Answer:
ωi = 15.4 rev/sec
Explanation:
Since the movement of the fan is rotating, we are thus dealing with Rotational motion. In rotational motion, for angular speed to take place also means angular acceleration is also occurring.
angular acceleration = α = (change in speed)/(change in time)
angular acceleration = α = Δw/Δt = (ω - ωi) /(t- t₀) ..........(equation 1)
α = (ω -ωi) /(t- 0)
α = (ω-ωi) /t
ωi = ω - αt ......................................(equation 2)
where ωi is the initial angular speed.
We replace the values for ω, t and α
ωi = 105 rad/sec - ( 4.4 rad/sec² )(1.85s) = 96.86 rad/s = 15.415747788 rev/sec
This statement is true. The greater the mass is in an object, it is indeed the higher resistance to a change in movement the object will have. That only mean that the mass of an object and its resistance to change of movement is directly proportional.
The springs stored energy is transferred to the cube as kinetic energy and then by the slop the KE is converted to height energy.
<span>0.5 . k . x^2 = 0.5 . m . v^2 = m . g . ∆h </span>
<span>0.5 . 50 . (0.1^2) = 0.05 . 9.8 . ∆h </span>
<span>∆h = 0.51 m = 51 cm </span>
<span>This is the height gained </span>
<span>Distance along the slope = ∆h / sin 60 = 0.589 = 59 cm </span>
<span>In the second case, the stored spring energy is converted into height energy AND frictional heat energy. </span>
<span>The height energy is m . g . d sin 60 where d is the distance the cube moves along the slope. </span>
<span>The Frictional energy converted is F . d </span>
<span>F ( the frictional force ) = µ . N </span>
<span>N ( the reaction to the component of the gravity force perpendicular to the surface of the slope ) = m . g . cos60 </span>
<span>Total energy converted </span>
<span>0.5 . k . x^2 = (m . g . dsin60) + (µ . m . g . cos60 . d ) </span>
<span>Solve for d </span>
<span>d = 0.528 = 53 cm</span>
Answer:
Explanation:
Momentum conservation
Kinetic energy conservation
Solve the system
