a differential band brake has a drum of diameter 800mm. the two ends of the band are fixed to the pins on the opposite sides of the fulcrum of the lever at a distance of a=40mm and b=200mm from the fulcrum. the angle of contact is 270 degree and mue = 0.2 .determine the brake torque when aa force of 600 N is applied to the lever at a distance of 800 mm from the fulcrum when.

dynamics of machine-page 202,. u ll get answer,.. booksdotgoogledotcodotin

page 202

Well, well, well, looks like we have a brake-related question on our hands! Let's break it down, shall we?

First off, let's calculate the effective radius of the drum. Since the drum diameter is given as 800mm, the radius would be half of that, which is 400mm.

Now, let's determine the applied force torque. The force applied to the lever is 600N, and it's being exerted at a distance of 800mm from the fulcrum. So, torque = force × distance. In this case, torque = 600N × 800mm.

But hold on a second, we need to convert that distance from millimeters to meters to have consistent units. Since 1 meter is equal to 1000 millimeters, 800mm would be equal to 0.8m.

So, torque = 600N × 0.8m. Now we're getting somewhere!

But remember, we're talking about a differential band brake here. The brake torque is given by the equation:

Brake torque = (μe × force × radius) / (a + b)

In this equation, μe represents the coefficient of friction, a is the distance of one end of the band from the fulcrum, and b is the distance of the other end of the band from the fulcrum.

In our case, μe = 0.2, force = 600N, radius = 400mm (or 0.4m), a = 40mm (or 0.04m), and b = 200mm (or 0.2m).

Now, we can plug in these values and calculate the brake torque:

Brake torque = (0.2 × 600N × 0.4m) / (0.04m + 0.2m)

But remember, we have to simplify that denominator before we continue. 0.04m + 0.2m = 0.24m.

So, Brake torque = (0.2 × 600N × 0.4m) / 0.24m.

And let's do the math...

Brake torque = (0.2 × 600N × 0.4m) / 0.24m

Brake torque = 480N m.

Ta-da! The brake torque when a force of 600N is applied to the lever is 480N m.

To determine the brake torque, we can follow these steps:

Step 1: Calculate the effective radius of the brake drum.
Effective radius (r) = Drum diameter / 2
= 800 mm / 2
= 400 mm

Step 2: Calculate the force applied to the brake drum.
Force (F) = Lever force / Distance from fulcrum to force application point
= 600 N / 800 mm
= 0.75 N/mm

Step 3: Calculate the angle of contact in radians.
Angle of contact (θ) = Angle of contact in degrees * (π / 180)
= 270° * (π / 180)
= 1.5π radians

Step 4: Calculate the force acting on the brake drum.
Force on brake drum (P) = F * sin(θ)
= 0.75 N/mm * sin(1.5π)
= 0.75 N/mm * (-1)
= -0.75 N/mm

Step 5: Calculate the effective length of the band.
Effective length (L) = Distance between the two fixed ends
= a + 2b
= 40 mm + 2 * 200 mm
= 440 mm

Step 6: Calculate the brake torque.
Brake torque (T) = P * L * mue * r / 1000
= -0.75 N/mm * 440 mm * 0.2 * 400 mm / 1000
= -0.75 N * mm * mm / mm * mm * 0.4
= -0.75 N * 440 * 0.4
= -132 Nm

Therefore, the brake torque when a force of 600 N is applied to the lever at a distance of 800 mm from the fulcrum is -132 Nm. Note that the negative sign indicates that the brake is being applied.

To determine the brake torque in this scenario, we'll need to use the formula for the torque produced by a force on a lever arm:

Torque = Force × Lever Arm

First, let's calculate the lever arm. Given that the force is applied at a distance of 800 mm from the fulcrum, the lever arm would be 800 mm.

Next, we need to calculate the tension in the band brake. The tension in the band brake can be determined using the following equation:

Tension = (Force × Distance a) / (2 × Radius × sineθ)

Given:
- Force = 600 N
- Distance a = 40 mm
- Angle of contact (θ) = 270 degrees
- Radius = Drum diameter / 2 = 800 mm / 2 = 400 mm

Before calculating the tension, we need to convert the angle from degrees to radians:

θ (in radians) = θ (in degrees) × π / 180
θ (in radians) = 270 × π / 180
θ (in radians) = 3π / 2

Now we can substitute the values and calculate the tension:

Tension = (600 N × 40 mm) / (2 × 400 mm × sin(3π / 2))
Tension = (24000 Nmm) / (800 mm × -1)
Tension = -30 N

Since we have the tension in the band brake, we can calculate the brake torque:

Brake Torque = Tension × Distance b

Given:
- Distance b = 200 mm

Brake Torque = -30 N × 200 mm
Brake Torque = -6000 Nmm

Therefore, the brake torque when a force of 600 N is applied to the lever at a distance of 800 mm from the fulcrum is -6000 Nmm. The negative sign indicates that the torque is in the opposite direction of the applied force.