the intersection.
2) The velocity of the car is 40 m/s
Explanation:
1)
The car is travelling with a constant acceleration starting from rest, so its position at time t (measured taking the intersection as the origin) is given by
where
is the acceleration
t is the time
On the other hand, the truck is travelling at a constant velocity, therefore its position at time t is given by
where
v = 20 m/s is the velocity of the truck
t is the time
The car overtakes the truck when the two positions are the same, so when
So, after a time of 8 seconds. Therefore, the distance covered by the car during this time is
So, the car overtakes the truck 160 m far from the intersection.
2)
The motion of the car is a uniformly accelerated motion, so the velocity of the car at time t is given by the suvat equation
where
v is the velocity at time t
u is the initial velocity
a is the acceleration
For the car in this problem, we have:
u = 0 (it starts from rest)
And we know that the car overtakes the truck when
t = 8 s
Substituting into the equation,
Learn more about accelerated motion:
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we know that center of mass is given as
r = (m₁ + m₂
)/(m₁ + m₂)
taking derivative both side relative to "t"
dr/dt = (m₁ d/dt + m₂ d
/dt)/(m₁ + m₂)
v = (m₁ + m₂
)/(m₁ + m₂)
taking derivative again relative to "t" both side
dv/dt = (m₁ d/dt + m₂ d
/dt)/(m₁ + m₂)
a= (m₁ + m₂
)/(m₁ + m₂)