Complete Question
The complete question is shown on the first uploaded image
Answer:
a
The tension is ![T = 48.255 \ N](https://tex.z-dn.net/?f=T%20%3D%20%2048.255%20%5C%20N)
b
The time taken is ![t = 0.226 \ s](https://tex.z-dn.net/?f=t%20%3D%20%200.226%20%5C%20s)
c
The position for maximum velocity is
S = 0
d
The maximum velocity is
Explanation:
The free body for this question is shown on the second uploaded image
From the question we are told that
The mass of the bob is ![m_b = 5 \ kg](https://tex.z-dn.net/?f=m_b%20%20%3D%20%205%20%5C%20kg)
The angle is ![\theta = 10^o](https://tex.z-dn.net/?f=%5Ctheta%20%3D%2010%5Eo)
The length of the string is ![L = 0.5 \ m](https://tex.z-dn.net/?f=L%20%3D%20%200.5%20%5C%20m)
The tension on the string is mathematically represented as
![T = mg cos \theta](https://tex.z-dn.net/?f=T%20%20%3D%20mg%20cos%20%5Ctheta)
substituting values
![T = 5 * 9.8 cos(10)](https://tex.z-dn.net/?f=T%20%3D%20%205%20%2A%209.8%20cos%2810%29)
![T = 48.255 \ N](https://tex.z-dn.net/?f=T%20%3D%20%2048.255%20%5C%20N)
The motion of the bob is mathematically represented as
![S = A sin (w t + \frac{\pi }{2} )](https://tex.z-dn.net/?f=S%20%3D%20%20A%20sin%20%28w%20t%20%20%2B%20%5Cfrac%7B%5Cpi%20%7D%7B2%7D%20%29)
=> ![S = A sin (wt)](https://tex.z-dn.net/?f=S%20%3D%20%20A%20sin%20%28wt%29)
Where
is the angular speed
and
is the phase change
At initial position S = 0
So ![wt = cos^{-1} (0)](https://tex.z-dn.net/?f=wt%20%20%3D%20cos%5E%7B-1%7D%20%280%29)
![wt = 1](https://tex.z-dn.net/?f=wt%20%20%3D%201)
Generally
can be mathematically represented as
![w = \frac{2 \pi }{T}](https://tex.z-dn.net/?f=w%20%3D%20%20%5Cfrac%7B2%20%5Cpi%20%7D%7BT%7D)
Where T is the period of oscillation which i mathematically represented as
![T = 2 \pi \sqrt{\frac{L}{g} }](https://tex.z-dn.net/?f=T%20%20%3D%20%202%20%5Cpi%20%5Csqrt%7B%5Cfrac%7BL%7D%7Bg%7D%20%7D)
So
![t = \frac{1}{w}](https://tex.z-dn.net/?f=t%20%20%20%3D%20%5Cfrac%7B1%7D%7Bw%7D)
![t = \frac{T}{2 \pi}](https://tex.z-dn.net/?f=t%20%20%20%3D%20%5Cfrac%7BT%7D%7B2%20%5Cpi%7D)
![t = \sqrt{\frac{L}{g} }](https://tex.z-dn.net/?f=t%20%3D%20%20%5Csqrt%7B%5Cfrac%7BL%7D%7Bg%7D%20%7D)
substituting values
![t = \sqrt{\frac{0.5}{9.8} }](https://tex.z-dn.net/?f=t%20%3D%20%20%5Csqrt%7B%5Cfrac%7B0.5%7D%7B9.8%7D%20%7D)
![t = 0.226 \ s](https://tex.z-dn.net/?f=t%20%3D%20%200.226%20%5C%20s)
Looking at the equation
![wt = 1](https://tex.z-dn.net/?f=wt%20%3D%20%201)
We see that maximum velocity of the bob will be at S = 0
i. e ![w = \frac{1}{t}](https://tex.z-dn.net/?f=w%20%3D%20%20%5Cfrac%7B1%7D%7Bt%7D)
The maximum velocity is mathematically represented as
![V_{max} = w A](https://tex.z-dn.net/?f=V_%7Bmax%7D%20%20%20%3D%20%20w%20A)
Where A is the amplitude which is mathematically represented as
![A = L sin \theta](https://tex.z-dn.net/?f=A%20%3D%20L%20sin%20%5Ctheta)
So
![V_{max} = \frac{2 \pi }{T } L sin \theta](https://tex.z-dn.net/?f=V_%7Bmax%7D%20%3D%20%5Cfrac%7B2%20%5Cpi%20%7D%7BT%20%7D%20%20L%20sin%20%5Ctheta)
