Answer:
a) 
b) 
c) Compressing is easier
Explanation:
Given:
Expression of force:
where:
when the spring is stretched
when the spring is compressed
hence,
a)
From the work energy equivalence the work done is equal to the spring potential energy:
here the spring is stretched so, 
Now,
The spring constant at this instant:
Now work done:
b)
When compressing the spring by 0.05 m
we have, 
<u>The spring constant at this instant:</u>
Now work done:
c)
Since the work done in case of stretching the spring is greater in magnitude than the work done in compressing the spring through the same deflection. So, the compression of the spring is easier than its stretching.
Answer:
The gravitational force exerted on the object is 75 N (answer D)
Explanation:
Hi there!
The gravitational force is calculated as follows:
F = m · g
Where:
F = force of gravity.
m = mass of the object.
g = acceleration due to gravity (unknown).
For a falling object moving in a straight line, its height at a given time can be calculated using the following equation:
y = y0 + v0 · t + 1/2 · a · t²
Where:
y = position at time t.
y0 = initial position.
v0 = initial velocity.
t = time.
g = acceleration due to gravity.
Let´s place the origin of the frame of reference at the point where the object is released so that y0 = 0. Let´s also consider the downward direction as negative.
Then, after 2 seconds, the height of the object will be -30 m:
y = y0 + v0 · t + 1/2 · g · t²
-30 m = 0 m + 0 m/s · 2 s + 1/2 · g · (2 s)²
-30 m = 1/2 · g · 4 s²
-30 m = 2 s ² · g
-30 m/2 s² = g
g = -15 m/s²
Then, the magnitude of the gravitational force will be:
F = m · g
F = 5 kg · 15 m/s²
F = 75 N
The gravitational force exerted on the object is 75 N (answer D)
Have a nice day!
Answer:
Intensity of beam 18 feet below the surface is about 0.02%
Explanation:
Using Lambert's law
Let dI / dt = kI, where k is a proportionality constant, I is intensity of incident light and t is thickness of the medium
then dI / I = kdt
taking log,
ln(I) = kt + ln C
I = Ce^kt
t=0=>I=I(0)=>C=I(0)
I = I(0)e^kt
t=3 & I=0.25I(0)=>0.25=e^3k
k = ln(0.25)/3
k = -1.386/3
k = -0.4621
I = I(0)e^(-0.4621t)
I(18) = I(0)e^(-0.4621*18)
I(18) = 0.00024413I(0)
Intensity of beam 18 feet below the surface is about 0.2%
Answer:
Change in kinetic energy is ( 26CL³)/3
Explanation:
Given :
Net force applied, F(x) = Cx² ....(1)
Displacement of the particle from xi = L to xf = 3L.
The work-energy theorem states that change in kinetic energy of the particle is equal to the net amount of work is done to displace the particle.
That is,
ΔK = W = ∫F·dx
Substitute equation (1) in the above equation.
ΔK = ∫Cx²dx
The limit of integration from xi = L to xf = 3L, so
Substitute the values of xi and xf in the above equation.
Answer:
a) Fₓ = 23.5 N
b) Net force = Fₓ
Explanation:
An image of the question as described is attached to this solution.
From the image attached, the forces acting on the box include the weight of the box, the normal reaction of the surface on the box, the applied force on the box and the Frictional force opposing the motion of the box (which is negligible and equal to 0)
a) From the diagram, the horizontal component of the force is
Fₓ = 25 cos 20° = 23.49 N = 25 N
b) Again, from the diagram attached, doing a force balance on the box, in the horizontal direction, we obtain
Net force = Fₓ - Frictional force
But frictional force is 0 N
Net force = Fₓ
Hope this Helps!!!
