Answer:
The speed after being pulled is 2.4123m/s
Explanation:
The work realize by the tension and the friction is equal to the change in the kinetic energy, so:
(1)
Where:
![W_T=T*x*cos(0)=32N*3.2m*cos(30)=88.6810J\\W_F=F_r*x*cos(180)=-0.190*mg*x =-0.190*10kg*9.8m/s^{2}*3.2m=59.584J\\ K_i=0\\K_f=\frac{1}{2}*m*v_f^{2}=5v_f^{2}](https://tex.z-dn.net/?f=W_T%3DT%2Ax%2Acos%280%29%3D32N%2A3.2m%2Acos%2830%29%3D88.6810J%5C%5CW_F%3DF_r%2Ax%2Acos%28180%29%3D-0.190%2Amg%2Ax%20%3D-0.190%2A10kg%2A9.8m%2Fs%5E%7B2%7D%2A3.2m%3D59.584J%5C%5C%20K_i%3D0%5C%5CK_f%3D%5Cfrac%7B1%7D%7B2%7D%2Am%2Av_f%5E%7B2%7D%3D5v_f%5E%7B2%7D)
Because the work made by any force is equal to the multiplication of the force, the displacement and the cosine of the angle between them.
Additionally, the kinetic energy is equal to
, so if the initial velocity
is equal to zero, the initial kinetic energy
is equal to zero.
Then, replacing the values on the equation and solving for
, we get:
![W_T+W_F=K_f-K_i\\88.6810-59.5840=5v_f^{2}\\29.097=5v_f^{2}](https://tex.z-dn.net/?f=W_T%2BW_F%3DK_f-K_i%5C%5C88.6810-59.5840%3D5v_f%5E%7B2%7D%5C%5C29.097%3D5v_f%5E%7B2%7D)
![\frac{29.097}{5}=v_f^{2}\\\sqrt{5.8194}=v_f\\2.4123=v_f](https://tex.z-dn.net/?f=%5Cfrac%7B29.097%7D%7B5%7D%3Dv_f%5E%7B2%7D%5C%5C%5Csqrt%7B5.8194%7D%3Dv_f%5C%5C2.4123%3Dv_f)
So, the speed after being pulled 3.2m is 2.4123 m/s
Answer:
The automobile's acceleration in that time interval is -2 m/s^2
Explanation:
The acceleration is defined as the rate of change of the velocity.
The average acceleration in a given lapse of time is calculated as:
A = (final velocity - initial velocity)/time.
In this case, we have:
initial velocity = 31 m/s
final velocity = 15 m/s
time = 8 seconds.
Then the average acceleration is:
A = (15m/s - 31m/s)/8s = -2 m/s^2
True
In fact, the weight of an object on the surface of the Earth is given by:
![F=mg](https://tex.z-dn.net/?f=F%3Dmg)
where m is the mass of the object and
![g=9.81 m/s^2](https://tex.z-dn.net/?f=g%3D9.81%20m%2Fs%5E2)
is the gravitational acceleration on Earth's surface. If we use the mass of the object, m=3.0 kg, we find
Answer:
Part a: When the road is level, the minimum stopping sight distance is 563.36 ft.
Part b: When the road has a maximum grade of 4%, the minimum stopping sight distance is 528.19 ft.
Explanation:
Part a
When Road is Level
The stopping sight distance is given as
![SSD=1.47 ut +\frac{u^2}{30 (\frac{a}{g} \pm G)}](https://tex.z-dn.net/?f=SSD%3D1.47%20ut%20%2B%5Cfrac%7Bu%5E2%7D%7B30%20%28%5Cfrac%7Ba%7D%7Bg%7D%20%5Cpm%20G%29%7D)
Here
- SSD is the stopping sight distance which is to be calculated.
- u is the speed which is given as 60 mi/hr
- t is the perception-reaction time given as 2.5 sec.
- a/g is the ratio of deceleration of the body w.r.t gravitational acceleration, it is estimated as 0.35.
