Answer:
The net force is zero, so the acceleration is zero
Explanation:
Newton's second law states that the acceleration of an object is proportional to the net force applied to it, according to the equation:
(1)
where
is the net force on the object
m is the mass of the object
a is its acceleration
In this problem, we have a sled acted upon two forces,
. So the net force on the sled is
(2)
however, we are told that the two forces are equal in magnitude but in opposite directions, so
![F_1 = F\\F_2 = -F](https://tex.z-dn.net/?f=F_1%20%3D%20F%5C%5CF_2%20%3D%20-F)
So, eq.(2) becomes
![\sum F = F+(-F) = 0](https://tex.z-dn.net/?f=%5Csum%20F%20%3D%20F%2B%28-F%29%20%3D%200)
and so eq.(1) becomes
![\sum F = ma = 0](https://tex.z-dn.net/?f=%5Csum%20F%20%3D%20ma%20%3D%200)
which means
![a=0](https://tex.z-dn.net/?f=a%3D0)
so the acceleration of the sled is zero, and if the sled was at rest, it will not move.
I will name block a as Ma=5 kg, block b as Mb=10 kg and mass of the pulley M=3 kg and radius as R. Since the system will accelerate in the direction of the block b because it has greater mass, I will take that direction as positive. Both blocks and the pulley have the same acceleration because the slipping on the pulley is neglected. First, the equations of motion:
Mb*g-Tg=MbαR and
Ta-Ma*g=MaαR,
where Ta and Tb are the tensions of the cord, g=9.81 m/s^2 and α is the angular accereration. Also a=αR where a is the acceleration of the system.
Now the equation of rotational dynamics of a solid body:
(Tb-Ta)R=Iα=(1/2)*M*R^2*α, where (1/2)*M*R^2 is the moment of inertia of a disc.
When we input Tb=Mb*g - Mb*α*R and Ta=Ma*g + Ma*α*R from the first two equations into the third we get: (Mb*g - Mb*α*R - Ma*α*R - Ma*g)*R=(1/2)*M*R^2*α.
We solve for α and get: α=(Mb*g-Ma*g)/((1/2)*MR+Mb*R+Ma*R)=2.97 rad/s^2.
We know that a=α*R and we easily get a=0.4455 m/s^2
Answer: degrees divided by 360
Explanation: