Answer:
a
![H =212.6 \ J](https://tex.z-dn.net/?f=H%20%20%3D212.6%20%5C%20%20J)
b
![v = 7.647 \ m/s](https://tex.z-dn.net/?f=v%20%20%3D%20%207.647%20%20%5C%20%20m%2Fs)
Explanation:
From the question we are told that
The child's weight is ![W_c = 287 \ N](https://tex.z-dn.net/?f=W_c%20%20%3D%20%20287%20%5C%20N)
The length of the sliding surface of the playground is ![L = 7.20 \ m](https://tex.z-dn.net/?f=L%20%3D%20%207.20%20%5C%20%20m)
The coefficient of friction is ![\mu = 0.120](https://tex.z-dn.net/?f=%5Cmu%20%3D%20%200.120)
The angle is ![\theta = 31.0 ^o](https://tex.z-dn.net/?f=%5Ctheta%20%3D%2031.0%20%5Eo)
The initial speed is ![u = 0.559 \ m/s](https://tex.z-dn.net/?f=u%20%3D%20%200.559%20%5C%20%20m%2Fs)
Generally the normal force acting on the child is mathematically represented as
=> ![N = mg * cos \theta](https://tex.z-dn.net/?f=N%20%20%3D%20%20mg%20%20%2A%20%20cos%20%5Ctheta)
Note ![m * g = W_c](https://tex.z-dn.net/?f=m%20%2A%20%20g%20%20%3D%20%20W_c)
Generally the frictional force between the slide and the child is
![F_f = \mu * mg * cos \theta](https://tex.z-dn.net/?f=F_f%20%20%3D%20%20%5Cmu%20%2A%20%20mg%20%20%2A%20%20cos%20%5Ctheta)
Generally the resultant force acting on the child due to her weight and the frictional force is mathematically represented as
![F =m* g sin(\theta) - F_f](https://tex.z-dn.net/?f=F%20%3Dm%2A%20g%20sin%28%5Ctheta%29%20-%20F_f)
Here F is the resultant force and it is represented as ![F = ma](https://tex.z-dn.net/?f=F%20%3D%20%20ma)
=> ![ma = m* g sin(31.0) - \mu * mg * cos (31.0)](https://tex.z-dn.net/?f=ma%20%3D%20%20%20m%2A%20g%20sin%2831.0%29%20%20-%20%5Cmu%20%2A%20%20mg%20%20%2A%20%20cos%20%2831.0%29)
=> ![a = g sin(31.0)- \mu * g * cos (31.0)](https://tex.z-dn.net/?f=a%20%3D%20%20g%20sin%2831.0%29-%20%20%5Cmu%20%2A%20%20g%20%20%2A%20%20cos%20%2831.0%29)
=> ![a = 9.8 * sin(31.0) - 0.120 * 9.8 * cos (31.0)](https://tex.z-dn.net/?f=a%20%3D%20%20%20%209.8%20%2A%20%20sin%2831.0%29%20-%200.120%20%2A%20%209.8%20%20%2A%20%20cos%20%2831.0%29)
=>![a = 4.039 \ m/s^2](https://tex.z-dn.net/?f=a%20%3D%20%204.039%20%5C%20m%2Fs%5E2)
So
![F_f = 0.120 * 287 * cos (31.0)](https://tex.z-dn.net/?f=F_f%20%20%3D%20%200.120%20%20%2A%20287%20%20%2A%20%20cos%20%2831.0%29)
=> ![F_f = 29.52 \ N](https://tex.z-dn.net/?f=F_f%20%20%3D%2029.52%20%5C%20%20N)
Generally the heat energy generated by the frictional force which equivalent tot the workdone by the frictional force is mathematically represented as
![H = F_f * L](https://tex.z-dn.net/?f=H%20%20%3D%20%20F_f%20%20%2A%20L)
=> ![H = 29.52 * 7.2](https://tex.z-dn.net/?f=H%20%20%3D%2029.52%20%2A%20%207.2)
=> ![H =212.6 \ J](https://tex.z-dn.net/?f=H%20%20%3D212.6%20%5C%20%20J)
Generally from kinematic equation we have that
![v^2 = u^2 + 2as](https://tex.z-dn.net/?f=v%5E2%20%20%3D%20%20u%5E2%20%20%2B%20%202as)
=> ![v^2 = 0.559^2 + 2 * 4.039 * 7.2](https://tex.z-dn.net/?f=v%5E2%20%20%3D%20%200.559%5E2%20%20%2B%20%202%20%2A%204.039%20%2A%207.2)
=> ![v = \sqrt{0.559^2 + 2 * 4.039 * 7.2}](https://tex.z-dn.net/?f=v%20%20%3D%20%20%5Csqrt%7B0.559%5E2%20%20%2B%20%202%20%2A%204.039%20%2A%207.2%7D)
=> ![v = 7.647 \ m/s](https://tex.z-dn.net/?f=v%20%20%3D%20%207.647%20%20%5C%20%20m%2Fs)
Single
Displacement Reaction Definition. A
single displacement reaction is a chemical reaction where one reactant is exchanged for one ion of a second reactant. It is also known as a
single replacement reaction.
