Answer:
a) 37.8 W
b) 2 Nm
Explanation:
180 g = 0.18 kg
We can also convert 180 revolution per minute to standard angular velocity unit knowing that each revolution is 2π and 1 minute equals to 60 seconds
180 rpm = 180*2π/60 = 18.85 rad/s
We can use the heat specific equation to find the rate of heat exchange of the steel drill and block:
[tex]\dot{E} = mc\Delta \dot{t} = 0.18*420*0.5 = 37.8 J/s[/tex]
Since the entire mechanical work is used up in producing heat, we can conclude that the rate of work is also 37.8 J/s, or 37.8 W
The torque T required to drill can be calculated using the work equation
[tex]E = T\theta[/tex]
[tex]\dot{E} = T\dot{\theta} = T\omega[/tex]
[tex]T = \frac{\dot{E}}{\omega} = \frac{37.8}{18.85} = 2 Nm[/tex]
