Answer:
is correct
Explanation:
in my think, first this due to ray emitted from the light those ray may be affect our skin or party of body.
A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and the speed when t = 4. f(t) = 12t² + 35 t + 1
Answer:
Velocity = 131 m/s
Speed = 131 m/s
Explanation:
Equation of motion, s = f(t) = 12t² + 35 t + 1
To get velocity of the particle, let us find the first derivative of s
v (t) = ds/dt = 24t + 35
At t = 4
v(4) = 24(4) + 35
v(4) = 131 m/s
Speed is the magnitude of velocity. Since the velocity is already positive, speed is also 131 m/s
Answer:
Part a)
![T = 42 N](https://tex.z-dn.net/?f=T%20%3D%2042%20N)
Part b)
![v_f = 11.8 m/s](https://tex.z-dn.net/?f=v_f%20%3D%2011.8%20m%2Fs)
Part c)
![t = 1.7 s](https://tex.z-dn.net/?f=t%20%3D%201.7%20s)
Part d)
![F = 159.7 N](https://tex.z-dn.net/?f=F%20%3D%20159.7%20N)
Explanation:
Part a)
While bucket is falling downwards we have force equation of the bucket given as
![mg - T = ma](https://tex.z-dn.net/?f=mg%20-%20T%20%3D%20ma)
for uniform cylinder we will have
![TR = I\alpha](https://tex.z-dn.net/?f=TR%20%3D%20I%5Calpha)
so we have
![T = \frac{1}{2}MR^2(\frac{a}{R^2})](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B1%7D%7B2%7DMR%5E2%28%5Cfrac%7Ba%7D%7BR%5E2%7D%29)
![T = \frac{1}{2}Ma](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B1%7D%7B2%7DMa)
now we have
![mg = (\frac{M}{2} + m)a](https://tex.z-dn.net/?f=mg%20%3D%20%28%5Cfrac%7BM%7D%7B2%7D%20%2B%20m%29a)
![a = \frac{mg}{(\frac{M}{2} + m)}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7Bmg%7D%7B%28%5Cfrac%7BM%7D%7B2%7D%20%2B%20m%29%7D)
![a = \frac{15 \times 9.81}{(6 + 15)}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B15%20%5Ctimes%209.81%7D%7B%286%20%2B%2015%29%7D)
![a = 7 m/s^2](https://tex.z-dn.net/?f=a%20%3D%207%20m%2Fs%5E2)
now we have
![T = \frac{12 \times 7}{2}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B12%20%5Ctimes%207%7D%7B2%7D)
![T = 42 N](https://tex.z-dn.net/?f=T%20%3D%2042%20N)
Part b)
speed of the bucket can be found using kinematics
so we have
![v_f^2 - v_i^2 = 2 a d](https://tex.z-dn.net/?f=v_f%5E2%20-%20v_i%5E2%20%3D%202%20a%20d)
![v_f^2 - 0 = 2(7)(10)](https://tex.z-dn.net/?f=v_f%5E2%20-%200%20%3D%202%287%29%2810%29)
![v_f = 11.8 m/s](https://tex.z-dn.net/?f=v_f%20%3D%2011.8%20m%2Fs)
Part c)
now in order to find the time of fall we can use another equation
![v_f - v_i = at](https://tex.z-dn.net/?f=v_f%20-%20v_i%20%3D%20at)
![11.8 - 0 = 7 t](https://tex.z-dn.net/?f=11.8%20-%200%20%3D%207%20t)
![t = 1.7 s](https://tex.z-dn.net/?f=t%20%3D%201.7%20s)
Part d)
as we know that cylinder is at rest and not moving downwards
so here we can use force balance
![F = T + Mg](https://tex.z-dn.net/?f=F%20%3D%20T%20%2B%20Mg)
![F = 42 + (12 \times 9.81)](https://tex.z-dn.net/?f=F%20%3D%2042%20%2B%20%2812%20%5Ctimes%209.81%29)
![F = 159.7 N](https://tex.z-dn.net/?f=F%20%3D%20159.7%20N)
Answer:
The final velocity of the bullet is 9 m/s.
Explanation:
We have,
Mass of a bullet is, m = 0.05 kg
Mass of wooden block is, M = 5 kg
Initial speed of bullet, v = 909 m/s
The bullet embeds itself in the block which flies off its stand. Let V is the final velocity of the bullet. The this case, momentum of the system remains conserved. So,
![mv=(m+M)V\\\\V=\dfrac{mv}{m+M}\\\\V=\dfrac{0.05\times 909}{0.050+5}\\\\V=9\ m/s](https://tex.z-dn.net/?f=mv%3D%28m%2BM%29V%5C%5C%5C%5CV%3D%5Cdfrac%7Bmv%7D%7Bm%2BM%7D%5C%5C%5C%5CV%3D%5Cdfrac%7B0.05%5Ctimes%20909%7D%7B0.050%2B5%7D%5C%5C%5C%5CV%3D9%5C%20m%2Fs)
So, the final velocity of the bullet is 9 m/s.
Answer:
Statement 1 and 3 are correct.
Explanation:
1. The mass moves downward, so the net acceleration of the block is straight downward.
2.The mass is sliding through the globe, so only the force of gravity is acting on the mass which pulls it in downward direction. The force of gravity has two components [mg sin∅] and [mg cos∅].