Water of density 1000 kg/m3 falls without splashing at a rate of 0.241 L/s from a height of 81.3 m into a 0.638 kg bucket on a scale. If the bucket is originally empty, what does the scale read 2.06 seconds after the first drop contacts the bucket? The acceleration due to gravity is 9.8 m/s2. Answer in units of N
The scale should read the weight of the acculumated water, plus the force needed to change the momentum of the falling drops to zero, plus the weight of the bucket.
weight of water=rate*time*desnity*g
change of momentum force=
massdrop*velocity drop/timebetween drops
= .241L(1kg/Liter) *sqrt(h*g*2)* 1/sec
weight bucket=massbucket*g
To find the reading on the scale 2.06 seconds after the first drop contacts the bucket, we need to calculate the force exerted by the falling water on the bucket.
First, let's determine the mass of the water that falls into the bucket during the given time period. We are given the rate of water flow, which is 0.241 L/s. To convert this to cubic meters per second (m^3/s), we need to multiply by 0.001 (since 1 L = 0.001 m^3) as follows:
0.241 L/s * 0.001 m^3/L = 0.000241 m^3/s
Next, we can calculate the mass of the water using the density formula:
Mass = Density * Volume
Given that the density of water is 1000 kg/m^3 and the volume of water flowing into the bucket in 2.06 seconds is:
Volume = Flow rate * Time
Volume = 0.000241 m^3/s * 2.06 s
Now we have the volume of water in cubic meters that falls into the bucket during 2.06 seconds. We can calculate the mass:
Mass = 1000 kg/m^3 * (0.000241 m^3/s * 2.06 s)
Next, let's calculate the initial velocity of the water just before it contacts the bucket. We can use the following kinematic equation:
v = u + at
where:
v = final velocity (which is 0 since the water stops splashing)
u = initial velocity
a = acceleration due to gravity (-9.8 m/s^2)
t = time (2.06 seconds)
0 = u + (-9.8 m/s^2 * 2.06 s)
Simplifying the equation, we find:
u = 9.8 m/s^2 * 2.06 s
Now that we know the initial velocity, we can calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
Since the velocity just before contact is 0, the final momentum is 0. The initial momentum can be calculated as follows:
Initial momentum = Mass of water * Initial velocity
Finally, we can determine the force exerted on the bucket by multiplying the change in momentum by the rate of change of momentum with respect to time:
Force = Change in momentum / Time
Now, let's plug in the values we have calculated:
Mass = 1000 kg/m^3 * (0.000241 m^3/s * 2.06 s)
u = 9.8 m/s^2 * 2.06 s
Initial momentum = Mass * u
Force = (Initial momentum - Final momentum) / 2.06 seconds
By calculating these values, we can find the reading on the scale in units of Newtons (N), which represents the force exerted by the falling water on the bucket after 2.06 seconds.