- G is the grade of the road, which is this case is 0 as the road is level
Substituting values
![SSD=1.47 ut +\frac{u^2}{30 (\frac{a}{g} \pm G)}\\SSD=1.47 \times 60 \times 2.5 +\frac{60^2}{30 \times (0.35-0)}\\SSD=220.5 +342.86 ft\\SSD=563.36 ft](https://tex.z-dn.net/?f=SSD%3D1.47%20ut%20%2B%5Cfrac%7Bu%5E2%7D%7B30%20%28%5Cfrac%7Ba%7D%7Bg%7D%20%5Cpm%20G%29%7D%5C%5CSSD%3D1.47%20%5Ctimes%2060%20%5Ctimes%202.5%20%2B%5Cfrac%7B60%5E2%7D%7B30%20%5Ctimes%20%280.35-0%29%7D%5C%5CSSD%3D220.5%20%2B342.86%20ft%5C%5CSSD%3D563.36%20ft)
So the minimum stopping sight distance is 563.36 ft.
Part b
When Road has a maximum grade of 4%
The stopping sight distance is given as
![SSD=1.47 ut +\frac{u^2}{30 (\frac{a}{g} \pm G)}](https://tex.z-dn.net/?f=SSD%3D1.47%20ut%20%2B%5Cfrac%7Bu%5E2%7D%7B30%20%28%5Cfrac%7Ba%7D%7Bg%7D%20%5Cpm%20G%29%7D)
Here
- SSD is the stopping sight distance which is to be calculated.
- u is the speed which is given as 60 mi/hr
- t is the perception-reaction time given as 2.5 sec.
- a/g is the ratio of deceleration of the body w.r.t gravitational acceleration, it is estimated as 0.35.
- G is the grade of the road, which is given as 4% now this can be either downgrade or upgrade
For upgrade of 4%, Substituting values
![SSD=1.47 ut +\frac{u^2}{30 (\frac{a}{g} \pm G)}\\SSD=1.47 \times 60 \times 2.5 +\frac{60^2}{30 \times (0.35+0.04)}\\SSD=220.5 +307.69 ft\\SSD=528.19 ft](https://tex.z-dn.net/?f=SSD%3D1.47%20ut%20%2B%5Cfrac%7Bu%5E2%7D%7B30%20%28%5Cfrac%7Ba%7D%7Bg%7D%20%5Cpm%20G%29%7D%5C%5CSSD%3D1.47%20%5Ctimes%2060%20%5Ctimes%202.5%20%2B%5Cfrac%7B60%5E2%7D%7B30%20%5Ctimes%20%280.35%2B0.04%29%7D%5C%5CSSD%3D220.5%20%2B307.69%20ft%5C%5CSSD%3D528.19%20ft)
<em>So the minimum stopping sight distance for a road with 4% upgrade is 528.19 ft.</em>
For downgrade of 4%, Substituting values
![SSD=1.47 ut +\frac{u^2}{30 (\frac{a}{g} \pm G)}\\SSD=1.47 \times 60 \times 2.5 +\frac{60^2}{30 \times (0.35-0.04)}\\SSD=220.5 +387.09 ft\\SSD=607.59ft](https://tex.z-dn.net/?f=SSD%3D1.47%20ut%20%2B%5Cfrac%7Bu%5E2%7D%7B30%20%28%5Cfrac%7Ba%7D%7Bg%7D%20%5Cpm%20G%29%7D%5C%5CSSD%3D1.47%20%5Ctimes%2060%20%5Ctimes%202.5%20%2B%5Cfrac%7B60%5E2%7D%7B30%20%5Ctimes%20%280.35-0.04%29%7D%5C%5CSSD%3D220.5%20%2B387.09%20ft%5C%5CSSD%3D607.59ft)
<em>So the minimum stopping sight distance for a road with 4% downgrade is 607.59 ft.</em>
As the minimum distance is required for the 4% grade road, so the solution is 528.19 ft.
Answer:
Bottom left corner for whatever group that is
Lithium, sodium, and potassium all react with water