Answer:
The speed of the crate is 0.52m/S
Explanation:
Hello!
The first step to solve this problem is to find the necessary torque to raise the load, for this we use the following equation
T=mgr
m=mass=1500kg
t=torque
g=gravity=9.81m/s^2
r=radius=180mm=0.18m
T=(1500)(0.18)(9.81)=2648.7Nm
the second step is to find the torque on the motor side using the reduction ratio for this we divide the torque found by 60
[tex]T=\frac{2648.7}{60} =44.145Nm[/tex]
The third step is to find the turning speed with the torque speed equation and solving the quadratic equation
T=[tex]-4x10^-5 n^2+0.0059n+100=T\\-4x10^-5 n^2+0.0059n+100=44.145[/tex]
The fourth step is to solve the quadratic equation which results in N =1656.6RPM(remember take the positive solution)
the fifth step is to find the speed of rotation at the output of the speed reducer for this we divide by 60
[tex]N=\frac{1656.6}{60} =27.61RPM[/tex]
finally to find the speed of the box remember that it is the product of the speed of rotation in Rad / s by the radius in m
V=[tex]V=(0.18m)27.61\frac{rev}{min} \frac{1min}{60s} \frac{2\pi }{rev} =0.52m/S[/tex]
The speed of the crate is 0.52m/S
