Answer:
The maximum mass that can fall on the mattress without exceeding the maximum compression distance is 16.6 kg
Explanation:
Hi there!
Due to conservation of energy, the potential energy (PE) of the mass at a height of 3.32 m will be transformed into elastic potential energy (EPE) when it falls on the mattress:
PE = EPE
m · g · h = 1/2 k · x²
Where:
m = mass.
g = acceleration due to gravity.
h = height.
k = spring constant.
x = compression distance
The maximum compression distance is 0.1289 m, then, the maximum elastic potential energy will be the following:
EPE =1/2 k · x²
EPE = 1/2 · 65144 N/m · (0.1289 m)² = 541.2 J
Then, using the equation of gravitational potential energy:
PE = m · g · h = 541.2 J
m = 541.2 J/ g · h
m = 541.2 kg · m²/s² / (9.8 m/s² · 3.32 m)
m = 16.6 kg
The maximum mass that can fall on the mattress without exceeding the maximum compression distance is 16.6 kg.
Answer:
1 N
Explanation:
From coulomb's law,
The force of attraction between two charges is inversely proportional to the square of the distance between the charges.
From the question,
Assuming the charges are the same in both case,
F ∝ /r²....................... Equation 1
Fr² = k
F'r'² = Fr²........................... Equation 2
Where F' = First Force, r'² = First distance, F = second force, r² = second distance.
make F the subject of the equation,
F = F'r'²/r².................... Equation 3
Given: F' = 4 N, r' = 3 m, r = 6 m
Substitute into equation 3
F = 4(3²)/6²
F = 36/36
F = 1 N
The question is incomplete. Here is the complete question.
Three crtaes with various contents are pulled by a force Fpull=3615N across a horizontal, frictionless roller-conveyor system.The group pf boxes accelerates at 1.516m/s2 to the right. Between each adjacent pair of boxes is a force meter that measures the magnitude of the tension in the connecting rope. Between the box of mass m1 and the box of mass m2, the force meter reads F12=1387N. Between the box of mass m2 and box of mass m3, the force meter reads F23=2304N. Assume that the ropes and force meters are massless.
(a) What is the total mass of the three boxes?
(b) What is the mass of each box?
Answer: (a) Total mass = 2384.5kg;
(b) m1 = 915kg;
m2 = 605kg;
m3 = 864.5kg;
Explanation: The image of the boxes is described in the picture below.
(a) The system is moving at a constant acceleration and with a force Fpull. Using Newton's 2nd Law:
Total mass of the system of boxes is 2384.5kg.
(b) For each mass, analyse each box and make them each a free-body diagram.
<u>For </u>
<u>:</u>
The only force acting On the box is force of tension between 1 and 2 and as all the system is moving at a same acceleration.
= 915kg
<u>For </u>
<u>:</u>
There are two forces acting on : tension caused by box 1 and tension caused by box 3. Positive referential is to the right (because it's the movement's direction), so force caused by 1 is opposing force caused by 3:
= 605kg
<u>For </u>
<u>:</u>
= 864.5kg
Answer:
F = 100 N
Explanation:
The torque is given by the expression
τ = F x r
where bold letters indicate vectors, the magnitude of this expression is
τ = F r sin θ
In general, when tightening a nut, the force is applied perpendicular to the arm, therefore θ = 90 and sin 90 = 1
τ = F r
F = τ / r
calculate
F = 30 / 0.30
F = 100 N
From our studies of the work of Professor Newton,
we have learned that
F = M a .
That is, the product of an object's mass and its acceleration
is equal to the net force acting on it.
An object in equilibrium is an object that has no acceleration.
In other words, it may be moving in a straight line at a speed
that does not change, or it may be just lying there before us.
In either case, since the object has no acceleration, we glance
at Newton's formula, and we instantly realize that the net force
on the object must be ZERO.
The object behaves just as if there were NO forces acting on it at all.
