The steering wheel of a car has a radius of 0.17 m, and the steering wheel of a truck has a radius of 0.24 m. The same force is applied in the same direction to each steering wheel. What is the ratio of the torque produced by this force in the truck to the torque produced in the car?
Vik/ram -- please use the same name for your posts.
Homework Posting Tips
Please show your work. Tutors will not do your homework for you. Please show your work for any question that you are posting.
The torque produced by a force applied at a distance from the center of rotation can be calculated using the formula:
Torque = Force x Distance
Let's assume the force applied is F.
For the car, the torque produced is given by:
Torque_car = F x radius_car
For the truck, the torque produced is given by:
Torque_truck = F x radius_truck
To find the ratio of the torque produced in the truck to the torque produced in the car, we can divide Torque_truck by Torque_car:
Ratio = Torque_truck / Torque_car
Ratio = (F x radius_truck) / (F x radius_car)
The force (F) cancels out from the equation, so we are left with:
Ratio = radius_truck / radius_car
Substituting the given values:
Ratio = 0.24 m / 0.17 m
Ratio = 1.41
Therefore, the ratio of the torque produced by the force in the truck to the torque produced in the car is approximately 1.41.
To find the ratio of the torque produced by the force in the truck to the torque produced in the car, we need to calculate the torque for each object and then divide them.
Torque (τ) is given by the equation:
τ = r * F * sin(θ)
Where:
- τ is the torque
- r is the radius of the steering wheel
- F is the applied force
- θ is the angle between the force and the lever arm (which in this case is the radius)
Assuming the force and the angle are the same for both the car and the truck, we can ignore them and focus only on the radii.
For the car:
τ_car = r_car * F
For the truck:
τ_truck = r_truck * F
To find the ratio, we divide the torque of the truck by the torque of the car:
Ratio = τ_truck / τ_car
= (r_truck * F) / (r_car * F)
= r_truck / r_car
Substituting the given values:
Ratio = 0.24 m / 0.17 m
≈ 1.41
Therefore, the ratio of the torque produced by the force in the truck to the torque produced in the car is approximately 1.41.