Respuesta :
Answer:
F2 = 834 N
Explanation:
We are given the following for the bicycle;
Diameter; d1 = 63 cm = 0.63 m
Mass; m = 1.75 kg
Resistive force; F1 = 121 N
For the sprocket, we are given;
Diameter; d2 = 8.96 cm = 0.0896 m
Radius; r2 = 0.0896/2 = 0.0448 m
Radial acceleration; α = 4.4 rad/s²
Now moment of inertia of the wheel which is assumed to be a hoop is given by; I = m(r1)²
Where r1 = (d1)/2 = 0.63/2
r1 = 0.315 m
Thus, I = 1.75 × 0.315²
I = 0.1736 Kg.m²
The torque is given by the relation;
I•α = F1•r1 - F2•r2
Where F2 is the force that must be applied by the chain to give the wheel an acceleration of 4.40 rad/s².
Thus;
0.1736 × 4.4 = (121 × 0.315) - (0.0448F2)
>> 0.76384 = 38.115 - (0.0448F2)
>> 0.0448F2 = 38.115 - 0.76384
>> F2 = (38.115 - 0.76384)/0.0448
>> F2 = 833.73 N
Approximately; F2 = 834 N
The force applied by a chain passing over a 8.96-cm-diameter sprocket in order to give the wheel an acceleration of 4.40 rad/s2 is F2 = 834 N
What is force?
Force is an external agent applied on any object to displace it from its position. Force is a vector quantity, so with magnitude it also requires direction. Direction is necessary to examine the effect of the force and to find the equilibrium of the force.
We are given the following for the bicycle;
Diameter; d1 = 63 cm = 0.63 m
Mass; m = 1.75 kg
Resistive force; F1 = 121 N
For the sprocket, we are given;
Diameter; d2 = 8.96 cm = 0.0896 m
Radius; r2 = 0.0896/2 = 0.0448 m
Radial acceleration; α = 4.4 rad/s²
Now the moment of inertia of the wheel which is assumed to be a hoop is given by;
[tex]I=mr_1^2[/tex]
Where
r1 = 0.315 m
I = 1.75 × 0.315²
I = 0.1736 Kg.m²
The torque is given by the relation;
[tex]I\alpha=F_1\times r_1-F_2\times r_2[/tex]
Where [tex]F_2[/tex] is the force that must be applied by the chain to give the wheel an acceleration of 4.40 rad/s².
0.1736 × 4.4 = (121 × 0.315) - (0.0448[tex]F_2[/tex])
0.76384 = 38.115 - (0.0448[tex]F_2[/tex])
[tex]F_2= \dfrac{38.115-0.7638}{0.0448}[/tex]
[tex]F_2=833.73\ N[/tex]
Approximately; F2 = 834 N
Thus the force applied by a chain passing over a 8.96-cm-diameter sprocket in order to give the wheel an acceleration of 4.40 rad/s2 is F2 = 834 N
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