Answer:
31.42383 m/s
Explanation:
g = Acceleration due to gravity = 9.81 m/s²
= Coefficient of kinetic friction = 0.48
s = Displacement = 0.935 m
= Mass of bean bag = 0.354 kg
= Mass of empty crate = 3.77 kg
= Speed of the bean bag
= Speed of the crate
Acceleration


From equation of motion

In this system the momentum is conserved

The speed of the bean bag is 31.42383 m/s
Answer:
T=4.24 N.m
Explanation:
Torque is equal to force for distance for sinus of the angle between the direction of the force and the distance, the distance between the mass and the pivot is 1 m, and to obtain the force that is the mass for the gravity in this case, we need to know the component that produces a torque in the pivot
F=0.5 kg* 9.8 m/
= 4.9 N
and we decompose the force in parallel direction to the rod and perpendicular direction to the rod, the magnitude that produces torque is the perpendicular component, because the torque is in function of the sinus
so, we obtain -> Fy= 4.9 N*sin(60)= 4.24 N
and, T= (4.24 N)*(1 m)*(Sin(90))= 4.24 N.m
anothe way to do it is,
T= (4.9 N)*(1 m)*(Sin(60))= 4.24 N.m, and we obtain the same result
Answer:
The velocity of wind with respect to cyclist is
.
Explanation:
speed of cyclist = 12 km/h east
speed of wind = 5 km/h south west
Write the speeds in the vector form

The velocity of wind with respect to cyclist is

To solve this problem we will apply the concepts related to energy conservation, so the potential energy in the package must be equivalent to its kinetic energy. From there we will find the speed of the package in the vertical component. The horizontal component is given, as it is the same as the one the plane is traveling to. Vectorially we will end up finding its magnitude. So,


Here,
m = Mass
g = Gravity
h = Height
v = Velocity
Rearranging to find the velocity

Replacing,


Using the vector properties the magnitude of the velocity vector would be given by,



Therefore the package is moving to 66.2m/s
Answer:
The magnetic field strength due to current flowing in the wire is9.322 x 10⁻⁶ T.
Explanation:
Given;
electric current, I = 21.3 A
distance of the magnetic field from the wire, R = 45.7 cm = 0.457 m
The strength of the resulting magnetic field at the given distance is calculated as;

Where;
μ₀ is permeability of free space = 4π x 10⁻⁷ T.m/A

Therefore, the magnetic field strength due to current flowing in the wire is 9.322 x 10⁻⁶ T.