Answer:
F = 183.153 N
Explanation:
given,
mass of the toothpick = 0.12 g = 0.00012 kg
initial velocity = 227 m/s
final velocity = 0 m/s
penetration depth = 16 mm = 0.016 m
using the equation of motion
v² - u² = 2 a s
0 - u² = 2 a s
- 221² = 2 × a × 0.016
a = 1526281.25 m/s²
Force is equal to
F = m a
= 0.00012 × 1526281.25
F = 183.153 N
Answer:
Compression in the spring, x = 3.7 cm
Explanation:
It is given that,
Mass of the book, m = 1.6 kg
It can be assumed the spring constant of the spring is, k = 840 N/m
As the book moves down, the change in potential energy of the book is converted to spring potential energy of compression. The mathematical expression is as follows :


x = 0.037 meters
or
x = 3.7 cm
So, the spring is compressed to a distance of 3.7 cm. Hence, this is the required solution.
Answer:
d = 2,042 10-3 m
Explanation:
The laser diffracts in the circular slit, so the process equation is
d sin θ= m λ
The first diffraction minimum occurs for m = 1
We can use trigonometry in the mirror
tan θ = Y / L
Where L is the distance from the Moon to Earth
Since the angle is extremely small
tan θ = sin θ / cos θ
Cos θ = 1
tant θ = sin θ = y / L
We replace
d y / L = λ
d = λ L / y
Let's calculate
d = 532 10⁻⁹ 3.84 10⁶/1 10³
d = 2,042 10-3 m