A constant retarding torque of 12 N*m stops a rolling 0.80 m diameter wheel in a distance of 15 m. How much work does the torque do?
work=force*distance=12*.4*15
To find the work done by the torque, you need to use the formula:
Work = Torque * Angle
However, we don't have the angle. Instead, we have the distance covered by the wheel. To find the angle, we can calculate the number of rotations the wheel has made.
The circumference of the wheel is given by:
Circumference = π * Diameter
Circumference = π * 0.80 m
Circumference = 2.50 m
To find the number of rotations, we divide the distance covered by the circumference of the wheel:
Number of rotations = Distance / Circumference
Number of rotations = 15 m / 2.50 m
Number of rotations = 6 rotations
Since the distance is equivalent to 6 rotations, the angle would be:
Angle = 2π * Number of rotations
Angle = 2π * 6
Angle = 12π radians
Now we can calculate the work done by the torque:
Work = Torque * Angle
Work = 12 N·m * 12π radians
Work = 144π N·m or approximately 452.39 N·m
Therefore, the work done by the torque is approximately 452.39 N·m.
To calculate the work done by the retarding torque, we need to know the formula for work and the relationship between torque and work.
The work done by a force is given by the formula:
Work = Force × Displacement × cos(θ)
In this case, the force we are interested in is the retarding torque, and the displacement is the distance over which the wheel stops.
However, we need to convert the torque into an equivalent force acting at the point where the force is applied.
The torque can be converted into a force by using the formula:
Torque = Force × Radius
We know the diameter of the wheel (0.80 m), so the radius can be calculated as half of the diameter:
Radius = Diameter/2 = 0.80 m/2 = 0.40 m
We have the torque value (12 N*m) and the radius (0.40 m), so we can rearrange the formula to solve for force:
Force = Torque/Radius = 12 N*m/0.40 m = 30 N
Now that we have the force and the displacement, we can calculate the work done by substituting the values into the work formula:
Work = Force × Displacement × cos(θ)
In this case, the angle (θ) is not mentioned, so we can assume it to be 0 degrees (cos(0) = 1). Thus, the formula becomes:
Work = Force × Displacement
Substituting the values, we get:
Work = 30 N × 15 m = 450 N*m = 450 Joules
Therefore, the work done by the retarding torque is 450 Joules.