a brake shoe applied to a drum by a lever ab which is pivoted at a fixed point a and rigidly fixed to the shoe. The radius of the drum is 160mm. The coefficient of friction at the brake lining is 0.3. If the drum rotates clockwise, find the braking torque due to the horizontal force of 600n at b
Where is point b?
To find the braking torque, we need to calculate the perpendicular distance between the point of rotation and the line of action of the force.
Given:
Radius of the drum (r) = 160 mm = 0.16 m
Force applied at point B (F) = 600 N
The perpendicular distance between the point of rotation (A) and the line of action of the force (B) can be found using the equation:
Torque (τ) = Force (F) × Perpendicular Distance (d)
Since the force is horizontal, the perpendicular distance (d) will be the vertical distance from point A to the line of action of the force.
Since the lever AB is fixed at point A and rigidly attached to the shoe, the vertical distance is equal to the radius of the drum.
Therefore,
Perpendicular Distance (d) = Radius of the drum (r) = 0.16 m
Now we can calculate the braking torque:
τ = F × d
= 600 N × 0.16 m
= 96 Nm
Therefore, the braking torque due to the horizontal force of 600 N at point B is 96 Nm.
To find the braking torque due to the horizontal force of 600N at point B, we need to consider the torque generated by the force and the friction between the brake shoe and drum.
First, let's calculate the lever arm, which is the perpendicular distance between the fixed point A (pivot) and point B on the lever. The lever arm is the distance at which the force is applied and determines the torque.
Since the lever AB is rigidly fixed to the shoe, we can assume that the distance between A and B is the same as the radius of the drum. Given that the radius of the drum is 160mm, the lever arm (AB) is also 160mm.
Next, let's calculate the braking torque due to the horizontal force at B. Torque is calculated by multiplying the force applied (F) by the lever arm (AB):
Torque (τ) = Force (F) * Lever Arm (AB)
τ = 600N * 160mm
However, before we proceed, let's convert the lever arm from millimeters to meters to match the SI unit of force (Newton). Since 1 meter is equal to 1000 millimeters, the lever arm in meters is:
Lever Arm (AB) = 160mm / 1000 = 0.16m
Now we can calculate the braking torque:
τ = 600N * 0.16m
Next, we need to consider the friction between the brake lining and the drum. The coefficient of friction (μ) is given as 0.3. The frictional force (Ff) can be calculated by multiplying the normal force (Fn) by the coefficient of friction:
Frictional Force (Ff) = Coefficient of Friction (μ) * Normal Force (Fn)
To find the normal force, we need to consider the weight of the drum. Assuming the weight of the drum is evenly distributed, the normal force is equal to the weight.
Knowing that weight (W) = mass (m) * gravitational acceleration (g), and the mass is not given, we cannot directly calculate the normal force. However, we can assume that the normal force is equal to the weight of the drum.
To find the weight of the drum, we need to know the mass. If the mass is provided, we can multiply it by the gravitational acceleration to find the weight.