Recall ![T = 2 \pi \sqrt{\frac{L}{g} }](https://tex.z-dn.net/?f=T%20%20%3D%20%202%20%5Cpi%20%5Csqrt%7B%5Cfrac%7BL%7D%7Bg%7D%20%7D)
substituting values
Answer:
a) 6.95 m/s
b) 1.42 seconds
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration due to gravity = 9.81 m/s²
![v^2-u^2=2as\\\Rightarrow -u^2=2as-v^2\\\Rightarrow -u^2=2\times -9.81\times 2.46-0^2\\\Rightarrow u=\sqrt{2\times 9.81\times 2.46}\\\Rightarrow u=6.95\ m/s](https://tex.z-dn.net/?f=v%5E2-u%5E2%3D2as%5C%5C%5CRightarrow%20-u%5E2%3D2as-v%5E2%5C%5C%5CRightarrow%20-u%5E2%3D2%5Ctimes%20-9.81%5Ctimes%202.46-0%5E2%5C%5C%5CRightarrow%20u%3D%5Csqrt%7B2%5Ctimes%209.81%5Ctimes%202.46%7D%5C%5C%5CRightarrow%20u%3D6.95%5C%20m%2Fs)
a) The vertical speed when it leaves the ground. is 6.95 m/s
![v=u+at\\\Rightarrow t=\frac{v-u}{a}\\\Rightarrow t=\frac{0-6.95}{-9.81}\\\Rightarrow t=0.71\ s](https://tex.z-dn.net/?f=v%3Du%2Bat%5C%5C%5CRightarrow%20t%3D%5Cfrac%7Bv-u%7D%7Ba%7D%5C%5C%5CRightarrow%20t%3D%5Cfrac%7B0-6.95%7D%7B-9.81%7D%5C%5C%5CRightarrow%20t%3D0.71%5C%20s)
Time taken to reach the maximum height is 0.71 seconds
![s=ut+\frac{1}{2}at^2\\\Rightarrow 2.46=0t+\frac{1}{2}\times 9.81\times t^2\\\Rightarrow t=\sqrt{\frac{2.46\times 2}{9.81}}\\\Rightarrow t=0.71\ s](https://tex.z-dn.net/?f=s%3Dut%2B%5Cfrac%7B1%7D%7B2%7Dat%5E2%5C%5C%5CRightarrow%202.46%3D0t%2B%5Cfrac%7B1%7D%7B2%7D%5Ctimes%209.81%5Ctimes%20t%5E2%5C%5C%5CRightarrow%20t%3D%5Csqrt%7B%5Cfrac%7B2.46%5Ctimes%202%7D%7B9.81%7D%7D%5C%5C%5CRightarrow%20t%3D0.71%5C%20s)
Time taken to reach the ground from the maximum height is 0.71 seconds
b) Time it stayed in the air is 0.71+0.71 = 1.42 seconds
Because they have different measurements and weight and mass and some measurements are the same
Cody ...
Everything on this page is solved with the SAME formula !
Distance = (speed) x (time) .
Before I get into how to solve each problem, we need to notice that
this whole sheet deals with speed, NOT velocity.
'Velocity' is speed AND THE DIRECTION OF THE MOTION.
Nothing on this page ever mentions direction, so there's no velocity
anywhere on the page.
Your teacher may not be happy if you talk about this on your homework,
but that's too bad. Just don't say "velocity" in any of your answers.
Say "speed", and if the teacher complains about that, then it's time to
let the teacher have it with both barrels.
1). Speed = (distance covered) / (time to cover the distance)
2). Speed = (distance covered) / (time to cover the distance)
3). Distance = (average speed of travel) x (time traveling at that speed)
4). Time to cover the distance = (distance) / (speed)
5). Car's speed = (distance the car covered) / (time the car took)
Sprinter speed = (distance the sprinter covered) / (time the sprinter took)
Calculate the car's speed.
Calculate the sprinter's speed.
... Look at the two speeds.
Decide which one is faster.
... Subtract the slower one from the faster one.
The difference is the answer to "by how much?" .
6). Distance = (speed) x (time spent moving at that speed)
7). Average speed = (TOTAL distance covered)
divided by
(time to cover the TOTAL distance).