A 1500 W winch is used to raise a load of bricks to a height of 25m. If the bricks need to reach this height in 1.5 minutes. What is the maximum allowable mass of the load bricks?
work = m g h = m * 9.8 * 25
power = work / time ... 1500 w = work / 90 s
m = (power * time) / (g * h)
Oh, we're playing with weights and heights! I hope these bricks aren't too heavy, or else I might need to lay down some bricks of my own! Let's do some calculations, shall we?
First, let's convert the time to seconds. 1.5 minutes is equal to 90 seconds, so now we're in the same time zone, I mean, time scale!
Next, let's use the formula for work: Work = Force x Distance. The power (P) is equal to Work divided by Time, so we can rearrange the formulas to find the force (F).
P = W/T
F x D = W
F = W/D
Now, let's plug in some values. Our power (P) is 1500 watts, and our distance (D) is 25 meters. Let's calculate the force (F) needed.
F = 1500/25
F = 60 Newtons
Finally, to find the maximum allowable mass, we can use the formula: Weight = Mass x Gravity. Since the force (F) is equal to the weight, we can rearrange the formula to find the mass (M).
F = M x G
M = F/G
Assuming the force of gravity (G) is approximately 9.8 m/s^2, let's calculate the maximum allowable mass!
M = 60/9.8
M ≈ 6.12 kilograms
So, the maximum allowable mass of the load of bricks is approximately 6.12 kilograms. Phew, I hope those bricks don't come crashing down on anyone's head! Safety first, after all!
To find the maximum allowable mass of the load bricks, we can use the work-energy principle. The work done by the winch is equal to the change in potential energy of the load.
The work done (W) is given by the formula:
W = m * g * h
Where:
m is the mass of the load (in kg)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height the load is raised (in meters)
Since we know the power of the winch (P) is 1500 W and the time it takes to raise the load (t) is 1.5 minutes, we can calculate the work done by the winch:
W = P * t
Converting the time to seconds:
t = 1.5 minutes = 1.5 * 60 seconds = 90 seconds
Now we can equate the work done by the winch with the work done in raising the load:
P * t = m * g * h
Plugging in the values, we have:
1500 * 90 = m * 9.8 * 25
Simplifying the equation:
135000 = m * 245
Dividing both sides by 245:
m = 135000 / 245
m ≈ 551.02 kg
Therefore, the maximum allowable mass of the load of bricks is approximately 551.02 kg.
To calculate the maximum allowable mass of the load of bricks, we can use the formula:
Power = Work / Time
Here, the power is given as 1500 W, the time is 1.5 minutes (or 90 seconds), and we need to find the work done, which is equal to the potential energy gained by lifting the load of bricks to a height of 25 meters.
First, let's convert the time to seconds:
Time = 1.5 minutes × 60 seconds/minute = 90 seconds
Now, let's calculate the work done:
Power = Work / Time
Rearranging the formula, we get:
Work = Power × Time
Substituting the given values:
Work = 1500 W × 90 s = 135,000 Joules
Since the work done is equal to the potential energy gained by lifting the load, we can calculate the maximum allowable mass using the formula:
Potential Energy = Mass × Gravity × Height
In this case, the potential energy gained is equal to the work done, so we have:
Mass × Gravity × Height = Work
Rearranging the formula, we get:
Mass = Work / (Gravity × Height)
Substituting the given values:
Mass = 135,000 J / (9.8 m/s^2 × 25 m) = 551.02 kg
Therefore, the maximum allowable mass of the load of bricks is approximately 551.02 kg.