Answer: 7.41 m/s
Explanation: By using the law of of energy, kinetic energy of the brick as it falls equals the potential energy before falling.
Kinetic energy = mv²/2, potential energy = mgh
mv²/2 = mgh
v²/2 = gh
v² = 2gh
v = √2gh
Where g = 9.8 m/s², h = 2.80m
v = √2×9.8×2.8 = 7.41 m/s
Answer:
The lever arm could decrease or increase depending of the initial angle.
Explanation:
The lever arm d is calculated by:
d = rsin(θ)
where r is the radius and θ the angle between the force and the radius.
So, the increse or decrees of d depends of the sin of the angle θ, if the initial angle is greather than 90° and the angle decrease to an angle closer to 90°, the lever arm will increase but if the initial angle is 90° or lower and the angle decrease, the lever arm will decrease.
The statement about pointwise convergence follows because C is a complete metric space. If fn → f uniformly on S, then |fn(z) − fm(z)| ≤ |fn(z) − f(z)| + |f(z) − fm(z)|, hence {fn} is uniformly Cauchy. Conversely, if {fn} is uniformly Cauchy, it is pointwise Cauchy and therefore converges pointwise to a limit function f. If |fn(z)−fm(z)| ≤ ε for all n,m ≥ N and all z ∈ S, let m → ∞ to show that |fn(z)−f(z)|≤εforn≥N andallz∈S. Thusfn →f uniformlyonS.
2. This is immediate from (2.2.7).
3. We have f′(x) = (2/x3)e−1/x2 for x ̸= 0, and f′(0) = limh→0(1/h)e−1/h2 = 0. Since f(n)(x) is of the form pn(1/x)e−1/x2 for x ̸= 0, where pn is a polynomial, an induction argument shows that f(n)(0) = 0 for all n. If g is analytic on D(0,r) and g = f on (−r,r), then by (2.2.16), g(z) =
(a)
KE = m v^2 / 2 = (1200 kg)(20 m/s)^2 / 2 = 240,000 J
(b)
The energy is entirely dissipated by the force of friction in the brake system.
(c)
W = delta KE = KEf - KEi = (0 - 240,000) J = -240,000 J
(d)
Fd = delta KE
F = (delta KE) / d = (-240,000 J) / (50 m) = -4800 N
The magnitude of the friction force is 4800 N.
