Answer:
elative magnitude of the two forces is the same and they are applied in a constant direction.
Explanation:
Newton's second law states that the sum of the forces is equal to the mass times the acceleration
∑ F = m a
in this case there are two forces on the x axis
F_applied - fr = 0
since they indicate that the velocity is constant, consequently
F_applied = fr
the relative magnitude of the two forces is the same and they are applied in a constant direction.
Answer:
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Explanation:
Strain energy is defined as the energy stored in a body due to deformation. The strain energy per unit volume is known as strain energy density and the area under the stress-strain curve towards the point of deformation. When the applied force is released, the whole system returns to its original shape.
Answer:
The expression would be ω =
Explanation:
Given that ω is the angular velocity
g is the acceleration due to gravity
L is the length
θ is the angle of downward tilt
For an object we compare the horizontal and vertical component of the forces acting on the body;
For vertical component
T sinθ = mg............1
For the horizontal component
T cos θ = .............2
R is our radius and is = L cos θ
v = ωR
substituting into equation 2 we have
T cos θ = m(ωR /R
T cos θ=m(ωR ..................3
Now comparing the vertical and the horizontal component we have;
equation 1 divided by equation 3 we have
T sin θ /T cos θ = mg / m(ωR
Tan θ = g / (ωR............4
Making ω the subject formula we have;
(ω = g/ R Tan θ
But R = L cos θ and Tan θ = sin θ/ cosθ
putting into equation 4 we have;
(ω = g /[( L cos θ) x( sin θ/ cosθ)]
(ω = g/ L sinθ
ω =
Therefor the expression for the angular velocity ω in terms of g, L and angle θ would be ω =
Answer:
Force,
Explanation:
It is given that,
Length of the room, l = 4 m
breadth of the room, b = 5 m
Height of the room, h = 3 m
Atmospheric pressure,
We know that the force acting per unit area is called pressure exerted. Its formula is given by :
So, the total force on the floor due to the air above the surface is . Hence, this is the required solution.
The height of the building is 60 m.
The velocity of the ball should be provided by
v = u + gt
here,
u is the initial velocity of the ball = 0
v = 0 + 9.8 x 3.5
v = 34.3 m/s
Now
When the ball hits the ground, energy is conserved;
mgh = ¹/₂mv²
gh = ¹/₂v²
h = (0.5 v²) / g
h = (0.5 x 34.3²) / (9.8)
h = 60.025 m
h = 60 m
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Answer:
The height of the building is 60 m.
Explanation:
Given;
mass of the mass of the ball, m = 3 kg
time of motion, t = 3.5 s
The velocity of the ball is given by;
v = u + gt
where;
u is the initial velocity of the ball = 0
v = 0 + 9.8 x 3.5
v = 34.3 m/s
When the ball hits the ground, energy is conserved;
mgh = ¹/₂mv²
gh = ¹/₂v²
h = (0.5 v²) / g
h = (0.5 x 34.3²) / (9.8)
h = 60.025 m
h = 60 m
Therefore, the height of the building is 60 m.
The extension of the spring in the elevator is 60 mm.
For the extension of the spring to be zero, the elevator must be moving downwards under free fall.
The given parameters;
The spring constant is calculated as follows;
F = kx
mg = kx
The tension on the spring in an elevator accelerating upwards is calculated as follows;
T = mg + ma
T = m(g + a)
T = 5(9.8 + 2)
T = 59 N
The extension of the spring is calculated as follows;
For the extension of the spring to be zero, the elevator must be under free fall, such that the tension on the spring is zero.
For free fall, a = g
T = m(g - a) = 0
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Answer:
a) the spring will stretch 60.19 mm with the same box attached as it accelerates upwards
b) spring will be relaxed when the elevator accelerates downwards at 9.81 m/s²
Explanation:
Given that;
Gravitational acceleration g = 9.81 m/s²
Mass m = 5 kg
Extension of the spring X = 50 mm = 0.05 m
Spring constant k = ?
we know that;
mg = kX
5 × 9.81 = k(0.05)
k = 981 N/m
a)
Given that; Acceleration of the elevator a = 2 m/s² upwards
Extension of the spring in this situation = X1
Force exerted by the spring = F
we know that;
ma = F - mg
ma = kX1 - mg
we substitute
5 × 2 = 981 × X1 - (5 ×9.81 )
X1 = 0.06019 m
X1 = 60.19 mm
Therefore the spring will stretch 60.19 mm with the same box attached as it accelerates upwards
B)
Acceleration of the elevator = a
The spring is relaxed i.e, it is not exerting any force on the box.
Only the weight force of the box is exerted on the box.
ma = mg
a = g
a = 9.81 m/s² downwards.
Therefore spring will be relaxed when the elevator accelerates downwards at 9.81 m/s²