Answer:
68.8 N 13.8°N of W
Explanation:
F₁ is 50 N 30°N of W. The terminal angle is 150°.
F₂ is 25 N 20°S of W. The terminal angle is -160°.
Graphically, you can add the vectors using head-to-tail method. Move F₂ so that the tail of the vector is at the head of F₁. The resultant vector will be from the tail of F₁ to the head of F₂.
Algebraically, find the x and y components of each vector.
F₁ₓ = 50 N cos(150°) = -43.3 N
F₁ᵧ = 50 N sin(150°) = 25 N
F₂ₓ = 25 N cos(-160°) = -23.5 N
F₂ᵧ = 25 N sin(-160°) = -8.6 N
The x and y components of the resultant vector are the sums:
Fₓ = -43.3 N + -23.5 N = -66.8 N
Fᵧ = 25 N + -8.6 N = 16.4 N
The magnitude of the resultant force is:
F = √(Fₓ² + Fᵧ²)
F = √((-66.8 N)² + (16.4 N)²)
F = 68.8 N
The direction of the resultant force is:
θ = tan⁻¹(Fᵧ / Fₓ)
θ = tan⁻¹(16.4 N / -66.8 N)
θ = 166.2°
θ = 13.8°N of W
Answer:
Explanation:
Compression
The region in a medium where the distance between the vibrating molecules is minimum is compression.
This is the region with higher air pressure than the surrounding .
Rarefaction
The region in a medium where the distance between the vibrating molecules is maximum is rarefaction.
This is the region with relatively low air pressure.
hope it helps :)
Answer:
See below
Explanation:
At point A the PE = mgh = 2 * 10 * 1 = 20 J
at point B, all of the PE , 20 J , is converted to Kinetic Energy
KE = 1/2 m v^2
20 = 1/2 (2)(v^2 )
20 = v^2 v = sqrt 20 = 4.47 m/s
for the friction part
vf = vo t + 1/2 a t^2 vf = final velocity = 0 (stopped)
vo = original velocity = 4.47 m/s
a = -1 m/s^2
0 = 4.47 t + 1/2 (-1) t^2
- .5t^2 + 4.47 t = 0
t ( -.5t+ 4.47) = 0 shows t = 4.47/.5 = 8.9 seconds
Answer:
a) Eg = 3,060.72 j
b) Ek = 2,080 j
c) Etotal = 5,140.72 j
Explanation:
The given parameters are;
The mass of the person, m = 65 kg
The height of the person, h = 4.8 m
The speed of the person, v = 8.0 m/s
a) The gravitational potential energy, 
= m·g·h
Where;
g = The acceleration due to gravity ≈ 9.81 m/s²
∴ Eg = 65 kg × 9.81 m/s² × 4.8 m = 3,060.72 j
Eg = 3,060.72 j
b) The kinetic energy, Ek = 1/2·m·v²
∴ Ek = 1/2 × 65 kg × (8.0 m/s)² = 2,080 j
Ek = 2,080 j
c) The constant total Mechanical Energy, Etotal = Eg + Ek
∴ Etotal = 3,060.72 j + 2,080 j = 5,140.72 j
Etotal = 5,140.72 j.
Answer:
(a) Stiffness is measured by Young modulus
(b) Strength is measured as tensile stress in force per unit area
(c) Ductility is measured by elongation and reduction of area.
(d) Toughness is measured by the amount of energy that a unit volume of the material has absorbed after being stressed up to the point of fracture.
(e) Hardness is obtained by measuring the size of the impression left by an indenter
Explanation:
Mechanical properties are helpful in determining whether or not a material can be produced in the desired shape and also resist the mechanical forces anticipated.
Given mechanical properties of metals and how they are measured is as follows:
(a) Stiffness is the ability of a material to resist deformation under stress. It is measured by Young modulus
(b) Strength is the ability of a material to resist the externally applied forces without breaking or yielding. It is measured as tensile stress in force per unit area
(c) Ductility is the property of a material enabling it to be drawn into a wire with the application of a tensile force. It is measured by elongation and reduction of area.
(d) Toughness is the property of a material to resist fracture due to high impact. It is measured by the amount of energy that a unit volume of the material has absorbed after being stressed up to the point of fracture.
(e) Hardness is the property of a metal, which gives it the ability to resist being permanently deformed, when a load is applied. It is obtained by measuring the size of the impression left by an indenter