Answer:
![t=2.51min](https://tex.z-dn.net/?f=t%3D2.51min)
Explanation:
The time taken by the light to travel a given distance is defined as:
![t=\frac{d}{c}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bd%7D%7Bc%7D)
Here c is obviously the speed of light. Now we convert the average distance form Venus to Earth to meters:
![28*10^{6}mi*\frac{1609.34}{1mi}=4.51*10^{10}m](https://tex.z-dn.net/?f=28%2A10%5E%7B6%7Dmi%2A%5Cfrac%7B1609.34%7D%7B1mi%7D%3D4.51%2A10%5E%7B10%7Dm)
Finally, we calculate the minutes taken by the light to travel from Venus to Earth:
![t=\frac{4.51*10^{10}m}{3*10^8\frac{m}{s}}\\t=150.33s*\frac{1min}{60s}=2.51min](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B4.51%2A10%5E%7B10%7Dm%7D%7B3%2A10%5E8%5Cfrac%7Bm%7D%7Bs%7D%7D%5C%5Ct%3D150.33s%2A%5Cfrac%7B1min%7D%7B60s%7D%3D2.51min)
Answer:
25.59 m/s²
Explanation:
Using the formula for the force of static friction:
--- (1)
where;
static friction force
coefficient of static friction
N = normal force
Also, recall that:
F = mass × acceleration
Similarly, N = mg
here, due to min. acceleration of the car;
![N = ma_{min}](https://tex.z-dn.net/?f=N%20%3D%20ma_%7Bmin%7D)
From equation (1)
![f_s = \mu_s ma_{min}](https://tex.z-dn.net/?f=f_s%20%3D%20%5Cmu_s%20ma_%7Bmin%7D)
However, there is a need to balance the frictional force by using the force due to the car's acceleration between the quarter and the wall of the rocket.
Thus,
![F = f_s](https://tex.z-dn.net/?f=F%20%3D%20f_s)
![mg = \mu_s ma_{min}](https://tex.z-dn.net/?f=mg%20%3D%20%5Cmu_s%20ma_%7Bmin%7D)
![a_{min} = \dfrac{mg }{ \mu_s m}](https://tex.z-dn.net/?f=a_%7Bmin%7D%20%3D%20%5Cdfrac%7Bmg%20%7D%7B%20%5Cmu_s%20m%7D)
![a_{min} = \dfrac{g }{ \mu_s }](https://tex.z-dn.net/?f=a_%7Bmin%7D%20%3D%20%5Cdfrac%7Bg%20%7D%7B%20%5Cmu_s%20%7D)
where;
and g = 9.8 m/s²
![a_{min} = \dfrac{9.8 \ m/s^2 }{0.383 }](https://tex.z-dn.net/?f=a_%7Bmin%7D%20%3D%20%5Cdfrac%7B9.8%20%5C%20m%2Fs%5E2%20%7D%7B0.383%20%7D)
![\mathbf{a_{min}= 25.59 \ m/s^2}](https://tex.z-dn.net/?f=%5Cmathbf%7Ba_%7Bmin%7D%3D%2025.59%20%5C%20m%2Fs%5E2%7D)
the path of an electron around the nucleus of an atom