So here's the question:
The Cleveland City Cable Railway had a 14-foot-diameter pulley to drive the cable. In order to keep the cable cars moving at a linear velocity of 16 miles per hours, how fast would the pulley need to turn (in revolutions per minute, 1mi = 5280 ft)?
Im pretty sure that Im just having trouble with the unit conversions. The correct answer should be 32.0 rpm. This is what I've been doing:
r=7 ft v=16mph
w=v/r
16mph x 60mins/1hr = 960 miles/min
7ft x 1mile/5280ft = 0.00322 miles
960miles/min divided by 0.001326 miles = 724114 radians/min
724114 radians/min x 1rev/2pi radians = 1137436.06 rpm
so as you can see im way off, and I have no idea where I went wrong.
The Cleveland City Cable Railway had a 14-foot-diameter pulley to drive the cable. In order to keep the cable cars moving at a linear velocity of 16 miles per hours, how fast would the pulley need to turn (in revolutions per minute, 1mi = 5280 ft)?
Im pretty sure that Im just having trouble with the unit conversions. The correct answer should be 32.0 rpm. This is what I've been doing:
r=7 ft v=16mph
w=v/r
16mph x 60mins/1hr = 960 miles/min
7ft x 1mile/5280ft = 0.00322 miles
960miles/min divided by 0.001326 miles = 724114 radians/min
724114 radians/min x 1rev/2pi radians = 1137436.06 rpm
so as you can see im way off, and I have no idea where I went wrong.