The moment of weight W about the pivot is 12 N m. The perpendicular distance of the
line of action of the force of the steam on the valve from the pivot is 0.2 m.
The area of the piston is 0.0003 m2.
Calculate
(i) the minimum steam force needed for the steam to escape
Well, looks like we have a steamy situation here! Let's crunch some numbers, shall we?
To calculate the minimum steam force needed for the steam to escape, we need to consider the moment of weight and the moment of the steam force.
The moment of weight (W) is given as 12 N m. Since we're dealing with moments, we know that moment = force × distance. So, W = force of weight × perpendicular distance. Given that the perpendicular distance is 0.2 m, we can rewrite the equation as W = weight × 0.2. Now we just need to solve for weight.
Weight = W / 0.2 = 12 N m / 0.2 m = 60 N.
Now let's move on to the moment of the steam force. The area of the piston is given as 0.0003 m². We know that pressure = force / area, so we can calculate the force of steam using the equation force = pressure × area. However, we need the minimum force, which means we need the minimum pressure.
Since the steam is just about to escape, we can assume that the system is in equilibrium. In other words, the clockwise moment caused by the weight is balanced by the counterclockwise moment caused by the steam force. So, we can equate the two moments.
Weight × distance = steam force × distance.
Plugging in the values we know, 60 N × 0.2 m = steam force × 0.2 m. Solving for steam force, we get:
Steam force = (60 N × 0.2 m) / 0.2 m = 60 N.
So, the minimum steam force needed for the steam to escape is 60 N.
I hope this answer wasn't too steamy for you!
To calculate the minimum steam force needed for the steam to escape, we need to consider the equilibrium of forces.
Since the moment of weight W about the pivot is 12 Nm and the perpendicular distance from the line of action of the weight to the pivot is not given, we can't determine the value of W.
However, we can calculate the force exerted by the steam on the valve.
Using the equation for torque:
Torque = Force x Distance
We have:
Torque (due to weight) = Force (due to steam) x Distance (from pivot to line of action of steam force)
Given that the torque due to weight is 12 Nm and the perpendicular distance of the line of action of the steam force from the pivot is 0.2 m, we can write the equation as:
12 Nm = Force (due to steam) x 0.2 m
Simplifying, we can find the force due to steam:
Force due to steam = 12 Nm / 0.2 m
Force due to steam = 60 N
Therefore, the minimum steam force needed for the steam to escape is 60 N.
To calculate the minimum steam force needed for the steam to escape, we need to understand the concept of moments and equilibrium.
A moment is a turning effect produced by a force around a pivot point. In this case, the moment of weight W about the pivot is given as 12 N m. This means that the weight W, acting on the valve, creates a turning effect of 12 N m around the pivot point.
To calculate the minimum steam force needed, we can use the principle of moments. According to this principle, for an object to be in equilibrium, the clockwise moments must be equal to the anticlockwise moments.
In this scenario, the weight W is acting downward, creating a clockwise moment. The force of the steam on the valve will create an anticlockwise moment. The perpendicular distance of the line of action of the force of the steam on the valve from the pivot is given as 0.2 m.
Now, we can calculate the minimum steam force needed. Let's assume the minimum steam force needed is F (in Newtons).
The moment of the steam force about the pivot can be calculated as follows:
Moment of steam force = Force of steam × Perpendicular distance from pivot
Anticlockwise moment = F × 0.2
According to the principle of moments, the clockwise moment (moment of weight W) is equal to the anticlockwise moment (moment of steam force).
Therefore,
Clockwise moment = Anticlockwise moment
12 N m = F × 0.2
From this equation, we can solve for F:
F = 12 N m / 0.2
Calculating this, we get:
F = 60 N
Therefore, the minimum steam force needed for the steam to escape is 60 Newtons.