The steering wheel of a car has a radius of 0.18 m, while the steering wheel of a truck has a radius of 0.25 m. The same force is applied in the same direction to each. What is the ratio of the torque produced by this force in the truck to the torque produced in the car
(Torque,truck)/(Truck,car)
= F,truck*R,truck/(F,car*R,truck)
= 0.25/0.18 = ___
since the forces are the same.
Ah, the age-old rivalry between the car and the truck. When it comes to torque, let's see what these vehicles bring to the table.
The torque produced by a force applied at a certain radius is given by the formula T = Fr, where T is the torque, F is the force, and r is the radius.
For the car, let's call its torque Tc and the applied force F. Since the radius of the steering wheel is 0.18 m, the torque produced by the force applied to the car's steering wheel is Tc = F * 0.18.
For the truck, its torque will be denoted as Tt, and the applied force is the same as the car, F. With a steering wheel radius of 0.25 m, the torque produced in the truck is Tt = F * 0.25.
Now, to calculate the ratio of the torque produced by the truck to the torque produced by the car, we divide Tt by Tc:
Tt / Tc = (F * 0.25) / (F * 0.18)
Thankfully, the applied force cancels out, leaving us with:
Tt / Tc = 0.25 / 0.18
And simplifying this ratio, we get:
Tt / Tc ≈ 1.39
So, the ratio of the torque produced by the force in the truck to the torque produced in the car is approximately 1.39. However, remember that actual driving skills and humor level may vary!
To find the ratio of the torque produced by the force in the truck to the torque produced in the car, we can use the formula for torque:
Torque = Force * Radius
Let's assume the force applied to both the car and the truck is F.
For the car, the torque produced is given by:
Torque_car = F * Radius_car
For the truck, the torque produced is given by:
Torque_truck = F * Radius_truck
Now, let's substitute the given values:
Radius_car = 0.18 m
Radius_truck = 0.25 m
Therefore, the ratio of the torque produced by the force in the truck to the torque produced in the car can be calculated as:
Ratio = Torque_truck / Torque_car
= (F * Radius_truck) / (F * Radius_car)
= Radius_truck / Radius_car
Plugging in the given values, we get:
Ratio = 0.25 m / 0.18 m
≈ 1.39
So, the ratio of the torque produced by the force in the truck to the torque produced in the car is approximately 1.39.
To find the ratio of the torque produced by the force in the truck to the torque produced in the car, we first need to understand the concept of torque.
Torque is the twisting force that causes an object to rotate around an axis. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation to the point of force application, which is the perpendicular distance, also known as the lever arm.
In this case, the steering wheel of the car and the truck are being rotated by the same force applied in the same direction. The torque produced is directly proportional to the force and the lever arm.
The torque equation is given by:
Torque = force × lever arm
The lever arm is the radius of the steering wheel since the force is applied at the edge of the wheel perpendicular to the axis of rotation.
For the car:
Torque_car = force × radius_car
For the truck:
Torque_truck = force × radius_truck
To find the ratio of torque between the truck and the car, we divide the torque of the truck by the torque of the car:
Ratio = Torque_truck / Torque_car
Substituting the torque equations we derived earlier:
Ratio = (force × radius_truck) / (force × radius_car)
The force cancels out as it is the same for both the car and the truck:
Ratio = radius_truck / radius_car
Now, we can substitute the given values of the radii:
Ratio = 0.25 m / 0.18 m
Simplifying:
Ratio = 1.39
Therefore, the ratio of the torque produced by the force in the truck to the torque produced in the car is approximately 1.39.