Answer:
x = 0.12 m
Explanation:
Let k be the spring force constant , x be the compression displacement of the spring and v be the speed of the box.
when the box encounters the spring, all the energy of the box is kinetic energy:
the energy relationship between the box and the spring is given by:
1/2(m)×(v^2) = 1/2(k)×(x^2)
(m)×(v^2) = (k)×(x^2)
x^2 = [(m)(v^2)]/k
x = \sqrt{ [(m)(v^2)]/k}
x = \sqrt{ [(0.299)((1.44)^2)]/(44.9)}
x = 0.12 m
Therefore, the mass will travel 0.12 m and come to rest.
= 0.491 m/s
Answer:
<h2>
2113 seconds</h2>
Explanation:
The general decay equation is given as
, then;
where;
is the fraction of the radioactive substance present = 1/16
is the decay constant
t is the time taken for decay to occur = 8,450s
Before we can find the half life of the material, we need to get the decay constant first.
Substituting the given values into the formula above, we will have;

Half life f the material is expressed as 


Hence, the half life of the material is approximately 2113 seconds
Answer:


Explanation:
Given that.
Force acting on the particle, 
Position of the particle, 
To find,
(a) Torque on the particle about the origin.
(b) The angle between the directions of r and F
Solution,
(a) Torque acting on the particle is a scalar quantity. It is given by the cross product of force and position. It is given by :




So, the torque on the particle about the origin is (32 N-m).
(b) Magnitude of r, 
Magnitude of F, 
Using dot product formula,




Therefore, this is the required solution.
Answer:
The tension in the string connecting block 50 to block 51 is 50 N.
Explanation:
Given that,
Number of block = 100
Force = 100 N
let m be the mass of each block.
We need to calculate the net force acting on the 100th block
Using second law of newton



We need to calculate the tension in the string between blocks 99 and 100
Using formula of force


We need to calculate the total number of masses attached to the string
Using formula for mass


We need to calculate the tension in the string connecting block 50 to block 51
Using formula of tension

Put the value into the formula



Hence, The tension in the string connecting block 50 to block 51 is 50 N.
Depends on what type of gass