Answer:
The final angular speed is 0.223 rad/s
Explanation:
By the conservation of angular moment:
ΔL=0
L₁=L₂
L₁ is the initial angular moment
L₂ is the final angular moment
L₁ is given by:
As the door is at rest its angular moment is zero and the angular moment of mud can be considered as a point object, then:
where
r is the distance from the support point to the axis of rotation (the mud hits at the center of the door; r=0.5 m)
v is the speed
m is the mass of the mud
L₂ is given by:
ωf is the final angular speed
The moment of inertia of the door can be considered as a rectangular plate:
M is the mass of the door
W is the width of the door
The moment of inertia of the mud is:
Hence,
The net force on the cart is
Force = (mass) x (acceleration) .
We know the mass = 1.5 kilogram, but we need to
calculate the acceleration.
Acceleration = (change in speed) / (time for the change)
Change in speed = (ending speed) minus (beginning speed)
= ( 0 ) - ( 2 m/s ) = -2 m/s
Acceleration = (change in speed) / (time for the change)
= ( -2 m/s ) / (3 sec)
= - 2/3 m/s² .
Finally ... Net force = (mass) x (acceleration)
= (1.5 kilogram) x ( - 2/3 m/s²)
= ( - 3/2 x 2/3 ) (kg-m/s²)
= - 1 newton .
The negative sign on the force means the force is applied
opposite to the direction the cart is moving. That gives
negative acceleration (slowing down), and the cart
eventually stops.
Answer:
Positive z direction.
Explanation:
The magnetic force acting on the electron is given by the formula as :
q is the charge on proton
v is the speed of proton
B is the magnetic field
It is mentioned that the proton is moving with a velocity in the positive x-direction. The uniform magnetic field B in the positive y-direction such taht,
q = +e
v = vi
B = Bj
Since, 
So, the magnetic force acting on the proton in positive z axis. Hence, the correct option is (d) "positive z direction".
Answer:
18 J
Explanation:
Work done: This can be defined as the product of force and distance acting on a body. The S. I unit of work is Joules (J)
From the question, the work that must be done in bringing the block to rest is equal to the kinetic energy of the block.
Ek = 1/2mv².................... Equation 1
Where Ek = kinetic eenrgy m = mass of the block, v = velocity of the block.
Given: m = 4 kg, v = 3 m/s.
Substituting into equation 1
Ek = 1/2(4)(3²)
Ek = 2(9)
Ek = 18 J.
Thus the work that must me done on the block to bring it to rest = 18 J.
Answer:
See the answers below.
Explanation:
To solve this problem we must use the following equation of kinematics.
where:
Vf = final velocity = 10 [m/s]
Vo = initial velocity = 40 [m/s]
t = time = 5 [s]
a = acceleration [m/s²]
Now replacing:
![10=40-a*5\\40-10=a*5\\30=5*a\\a=6[m/s^{2}]](https://tex.z-dn.net/?f=10%3D40-a%2A5%5C%5C40-10%3Da%2A5%5C%5C30%3D5%2Aa%5C%5Ca%3D6%5Bm%2Fs%5E%7B2%7D%5D)
Note: The negative sign in the above equation means that the velecity is decreasing.
2)
To solve this second part we must use the following equation of kinematics.
where:
x = distance [m]
![(10)^{2} =(40)^{2} -2*6*x\\100=1600-12*x\\12*x=1600-100\\12*x=1500\\x=125[m]](https://tex.z-dn.net/?f=%2810%29%5E%7B2%7D%20%3D%2840%29%5E%7B2%7D%20-2%2A6%2Ax%5C%5C100%3D1600-12%2Ax%5C%5C12%2Ax%3D1600-100%5C%5C12%2Ax%3D1500%5C%5Cx%3D125%5Bm%5D)
