It would mean that you could not know the precise volume of the sand. Only the volume of the sand plus the water that was making it damp.
In the experiments listed, the effects are easy to deduce by understanding that the water in the sand adds volume to the 'sample' being measured.
So in the case of calculating air space you would calculate <em>less</em> air space.
Answer:
3.90 degrees
Explanation:
Let g= 9.81 m/s2. The gravity of the 30kg grocery cart is
W = mg = 30*9.81 = 294.3 N
This gravity is split into 2 components on the ramp, 1 parallel and the other perpendicular to the ramp.
We can calculate the parallel one since it's the one that affects the force required to push up
F = WsinΘ
Since customer would not complain if the force is no more than 20N
F = 20
![294.3sin\theta = 20](https://tex.z-dn.net/?f=294.3sin%5Ctheta%20%3D%2020)
![sin\theta = 20/294.3 = 0.068](https://tex.z-dn.net/?f=sin%5Ctheta%20%3D%2020%2F294.3%20%3D%200.068)
![\theta = sin^{-1}0.068 = 0.068 rad = 0.068*180/\pi \approx 3.90^0](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20sin%5E%7B-1%7D0.068%20%3D%200.068%20rad%20%3D%200.068%2A180%2F%5Cpi%20%5Capprox%203.90%5E0)
So the ramp cannot be larger than 3.9 degrees
Answer:
by answering your question
Answer:
The value is ![v = 2.3359 *10^{4} \ m/s](https://tex.z-dn.net/?f=v%20%20%3D%20%202.3359%20%2A10%5E%7B4%7D%20%5C%20m%2Fs)
Explanation:
From the question we are told that
The initial speed is ![u = 2.05 *10^{4} \ m/s](https://tex.z-dn.net/?f=u%20%3D%20%202.05%20%2A10%5E%7B4%7D%20%5C%20%20m%2Fs)
Generally the total energy possessed by the space probe when on earth is mathematically represented as
![T__{E}} = KE__{i}} + KE__{e}}](https://tex.z-dn.net/?f=T__%7BE%7D%7D%20%3D%20%20KE__%7Bi%7D%7D%20%2B%20%20KE__%7Be%7D%7D)
Here
is the kinetic energy of the space probe due to its initial speed which is mathematically represented as
=>
=> ![KE_i = 2.101 *10^{8} \ \ m \ \ J](https://tex.z-dn.net/?f=KE_i%20%3D%20%202.101%20%2A10%5E%7B8%7D%20%5C%20%5C%20m%20%5C%20%5C%20J)
And
is the kinetic energy that the space probe requires to escape the Earth's gravitational pull , this is mathematically represented as
![KE_e = \frac{1}{2} * m * v_e^2](https://tex.z-dn.net/?f=KE_e%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%2A%20%20m%20%2A%20%20v_e%5E2)
Here
is the escape velocity from earth which has a value ![v_e = 11.2 *10^{3} \ m/s](https://tex.z-dn.net/?f=v_e%20%3D%20%2011.2%20%2A10%5E%7B3%7D%20%5C%20%20m%2Fs)
=> ![KE_e = \frac{1}{2} * m * (11.3 *10^{3})^2](https://tex.z-dn.net/?f=KE_e%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%2A%20%20m%20%2A%20%20%2811.3%20%2A10%5E%7B3%7D%29%5E2)
=> ![KE_e = 6.272 *10^{7} \ \ m \ \ J](https://tex.z-dn.net/?f=KE_e%20%3D%20%206.272%20%2A10%5E%7B7%7D%20%5C%20%20%5C%20%20m%20%20%5C%20%5C%20%20%20J)
Generally given that at a position that is very far from the earth that the is Zero, the kinetic energy at that position is mathematically represented as
![KE_p = \frac{1}{2} * m * v^2](https://tex.z-dn.net/?f=KE_p%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%2A%20%20m%20%2A%20%20v%5E2)
Generally from the law energy conservation we have that
So
![2.101 *10^{8} m + 6.272 *10^{7} m = \frac{1}{2} * m * v^2](https://tex.z-dn.net/?f=2.101%20%2A10%5E%7B8%7D%20%20m%20%20%2B%20%206.272%20%2A10%5E%7B7%7D%20%20m%20%20%3D%20%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%2A%20%20m%20%2A%20%20v%5E2)
=> ![5.4564 *10^{8} = v^2](https://tex.z-dn.net/?f=5.4564%20%2A10%5E%7B8%7D%20%3D%20%20%20v%5E2)
=> ![v = \sqrt{5.4564 *10^{8}}](https://tex.z-dn.net/?f=v%20%3D%20%20%5Csqrt%7B5.4564%20%2A10%5E%7B8%7D%7D)
=> ![v = 2.3359 *10^{4} \ m/s](https://tex.z-dn.net/?f=v%20%20%3D%20%202.3359%20%2A10%5E%7B4%7D%20%5C%20m%2Fs)