A motorist is trying to loosen a stubborn lugnut by standing on the end of a wrench. The wrench is inclined 33.8 degrees above the horizontal and the distance from the center of the nut to the end of the wrench is 0.60 m. Assuming the motorist does not bounce up and down on the wrench, how much torque can a 90 kg motorist create on the lugnut by standing on the end of the wrench?
To calculate the torque, we can use the equation:
Torque = Force × Distance × sin(θ)
Where:
- Torque is the rotational force (measured in Newton-meters or Nm)
- Force is the perpendicular force applied (measured in Newtons or N)
- Distance is the distance between the point of rotation and the force applied (measured in meters or m)
- θ (theta) is the angle between the force and the lever arm (measured in degrees)
In this case, the motorist's weight will be the force applied, and the distance will be the length of the lever arm (0.60 m).
First, we need to calculate the perpendicular force applied by the motorist, which is the weight:
Force = mass × gravity
The mass of the motorist is given as 90 kg, and the acceleration due to gravity is approximately 9.8 m/s².
Force = 90 kg × 9.8 m/s² = 882 N
Now, we can calculate the torque:
Torque = Force × Distance × sin(θ)
Since the wrench is inclined at an angle of 33.8 degrees above the horizontal, we need to convert it to radians:
θ (in radians) = θ (in degrees) × π/180
θ = 33.8 degrees × π/180 ≈ 0.590 radians
Torque = 882 N × 0.60 m × sin(0.590)
Using a calculator, we find:
Torque ≈ 309.84 Nm
Therefore, the motorist can create approximately 309.84 Nm of torque on the lugnut by standing on the end of the wrench.