Water falls without splashing at a rate of 0.250 L/s from a height of 2.60 m into a 0.750kg bucket on a scale. If the bucket is originally empty, what does the scale read innewtons 3.00 s after water starts to accumulate in it?

To find the reading on the scale 3.00 seconds after water starts to accumulate in the bucket, we need to consider the change in momentum of the water and the bucket.

Step 1: Calculate the momentum of the water The momentum of an object is given by the formula: momentum = mass × velocity.

Given:

• Rate of water falling = 0.250 L/s
• Density of water = 1 kg/L (since 1 L of water has a mass of 1 kg)
• Height of the fall = 2.60 m

To find the velocity of the falling water, we can use the equation: velocity = √(2 × acceleration × height), where acceleration due to gravity is approximately 9.8 m/s².

velocity = √(2 × 9.8 m/s² × 2.60 m) velocity ≈ √(51.04 m²/s²) velocity ≈ 7.14 m/s

Now, we can calculate the mass of water falling in 3.00 seconds: mass of water = rate of water falling × time mass of water = 0.250 L/s × 3.00 s mass of water = 0.750 kg

Using the formula for momentum, we can find the momentum of the water: momentum of water = mass of water × velocity momentum of water = 0.750 kg × 7.14 m/s momentum of water ≈ 5.355 kg·m/s

Step 2: Calculate the change in momentum of the bucket Since the bucket is initially empty, the change in momentum of the bucket is equal to the momentum of the water.

change in momentum of the bucket = momentum of water change in momentum of the bucket ≈ 5.355 kg·m/s

Step 3: Calculate the reading on the scale The reading on the scale is equal to the weight of the bucket, which is the force exerted on it due to the change in momentum.

Using the formula: force = change in momentum ÷ time, we can find the force exerted on the bucket.

force = change in momentum of the bucket ÷ time force = 5.355 kg·m/s ÷ 3.00 s force ≈ 1.785 N

Therefore, the scale would read approximately 1.785 Newtons 3.00 seconds after water starts to accumulate in the bucket.