A 97.1 kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.63 r
1 answer:
Answer:
the final angular velocity of the platform with its load is 1.0356 rad/s
Explanation:
Given that;
mass of circular platform m = 97.1 kg
Initial angular velocity of platform ω₀ = 1.63 rad/s
mass of banana = 8.97 kg
at distance r = 4/5 { radius of platform }
mass of monkey = 22.1 kg
at edge = R
R = 1.73 m
now since there is No external Torque
Angular momentum will be conserved, so;
mR²/2 × ω₀ = [ mR²/2 + (
R)² +
R² ]w
m/2 × ω₀ = [ m/2 + (
)² +
]w
we substitute
w = 97.1/2 × 1.63 / ( 97.1/2 + 8.97(16/25) + 22.1
w = 48.55 × [ 1.63 / ( 48.55 + 5.7408 + 22.1 )
w = 48.55 × [ 1.63 / ( 76.3908 ) ]
w = 48.55 × 0.02133
w = 1.0356 rad/s
Therefore; the final angular velocity of the platform with its load is 1.0356 rad/s
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(a) 4.0 s
The acceleration of the car is given by
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u is the initial velocity
t is the time interval
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v = 0 (the final speed is zero since the car comes to a stop)
u = 20 m/s is the initial velocity
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(b) 40 m
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where
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u = 20 m/s is the initial velocity
a = -5.0 m/s^2 is the acceleration of the car
d is the stopping distance
Solving the equation for d, we find
(c)
The deceleration is given by the problem, and its value is .
(d) 5000 N
The net force applied on the car is given by
where
m is the mass of the car
a is the magnitude of the acceleration
For this car, we have
m = 1000 kg is the mass
is the magnitude of the acceleration
Solving the formula, we find
(e)
The work done by the force applied by the car is
where
F is the force applied
d is the total distance covered
Here we have
F = 5000 N
d = 40 m (stopping distance)
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(f) The kinetic energy is converted into thermal energy
Explanation:
when the breaks are applied, the wheels stop rotating. The car slows down, as a result of the frictional forces between the brakes and the tires and between the tires and the road. Due to the presence of these frictional forces, the kinetic energy is converted into thermal energy/heat, until the kinetic energy of the car becomes zero (this occurs when the car comes to a stop, when v = 0).