Answer:
![[F]=[MLT^{-2}]](https://tex.z-dn.net/?f=%5BF%5D%3D%5BMLT%5E%7B-2%7D%5D)
Explanation:
Newton’s second law states that the acceleration a of an object is proportional to the force F acting on it is inversely proportional to its mass m. The mathematical expression for the second law of motion is given by :
F = m × a
F is the applied force
m is the mass of the object
a is the acceleration due to gravity
We need to find the dimensions of force. The dimension of force m and a are as follows :
![[m]=[M]](https://tex.z-dn.net/?f=%5Bm%5D%3D%5BM%5D)
![[a]=[LT^{-2}]](https://tex.z-dn.net/?f=%5Ba%5D%3D%5BLT%5E%7B-2%7D%5D)
So, the dimension of force F is, . Hence, this is the required solution.
From reliable sources in the internet, the half-live of carbon-14 is given to be 5,730 years. In a span of 10,000 to 12,000 years, there are almost or little more than 2 half-lives. Thus, there should be
A(t) = A(0)(1/2)^t
where t is the number of half-lives, in this case 2. Thus, only about 1/4 of the original amount will be left.
As long as it sits on the shelf, its potential energy
relative to the floor is . . .
Potential energy = (mass) x (gravity) x (height) =
(3 kg) x (9.8 m/s²) x (0.8m) = <u>23.52 joules</u> .
If it falls from the shelf and lands on the floor, then it has exactly that
same amount of energy when it hits the floor, only now the 23.52 joules
has changed to kinetic energy.
Kinetic energy = (1/2) x (mass) x (speed)²
23.52 joules = (1/2) x (3 kg) x (speed)²
Divide each side by 1.5 kg : 23.52 m²/s² = speed²
Take the square root of each side: speed = √(23.52 m²/s²) = <em>4.85 m/s </em> (rounded)
Answer:
0.775 m
Explanation:
As the car collides with the bumper, all the kinetic energy of the car (K) is converted into elastic potential energy of the bumper (U):
where we have
is the spring constant of the bumper
x is the maximum compression of the bumper
is the mass of the car
is the speed of the car
Solving for x, we find the maximum compression of the spring:
