force in component form is given as
F~ = Fx ˆı + Fy ˆj
given that : Fx = 4 N, Fy = −3 N
hence the force equation looks like
F~ = 4 ˆı + (- 3) ˆj
F~ = 4 ˆı - 3 ˆj
displacement is given as
~s = sx ˆı + sy ˆj
given that : sx = 1 m, and sy = 1 m
hence the displacement is given as
~s = 1 ˆı + 1 ˆj
work done is the dot product of force and displacement . hence work done is given as
W = F~.~s
W = (4 ˆı - 3 ˆj) . (1 ˆı + 1 ˆj )
W = (4 x 1) ( ˆı.ˆı) - (3 x 1) (ˆj.ˆj)
W = 4 - 3
W = 1 J
θ = angle between F~ and ~s = ?
hence the work done by the force comes out to be 1 J
|F~| = magnitude of force = sqrt(Fx² + Fy²) = sqrt((4)² + (-3)²) = 5 N
|~s| = magnitude of displacement = sqrt(sx² + sy²) = sqrt((1)² + (1)²) = sqrt(2)
we know that work done is given as
W = |F~| |~s| Cosθ
1 = (5) (sqrt(2) Cosθ
Cosθ = 0.142
θ = Cos⁻¹(0.142)
θ = 81.84 deg
Impulse equals Change in Momentum
F = average applied force = to be determined
Δt = time during which the force is applied = 0.50 s
m = mass = 1,700 kg
Δp = change in momentum = to be determined
Δv = change in velocity = to be determined
v1 = initial velocity = 50.0 km/h = 50,000 m/h = 13.9 m/s
v2 = final velocity = 0.00 km/h = 0.00 m/s
F∙Δt = Δp
F∙Δt = m∙Δv
F∙Δt = m∙(v2 - v1)
F = m∙(v2 - v1) / Δt
F = 1,700 kg∙(0.00 m/s - 13.9 m/s) / 0.50 s
<span>F = -47,222 N The negative sign means that the force vector is </span>
<span>applied AGAINST the momentum vector of the rhinoceros.</span>
Answer:
22.4 cm
Explanation:
The total mechanical energy of the particle Etot = K + U where K = kinetic energy = 1/2mv² where m = mass of particle = 100 g =0.1 kg and v = speed of particle = 2 m/s and U = potential energy = 1/2kx² where k = spring constant and x = displacement
Etot = K + U
U = Etot - K
U = Etot - 1/2mv²
Since Etot = 0.45 J, substituting the values of the other variables into the equation, we have
U = Etot - 1/2mv²
U = 0.45 J - 1/2 × 0.1 kg × (2 m/s)²
U = 0.45 J - 1/2 × 0.1 kg × 4 m²/s²
U = 0.45 J - 0.1 kg × 2 m²/s²
U = 0.45 J - 0.2 J
U = 0.25 J
Now U = 1/2kx² and the angular frequency ω = √(k/m) ⇒ ω²m = k
So, U = 1/2ω²mx²
x² = 2U/ω²m
x = (√2U/m)/ω
since ω = 10 rad/s, substituting the values of the variables into the equation, we have
x = (√2U/m)/ω
x = (√2 × 0.25 J/0.1 kg)/10 rad/s
x = (√0.5 J/0.1 kg)/10 rad/s
x = (√5 J/kg)/10 rad/s
x = 2.24/10 m
x = 0.224 m
x = 22.4 cm
Answer:
“So while yes, it is true that fat doesn't transform into energy… it is the transformation of fat into carbon dioxide that creates energy.” She says when our bodies give the signal that it needs more energy, lipase in fat cells helps release the fat into circulation
Explanation:
“So while yes, it is true that fat doesn't transform into energy… it is the transformation of fat into carbon dioxide that creates energy.” She says when our bodies give the signal that it needs more energy, lipase in fat cells helps release the fat into circulation