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Inga [223]
3 years ago
10

A swimmer can swim at a velocity v in still water. She swims upstream a distance d against the current, which has a velocity u.

She then swims back to her starting point. A) how long does it take her to make the round-trip? B) what is her average speed for the trip? C) for what value of u u is her average speed the greatest?
Physics
1 answer:
xxTIMURxx [149]3 years ago
4 0
Upstream speed: v - u
Downstream speed: v + u
Total distance: 2d

A) total time = d / (v - u)  + d / (v + u)

B) Average speed = total distance / total time
V(av) = 2d / [ d / (v -  u) + d / (v + u) ]
V(av) = 2d / [d(v + u + v - u) / (v - u)(v + u) ]
V(av) = (v² - u²) / v

C) If u is 0, her average speed will be the greatest, equal to v
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The wheel having a mass of 100 kg and a radius of gyration about the z axis of kz=300mm, rests on the smooth horizontal plane.a.
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a) 20 rad/s

b) 6 m/s

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b) Force acting on the wheel is 200 N

mass of the wheel is 100 kg

From Newton's second law of motion, F = m × a

Where F is the net force acting on the body

m is mass of the body

a is the acceleration of the body

By substituting the values we get, a = 2 m/s²

As acceleration is constant, we can use the below formula for calculating the final velocity of the object

v = u + a × t

Where v is the final velocity

u is the initial velocity

a is the acceleration

t is the time taken

u = 0 (∵ it starts from rest)

By substituting the values we get

v = 0 + 2 × 3 = 6 m/s

∴ Speed of center of mass after 3 seconds = 6 m/s

a) As the wheel rotates about z-axis, radius of gyration will be the radius of wheel

∴ Radius of the wheel = 300 mm

Torque acting on the wheel about axis of rotation = 300 mm × 200 N =

60 N·m

Torque = (Moment of inertia) × (angular acceleration)

Assuming that the mass of spokes of the wheel to be negligible,

Moment of inertia of the wheel about axis of rotation = 100 × 300² × 10^{-6} = 9 kg·m²

Then,

60 = 9 × (angular acceleration)

∴ angular acceleration ≈ 6·67 rad/s²

As angular acceleration of the wheel is constant, we can use the below formula for calculation of final angular speed

w_{f} = w_{i} + α × t

Where

w_{f} is the final angular velocity

w_{i} is the initial angular velocity

α is the angular acceleration

t is the time taken

w_{i} is 0 (∵ initially it starts from rest)

By substituting the values we get

w_{f} = 6·67 × 3 = 20 rad/s

∴ Angular velocity of the wheel after three seconds = 20 rad/s

3 0
3 years ago
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