Answer:
2.24kJ
Explanation:
Kinetic energy is the energy that a object possesses due to its motion.
Let kinetic Energy (KE),
Here both the Bicycle and the girl is travelling at the given speed , therefore we have to consider the total mass
according ti the definition ,
Answer:
0.339 kgm²
Explanation:
We know the period of this pendulum, T = 2π√(I/mgh) where I = moment of inertia of the object about the pivot axis, m = mass of object = 2.15 kg, g = acceleration due to gravity = 9.8 m/s² and h = distance of center of mass of object from pivot point = 0.163 m.
Since T = 2π√(I/mgh), making I subject of the formula, we have
I = mghT²/4π²
Now since it takes 241 s to complete 113 cycles, then it takes 241 s/113 cycles to complete one cycle.
So, T = 241 s/113 = 2.133 s
So, Substituting the values of the variables into I, we have
I = mghT²/4π²
I = 2.15 kg × 9.8 m/s² × 0.163 m × (2.133 s)²/4π²
I = 15.63/4π² kgm²
I = 0.396 kgm²
Now from the parallel axis theorem, I = I' + mh² where I' = moment of inertia of object with respect to its center of mass about an axis parallel to the pivot axis
I' = I - mh²
I' = 0.396 kgm² - 2.15 kg × (0.163 m)²
I' = 0.396 kgm² - 0.057 kgm²
I' = 0.339 kgm²
since child is moving along with the wagon and we need to find the acceleration of child inside that wagon then in this case the system of interest must be child + wagon
System of interest will be the system that is used to find the force or acceleration using Newton's law
Here we have to assume that system on which if we will calculate the forces then the net value of force on that system will help to calculate the unknown quantities
So here our system will be boy + wagon
Answer:
d = 57.7 m
Explanation:
For this exercise we will use energy work theorems
W = ΔEm
Let's calculate the work of the rubbing force on the ramp
W = -fr d
The negative sign is because the force of friction opposes the movement
Newton's second law in the axis perpendicular to the ramp gives
N- W cos 21.8 = 0
N = mg cos 21.8
The equation for the force of friction is
fr = μN
fr = μ mg cos 21.8
Let's replace
W = - μ mg d cos 21.8
Let's look for energy in two points
Initial just before entering the ramp
Emo = K = ½ m v²
End the highest point where the body stops
= U = mg y
We use trigonometry to find the height (y)
sin 21.8 = y / d
y = d sin 21.8
= m g d sin 21.8
Let's replace
W = ΔEm = - Em₀
- μ mg d cos 21.8 = mgd sin21.8 - ½ m v²
m g d (sin21.8 + μ cos 21.8) = ½ m v²
d = v² / (2 (sin21.8 + μ cos21.8))
d = 7.10² / (2 (sin21.8 + 0.0704 cos 21.8))
d = 50.41 /0.87345
d = 57.7 m
Answer:
X component= 46 N
Y component= 80 N
Magnitude =( 46 ^2 + 80^2 )^0.5 = 92.3 N
