Answer:
x(t) = - 6 cos 2t
Explanation:
Force of spring = - kx
k= spring constant
x= distance traveled by compressing
But force = mass × acceleration
==> Force = m × d²x/dt²
===> md²x/dt² = -kx
==> md²x/dt² + kx=0 ------------------------(1)
Now Again, by Hook's law
Force = -kx
==> 960=-k × 400
==> -k =960 /4 =240 N/m
ignoring -ve sign k= 240 N/m
Put given data in eq (1)
We get
60d²x/dt² + 240x=0
==> d²x/dt² + 4x=0
General solution for this differential eq is;
x(t) = A cos 2t + B sin 2t ------------------------(2)
Now initially
position of mass spring
at time = 0 sec
x (0) = 0 m
initial velocity v= = dx/dt= 6m/s
from (2) we have;
dx/dt= -2Asin 2t +2B cost 2t = v(t) --- (3)
put t =0 and dx/dt = v(0) = -6 we get;
-2A sin 2(0)+2Bcos(0) =-6
==> 2B = -6
B= -3
Putting B = 3 in eq (2) and ignoring first term (because it is not possible to find value of A with given initial conditions) - we get
x(t) = - 6 cos 2t
==>
Answer:
v = 2591.83 m/s
Explanation:
Given that,
The electric field is 1.27 kV/m and the magnetic field is 0.49 T. We need to find the electron's speed if the fields are perpendicular to each other. The magnetic force is balanced by the electric force such that,
So, the speed of the electron is 2591.83 m/s.
Answer:
2 m/s
Explanation:
= Mass of red truck = 1000 kg
= Mass of green truck= 3000 kg
= Initial Velocity of red truck = 6 m/s
= Initial Velocity of green truck
= Velocity with which they move together = 0
For elastic collision
Velocity of the green truck is 2 m/s
Answer:
P= 390 W
Explanation:
In physics, power is the rate of doing work or of transferring heat, i.e. the amount of energy transferred or converted per unit time. Work is a force F applied over a distance x. Matemathicaly it means
P = dW/dt ≈ d(F * x)/dt = xdF/dt + Fdx/dt. If force is constant dF/dt=0 so P=F dx/dt = P*v, where v is velocity, the rate of distance per unit time.
We have force and velocity. Newton is unit of Kg*m/s2, hence
P= 150 kgm/s2 * 2.6 m/s =390 Kgm2/s3 = 390 W, where W is Watts and is an unit of power
