The different in size of each of the rope's pullers, correspond to a difference in the magnitude of the applied force, such that
1 answer:
Answer:
F = - 50 N
Hence, the magnitude of resultant force is 50 N and its direction is leftwards.
Explanation:
The magnitude of the resultant force is always equal to the sum of all forces. While, the direction of resultant force will be equal to the direction of the force with greater magnitude:
considering right direction to be positive:
F₁ = Force applied on right rope = 150 N
F₂ = Force applied on left rope = 200 N
Therefore, the resultant force can be found by using these values in equation:
<u>F = - 50 N</u>
<u>Hence, the magnitude of resultant force is 50 N and its direction is leftwards.</u>
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Answer:
The speed of the student just before she lands, v₂ is approximately 8.225 m/s
Explanation:
The given parameters are;
The mass of the physic student, m = 43.0 kg
The height at which the student is standing, h = 12.0 m
The radius of the wheel, r = 0.300 m
The moment of inertia of the wheel, I = 9.60 kg·m²
The initial potential energy of the female student, P.E.₁ = m·g·h₁
Where;
m = 43.0 kg
g = The acceleration due to gravity ≈ 9.81 m/s²
h = 12.0 h
∴ P.E.₁ = 43 kg × 9.81 m/s² × 12.0 m = 5061.96 J
The kinetic rotational energy of the wheel and kinetic energy of the student supporting herself from the rope she grabs and steps off the roof, K₁, is given as follows;
The initial kinetic energy, 1/2·m·v₁² and the initial kinetic rotational energy, 1/2·m·ω₁² are 0
∴ K₁ = 0 + 0 = 0
The final potential energy of the student when lands. P.E.₂ = m·g·h₂ = 0
Where;
h₂ = 0 m
The final kinetic energy, K₂, of the wheel and student is give as follows;
Where;
v₂ = The speed of the student just before she lands
ω₂ = The angular velocity of the wheel just before she lands
By the conservation of energy, we have;
P.E.₁ + K₁ = P.E.₂ + K₂
∴ m·g·h₁ + = m·g·h₂ +
Where;
ω₂ = v₂/r
∴ 5061.96 J + 0 = 0 +
5,061.96 J = 21.5 kg × v₂² + 53. kg × v₂² = 21.5 kg × v₂² + 160/3 kg × v₂²
v₂² = 5,061.96 J/(21.5 kg + 160/3 kg) ≈ 67.643118 m²/s²
v₂ ≈ √(67.643118 m²/s²) ≈ 8.22454363 m/s
The speed of the student just before she lands, v₂ ≈ 8.225 m/s.
The total average velocity 
(I assume west as positive direction) is given by the total displacement, S, divided by the total time taken, t:
where:
-The total displacement S is the algebraic sum of the displacement in the first part of the motion (
, due west) and of the displacement in the second part of the motion (
, due east).
-The total time taken t is the time taken for the first part of the motion,
, and the time taken for the second part of the motion, 
. can be found by using the average velocity and the displacement of the first part:
, instead, can be written as 
, where 
is the average velocity of the second part of the motion (with a negative sign, since it is due east).
Therefore, we can rewrite the initial equation as:
And by solving it, we find the displacement in the second part of the motion (i.e. how far did the backpacker move east):
where:
-The total displacement S is the algebraic sum of the displacement in the first part of the motion (
-The total time taken t is the time taken for the first part of the motion,
Therefore, we can rewrite the initial equation as:
And by solving it, we find the displacement in the second part of the motion (i.e. how far did the backpacker move east):
Complete Question
The complete question is shown on the first and second uploaded image
Answer:
The velocity is
Explanation:
The kinetic energy of the 9 kg can be determined by these expression
Kinetic energy of 9 kg block = initial energy stored - energy lost as a result of friction
Now to obtain the initial energy stored
Let U denote the initial energy stored and
Where x is the length the spring is displaced
k is the force constant of the string
Now referring to the formula above
i.e Kinetic energy of 9 kg block = initial energy stored - energy lost as a result of friction
and we are told that coefficient of friction = 0.4 and the mass is 9 kg ,the acceleration due to gravity this displacement length of spring = 0.6
Therefore
