Answer:
A) 6.5 m/s²
Explanation:
Mass of the bucket, m = 3.0 kg
depth of the well, d = 10 m
tension on the rope, T = 9.8 N
The net downward force on the bucket is given as;
T = mg - ma
where;
a is downward acceleration of the bucket
9.8 = (3 x 9.8) - 3a
9.8 = 29.4 - 3a
3a = 29.4 - 9.8
3a = 19.6
a = 19.6 / 3
a = 6.53 m/s² downwards
Therefore, the acceleration of the bucket is 6.53 m/s² downwards
Answer:
So airplane will be 1324.9453 m apart after 2.9 hour
Explanation:
So if we draw the vectors of a 2d graph we see that the difference in angles is = 83 - 44.3 =
Distance traveled by first plane = 730×2.9 = 2117 m
And distance traveled by second plane = 590×2.9 = 1711 m
We represent these distances as two sides of the triangle, and the distance between the planes as the side opposing the angle 38.7.
Using the law of cosine, representing the distance between the planes, we see that:
d = 1324.9453 m
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:
275 kPa
Explanation:
mass of the gas=m=1.5 kg
initial volume if the gas=V₁=0.04 m³
initial pressure of the gas= P₁=550 kPa
as the condition is given final volume is double the initial volume
V₂=final volume
V₂=2 V₁
As the temperature is constant
T₁=T₂=T
=
putting the values in the equation.
=
P₂=
P₂=
P₂=275 kPa
So the final pressure of the gas is 275 kPa.
Answer:
Change in velocity, change in direction, change in both velocity and direction
Explanation: