What subject is he......... now? Vietnamese.A. to learnB. learnC. learningD. learned
1 answer:
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Answer:
a) 2.18 m/s^2
b) 9.83 m/s
Explanation:
The flywheel has a moment of inertia
J = m * k^2
Where
J: moment of inertia
k: radius of gyration
In this case:
J = 144 * 0.45^2 = 29.2 kg*m^2
The block is attached through a wire that is wrapped around the wheel. The weight of the block causes a torque.
T = p * r
r is the radius of the wheel.
T = m1 * g * r
T = 18 * 9.81 * 0.6 = 106 N*m
The torque will cause an acceleration on the flywheel:
T = J * γ
γ = T/J
γ = 106/29.2 = 3.63 rad/s^2
SInce the block is attached to the wheel the acceleration of the block is the same as the tangential acceleration at the eddge of the wheel:
at = γ * r
at = 3.63 * 0.6 = 2.81 m/s^2
Now that we know the acceleration of the block we can forget about the flywheel.
The equation for uniformly accelerated movement is:
X(t) = X0 + V0*t + 1/2*a*t^2
We can set a frame of reference that has X0 = 0, V0 = 0 and the X axis points in the direction the block will move. Then:
X(t) = 1/2*a*t^2
Rearranging
t^2 = 2*X(t)/a
It will reach the 1.8 m in 3.6 s.
Now we use the equation for speed under constant acceleration:
V(t) = V0 + a*t
V(3.6) = 2.81 * 3.6 = 9.83 m/s
Answer:
Fa = 57.32 N
Explanation:
given data
mass = 5 kg
acceleration = 4 m/s²
angular velocity ω = 2 rad/s
solution
first we take here moment about point A that is
∑Ma = Iα + ∑Mad ...............1
put here value and we get
so here I = ( ) × m × L² ................2
I = ( ) × 5 × 0.8²
I = 0.267 kg-m²
and
a is = r × α
a = 0.4 α
so now put here value in equation is 1
0 = 0.267 α + m r α (0.4) - m A (0.4)
0 = 0.267 α + 5 (0.4α) (0.4 ) - 5 (4) 0.4
so angular acceleration α = 7.5 rad/s²
so here force acting on x axis will be
∑ F(x) = m a(x) ..............3
a(x) = m a - m rα
put here value
a(x) = 5 × 4 - 5 × 0.4 × 7.5
a(x) = 5 N
and
force acting on y axis will be
∑ F(y) = m a(y) .............. 4
a(y) - mg = mrω²
a(y) - 5 × 9.81 = 5 × 0.4 × 2²
a(y) = 57.1 N
so
total force at A will be
Fa = ...............5
Fa =
Fa = 57.32 N
