Answer:
The greatest common factor (GCF) is the greatest factor that is common to two or more numbers (they share it). The greatest common factor of two (or more) numbers is the product of all the prime factors the numbers have in common.
Explanation:
Answer:
x(t) = d*cos ( wt )
w = √(k/m)
Explanation:
Given:-
- The mass of block = m
- The spring constant = k
- The initial displacement = xi = d
Find:-
- The expression for displacement (x) as function of time (t).
Solution:-
- Consider the block as system which is initially displaced with amount (x = d) to left and then released from rest over a frictionless surface and undergoes SHM. There is only one force acting on the block i.e restoring force of the spring F = -kx in opposite direction to the motion.
- We apply the Newton's equation of motion in horizontal direction.
F = ma
-kx = ma
-kx = mx''
mx'' + kx = 0
- Solve the Auxiliary equation for the ODE above:
ms^2 + k = 0
s^2 + (k/m) = 0
s = +/- √(k/m) i = +/- w i
- The complementary solution for complex roots is:
x(t) = [ A*cos ( wt ) + B*sin ( wt ) ]
- The given initial conditions are:
x(0) = d
d = [ A*cos ( 0 ) + B*sin ( 0 ) ]
d = A
x'(0) = 0
x'(t) = -Aw*sin (wt) + Bw*cos(wt)
0 = -Aw*sin (0) + Bw*cos(0)
B = 0
- The required displacement-time relationship for SHM:
x(t) = d*cos ( wt )
w = √(k/m)
Answer: 1200 kg
Explanation: Taking into account the Newton's second law, the mass of the vehicle is 1200 kg.
In first place, acceleration in a body occurs when a force acts on a body. There are two factors that influence the acceleration of an object: the net force acting on it and the mass of the body.
Newton's second law states that this force will change the speed of an object because the speed and / or direction will change. These changes in velocity are called acceleration.
So, Newton's second law defines the relationship between force and acceleration mathematically. This law says that the acceleration of an object is directly proportional to the sum of all the forces acting on it and inversely proportional to the mass of the object.
Mathematically, Newton's second law is expressed as:
F= m×a
where:
F = Force [N]
m = Mass [kg]
a = Acceleration [m/s²]
In this case, you know:
F= 1800 N
m= ?
a= 1.5 m/s²
Replacing:
1800 N= m× 1.5 m/s²
Solving:
m= 1800 N÷1.5 m/s²
m= 1200 kg
Finally, the mass of the vehicle is 1200 kg.
Answer:
because it weighs more than water
