Let the angle be Θ (theta)
Let the mass of the crate be m.
a) When the crate just begins to slip. At that moment the net force will be equal to zero and the static friction will be at the maximum vale.
Normal force (N) = mg CosΘ
μ (coefficient of static friction) = 0.29
Static friction = μN = μmg CosΘ
Now, along the ramp, the equation of net force will be:
mg SinΘ - μmg CosΘ = 0
mg SinΘ = μmg CosΘ
tan Θ = μ
tan Θ = 0.29
Θ = 16.17°
b) Let the acceleration be a.
Coefficient of kinetic friction = μ = 0.26
Now, the equation of net force will be:
mg sinΘ - μ mg CosΘ = ma
a = g SinΘ - μg CosΘ
Plugging the values
a = 9.8 × 0.278 - 0.26 × 9.8 × 0.96
a = 2.7244 - 2.44608
a = 0.278 m/s^2
Hence, the acceleration is 0.278 m/s^2
Answer:
kg
Explanation:
easy question to be honest
Where are the factors ... to this question
Answer:
ωf = 0.16 rad/s
Explanation:
Moment of inertia of the child = mr² = 20(1.6²) = 51.2 kg•m²
Moment of Inertia of the MGR = ½mr² = ½(180)1.6² = 230.4 kg•m²
(ASSUMING it is a uniform disk)
Initial angular momentum of the child = Iω = I(v/r) = 51.2(1.4/1.6) = 44.8 kg•m²/s
Conservation of angular momentum
44.8 = (51.2 + 230.4)ωf
ωf = 0.15909090...
Answer:
Yes, if the system has friction, the final result is affected by the loss of energy.
Explanation:
The result that you are showing is the conservation of mechanical energy between two points in the upper one, the energy is only potential and the lower one is only kinetic.
In the case of some type of friction, the change in energy between the same points is equal to the work of the friction forces
= ΔEm
=
-Em₀
As we can see now there is another quantity and for which the final energy is lower and therefore the final speed would be less than what you found in the case without friction.
=
+ Em₀
Remember that the work of the rubbing force is negative, let's write the work of the rubbing force explicitly, to make it clearer
½ m v² = -fr d + mgh
v = √(-fr d 2/m + 2 gh)
v = √ (2gh - 2fr d/m)
Now it is clear that there is a decrease in the final body speed.
Consequently, if the system has friction, the final result is affected by the loss of energy.