THe steering wheel of a car has a diameter of 60cm and turns a shaft 4cm in diameter (a) If a 90nt force is needed to turn the wheel, what torque is exerted on the wheel? (b) What force is applied tangentially to the surface of the shaft?
To calculate the torque exerted on the wheel and the force applied tangentially to the surface of the shaft, we can use the relation:
Torque (τ) = Force (F) × Radius (r)
First, let's calculate the radius of the steering wheel.
(a) Radius of the steering wheel:
The diameter of the steering wheel is given as 60 cm, which means the radius is half of the diameter.
Radius (r) = 60 cm / 2 = 30 cm = 0.3 meters
Next, we can use the torque formula to find the torque exerted on the wheel.
(b) Torque exerted on the wheel:
Force (F) = 90 N (given)
Torque (τ) = Force (F) × Radius (r)
τ = 90 N × 0.3 m
τ = 27 Nm
Therefore, the torque exerted on the steering wheel is 27 Nm.
To find the force applied tangentially to the surface of the shaft, we can use the torque formula with the radius of the shaft.
Radius of the shaft (r) = 4 cm = 0.04 meters
Force (F) = ?
We'll rearrange the torque formula to solve for force:
Torque (τ) = Force (F) × Radius (r)
Force (F) = Torque (τ) / Radius (r)
Force (F) = 27 Nm / 0.04 m
Force (F) = 675 N
Therefore, the force applied tangentially to the surface of the shaft is 675 N.
To find the torque exerted on the wheel and the force applied tangentially to the surface of the shaft, we can use the principles of torque and the relationship between torque and force.
(a) Torque is the product of force and the distance from the axis of rotation. In this case, the axis of rotation is the steering wheel. The formula for torque is:
Torque = Force x Distance
In this case, the force is given as 90 N. To find the distance, we need to use the diameter of the steering wheel. The diameter is twice the radius, so the radius of the steering wheel is 60 cm / 2 = 30 cm = 0.3 m.
The distance from the axis of rotation is the radius of the steering wheel. So,
Torque = 90 N x 0.3 m
= 27 Nm
Therefore, the torque exerted on the wheel is 27 Nm.
(b) The force applied tangentially to the surface of the shaft is equal to the force applied to turn the wheel. Since the steering wheel turns the shaft, the force remains the same.
Therefore, the force applied tangentially to the surface of the shaft is 90 N.