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Answer:
a) 20 rad/s
b) 6 m/s
Explanation:
b) Force acting on the wheel is 200 N
mass of the wheel is 100 kg
From Newton's second law of motion, F = m × a
Where F is the net force acting on the body
m is mass of the body
a is the acceleration of the body
By substituting the values we get, a = 2 m/s²
As acceleration is constant, we can use the below formula for calculating the final velocity of the object
v = u + a × t
Where v is the final velocity
u is the initial velocity
a is the acceleration
t is the time taken
u = 0 (∵ it starts from rest)
By substituting the values we get
v = 0 + 2 × 3 = 6 m/s
∴ Speed of center of mass after 3 seconds = 6 m/s
a) As the wheel rotates about z-axis, radius of gyration will be the radius of wheel
∴ Radius of the wheel = 300 mm
Torque acting on the wheel about axis of rotation = 300 mm × 200 N =
60 N·m
Torque = (Moment of inertia) × (angular acceleration)
Assuming that the mass of spokes of the wheel to be negligible,
Moment of inertia of the wheel about axis of rotation = 100 × 300² × = 9 kg·m²
Then,
60 = 9 × (angular acceleration)
∴ angular acceleration ≈ 6·67 rad/s²
As angular acceleration of the wheel is constant, we can use the below formula for calculation of final angular speed
=
+ α × t
Where
is the final angular velocity
is the initial angular velocity
α is the angular acceleration
t is the time taken
is 0 (∵ initially it starts from rest)
By substituting the values we get
= 6·67 × 3 = 20 rad/s
∴ Angular velocity of the wheel after three seconds = 20 rad/s
Answer:
95.9°
Explanation:
The diagram illustrating the action of the two forces on the object is given in the attached photo.
Using sine rule a/SineA = b/SineB, we can obtain the value of B° as shown in the attached photo as follow:
a/SineA = b/SineB,
83/Sine52 = 56/SineB
Cross multiply to express in linear form
83 x SineB = 56 x Sine52
Divide both side by 83
SineB = (56 x Sine52)/83
SineB = 0.5317
B = Sine^-1(0.5317)
B = 32.1°
Now, we can obtain the angle θ, between the two forces as shown in the attached photo as follow:
52° + B° + θ = 180° ( sum of angles in a triangle)
52° + 32.1° + θ = 180°
Collect like terms
θ = 180° - 52° - 32.1°
θ = 95.9°
Therefore, the angle between the two forces is 95.9°
