water density 1000 kg m3 falls without splashing at a rate of .37 L/s from a height of 45.3 m into a .610 kg bucket. if the scale is originally empty, what does the scale read 1.76 s after the first drop contacts the bucket?
To find the weight reading on the scale 1.76 seconds after the first drop contacts the bucket, we need to consider the mass of the water that has fallen into the bucket at that time.
First, let's calculate the mass of the water that has fallen into the bucket. We know that the density of water is 1000 kg/m³ and the volume rate of water falling into the bucket is 0.37 L/s.
To convert the volume rate to cubic meters per second, we need to convert liters to cubic meters. Since 1 L = 0.001 m³, the volume rate is 0.37 × 0.001 = 0.00037 m³/s.
The mass of water fallen into the bucket is calculated by multiplying the density by the volume:
mass = density × volume = 1000 kg/m³ × 0.00037 m³/s = 0.37 kg/s
Now, let's calculate the time it took for the water to fall onto the scale. Since the scale reading is required 1.76 seconds after the first drop contacts the bucket, it means it took 1.76 seconds for the water to fall from a height of 45.3 m into the bucket.
Next, we need to find the net mass on the scale. This consists of the mass of the empty bucket plus the mass of the water fallen into the bucket.
The mass of the empty bucket is given as 0.610 kg.
Using the equation: mass = mass_bucket + mass_water.
mass = 0.610 kg + (0.37 kg/s × 1.76 s) = 0.610 kg + 0.6512 kg = 1.2612 kg
Therefore, the scale would read approximately 1.2612 kg 1.76 seconds after the first drop contacts the bucket.
Note: This calculation assumes that there is no splashing or loss of water during the falling process.