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Firdavs [7]
3 years ago
5

A wheel of mass 4kg is pulled up a plane inclined at 30° to the horizontal by a force of 45N applied to the axle and parallel to

the plane. If the wheel has a radius of 0.5m and the moment of inertia 0.5kgm?, calculate the translational velocity acquired after travelling 12m up the plane, assuming the wheel is initially at rest (6 marks)​
Physics
1 answer:
Len [333]3 years ago
5 0

Answer:

v = 10 m/s

Explanation:

Let's assume the wheel does not slip as it accelerates.

Energy theory is more straightforward than kinematics in my opinion.

Work done on the wheel

W = Fd = 45(12) = 540 J

Some is converted to potential energy

PE = mgh = 4(9.8)12sin30 = 235.2 J

As there is no friction mentioned, the remainder is kinetic energy

KE = 540 - 235.2 = 304.8 J

KE = ½mv² + ½Iω²

ω = v/R

KE = ½mv² + ½I(v/R)² = ½(m + I/R²)v²

v = √(2KE / (m + I/R²))

v = √(2(304.8) / (4 + 0.5/0.5²)) = √101.6

v = 10.07968...

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A woman pushes a 27 kg lawnmower at a steady speed. She exerts a 120 N force in a direction 35◦ below the horizontal. The accele
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The vertical force exerted on the lawn is 68.8 N downward

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The vertical force exerted by the lawnmower on the lawn is equal to the vertical component of the force applied, therefore:

F_y = F sin \theta

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In this problem:

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Learn more about vector components and forces here:

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A kayaker moves 26 meters southward, then 18 meters
Svetllana [295]

Total distance: 56 meters. Magnitude and direction of displacement: 20 meters South.

Explanation:

The term distance refers to space between one point and other, or the total space a body or object covered while moving. In the case presented, this can be calculated by adding the partial distances given. This means the total distance is  56 meters as 26 meters + 18 meters + 12 meters = 56 meters.

On the other hand, displacement considers the distance from the initial position to the final position, and the direction of movement. This means partial distances should not be added but each movement should be considered according to the direction. The process is shown below:

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This is seen when the base number is still at rest and the force of gravity on the Earth acting on her.

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