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Answer:
τ =9.41 * 10⁻⁴ N*m
Explanation:
Kinematics of the CD
The CD rotates with constant angular acceleration and its angular acceleration is calculated as follows:
Formula (1)
Where:
α : angular acceleration. (rad/s²)
ωf: final angular velocity (rad/s)
ωi : initial angular velocity (rad/s)
t = time interval (s)
Data
ωf= 20 rad/s
ωi =0
t = 0.65 s.
Calculating of the angular acceleration of the CD
We replace data in the formula (1)
α = 30.77 rad/s²
Newton's second law in rotation:
F = ma has the equivalent for rotation:
τ = I * α Formula (2)
where:
τ : It is the net torque applied to the body. (N*m)
I : it is the moment of inertia of the body with respect to the axis of rotation (kg*m²)
α : It is angular acceleration. (rad/s²)
Calculating of the moment of inertia of the CD
The moment of inertia of a disk with respect to an axis perpendicular to the plane and passing through its center is calculated by the following formula:
I = (1/2) M*R² Formula (3)
Data
M= 17 g = 17/1000 kg = 0.017 kg : CD mass
R= 6.0 cm= 6/100 m = 0.06 m : CD radius
We replace data in the formula (3) :
I = (1/2) ( 0.017 kg)*(0.06 m)² = 3.06 * 10⁻⁵ kg*m²
Calculating of the net torque acting on the CD
Data
α = 30.77 rad/s²
I = 3.06 * 10⁻⁵ kg*m²
We replace data in the formula (2) :
τ = I * α
τ =( 3.06 * 10⁻⁵ kg*m²) * (30.77 rad/s²)
τ =9.41 * 10⁻⁴ N*m
Answer: F = 113.4.N
Explanation: Net Force is the total forces acting in an object. In this case, there are two forces acting on the charge: one due to magnetic field (Fm) and another due to electric field (Fe). So, net force is
F = Fe + Fm
Force due to electric field
To determine this force:
Fe = q.E, where q is the charge and E is electric field.
Calculating:
Fe = q.E
Fe = 1.8..4.6.
Fe = 8.28.N
Force due to magnetic field: It can only happens when the charge is in movement, so
Fm = q.(v×B), where v represents velocity and B is magnetic field
The cross product indicates that force is perpendicular to the velocity and the field.
Calculating:
Fm = q.v.B.senθ
As θ=90°,
Fm = q.v.B
Fm = 1.8..3.1.
.1.2.
Fm = 6.696.N
F, Fm and Fe make a triangle. So, using Pythagorean theorem:
F =
F =
F = 113.4.N
The net force acting on the charge is F = 113.4.N
Answer:
1.V= 640.48 m/s :total velocity in t= 5s
2. Y= 5.79m : vertical distance above the height of release (in meters) where the ball will hit a wall 13.0 m away
3. v =25m/s
4. s= (-1.5t³+26t ) m
Explanation:
1. Parabolic movement in the x-y plane , t=5s
V₀=638.6 m/s=Vx :Constant velocity in x
Vy=V₀y +gt= 0+9.8*5 = 49 m/s : variable velocity in y
V= 640.48 m/s : total velocity in t= 5s
2.
x=v₀x*t
13=v₀x*t
13=17.49*t
t=13/17.49=0.743s : time for 13.0 m away
th=v₀y/g=11.44/9.8= 1,17s :time for maximum height
at t=0.743 sthe ball is going up ,then g is negative
y=v₀y*t - 1/2 *g¨*t²
y=11.44*0.743 -1/2*9.8*0.743²
y= 5.79m : vertical distance above the height of release (in meters) where the ball will hit a wall 13.0 m away
3. s = (1t3 + -5t2 + 3) m
v=3t²-10t=3*25-50=75-50=25m/s
at t=0, s=3 m
at t=5s s=5³-5*5²+3
4. a = (-9t) m/s2
a=dv/dt=-9t
dv=-9tdt
v=∫ -9tdt
v=-9t²/2 + C1 equation (1)
in t=0 , v₀=26m/s ,in the equation (1) C1= 26
v=-9t²/2 + 26=ds/dt
ds=( -9t²/2 + 26)dt
s= ∫( -9t²/2 + 26)dt
s= -9t³/6+26t+C2 Equation 2
t = 0, s = 0 , C2=0
s= (-9t³/6+26t ) m
s= (-1.5t³+26t ) m