the load which a crane can lift up is directly proportional to the mass and inversely proportional to the height throught which the load is lifted . if a load of 40t and mass of 175gm is lifted through height 70m what load will be carried through height 50m given the mass as 250gm
L = k*m/h so Lh/m = k is constant. You want
L such that
50L/250 = (40*70)/175
now just solve for L
Well, let's calculate this with a touch of humor! According to the given information, we know that the load is directly proportional to the mass and inversely proportional to the height. So, let's do some math and fun!
First, we have a load of 40 tons and a mass of 175 grams. Now, let's find out how many grams of load will be carried through a height of 70 meters. We can use the equation:
Load1/Mass1 = Load2/Mass2
By substituting the given values, we have:
40 tons/175 grams = Load2/250 grams
Now, let's solve it with a little brain exercise. If you cross-multiply the equation, it becomes:
40 tons * 250 grams = 175 grams * Load2
Dividing both sides by 175 grams, we get:
Load2 = (40 tons * 250 grams) / 175 grams
After simplifying and converting tons to grams, we end up with:
Load2 = 57,142.86 grams
So, the load that will be carried through a height of 70 meters, given the mass of 250 grams, is approximately 57,142.86 grams.
Now, let's get ready to calculate the load that will be carried through a height of 50 meters! Are you bracing yourself?
Using the same equation, we can substitute the values:
40 tons / 175 grams = Load3 / 250 grams
When we cross-multiply and simplify, we find:
Load3 = (40 tons * 250 grams) / 175 grams
After converting tons to grams, we have:
Load3 = 57,142.86 grams
Surprise! The load that will be carried through a height of 50 meters, given the mass of 250 grams, is also approximately 57,142.86 grams!
So, in conclusion, whether you go up 70 meters or 50 meters, it seems like you'll be carrying the same load. It's like a weightlifting champion! Just make sure not to drop any dumbbells on your toes. Safety first!
To solve this problem, we can use the equation:
Load = k * (mass / height)
Since the load is directly proportional to the mass and inversely proportional to the height, we can assume there is a constant of proportionality, k.
We are given that a load of 40t (40,000 kg) and mass of 175g (0.175 kg) is lifted through a height of 70m.
Let's first solve for k.
Load = k * (mass / height)
40,000 = k * (0.175 / 70)
Now, we can solve for k:
k = 40,000 / (0.175 / 70)
k = 40,000 / (0.0025)
k = 16,000,000
Now that we have the value of k, we can find the load to be carried through a height of 50m, given a mass of 250g (0.25 kg).
Load = k * (mass / height)
Load = 16,000,000 * (0.25 / 50)
Load = 80,000 kg or 80t
Therefore, the load to be carried through a height of 50m, given a mass of 250g, will be 80t.
To solve this problem, we need to use the concept of direct and inverse proportionality. Let's break down the problem step by step.
First, we are given that the load a crane can lift up is directly proportional to the mass and inversely proportional to the height through which the load is lifted. This means that the formula relating load (L), mass (M), and height (H) is:
L = k * (M/H)
where k is the constant of proportionality.
Next, we are given a load of 40t (tonnes) and a mass of 175gm (grams) lifted through a height of 70m. We can use these values to find the value of k.
40t = k * (175gm/70m)
Let's convert the mass of 175gm to tonnes by dividing it by 1000:
40t = k * (0.175t/70m)
Now, let's solve for k by simplifying the equation:
40 = k * 0.0025
Dividing both sides of the equation by 0.0025:
k = 40 / 0.0025
k ≈ 16000
Now that we have the value of k, we can use it to find the load that will be carried through a height of 50m, given a mass of 250gm. Let's substitute these values into the formula:
L = 16000 * (250gm/50m)
Again, let's convert the mass of 250gm to tonnes:
L = 16000 * (0.25t/50m)
Simplifying the equation:
L = 16000 * 0.005
L ≈ 80t
Therefore, the load that will be carried through a height of 50m, given a mass of 250gm, will be approximately 80 tonnes.