Answer:
T ambient = 10 degrees
Explanation:
Using Newton's Law of Cooling:
T(t) = Tamb + (Ti - Tamb)*e^(-kt) ..... Eq 1
Ti = 100
We have two points to evaluate the above equation as follows:
T = 70 @ t = 10 using Eq 1
70 = Tamb + (100 - Tamb)*e^(-10k) ... Eq 2
T = 50 @ t = 20 using Eq 1
50 = Tamb + (100 - Tamb)*e^(-20k) ... Eq 3
Solving the above Eq 2 and Eq 3 simultaneously:
Using Eq 2:
(70 - Tamb) / (100 - Tamb) = e^(-10k)
Squaring both sides we get:
((70 - Tamb) / (100 - Tamb))^2 = e^(-20k) .... Eq 4
Substitute Eq 4 into Eq 3
50 = Tamb + (100 - Tamb)*((70 - Tamb) / (100 - Tamb))^2
After simplification:
50 = (Tamb (100-Tamb) + (70-Tamb)^2) / (100 - Tamb)
5000 - 50*Tamb = 4900 - 40*Tamb
Tamb = 100 / 10 = 10 degrees
Answer:
500000000
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Answer:
P = 17.28*10⁶ N
Explanation:
Given
L = 250 mm = 0.25 m
a = 0.54 m
b = 0.40 m
E = 95 GPa = 95*10⁹ Pa
σmax = 80 MPa = 80*10⁶ Pa
ΔL = 0.12%*L = 0.0012*0.25 m = 3*10⁻⁴ m
We get A as follows:
A = a*b = (0.54 m)*(0.40 m) = 0.216 m²
then, we apply the formula
ΔL = P*L/(A*E) ⇒ P = ΔL*A*E/L
⇒ P = (3*10⁻⁴ m)*(0.216 m²)*(95*10⁹ Pa)/(0.25 m)
⇒ P = 24624000 N = 24.624*10⁶ N
Now we can use the equation
σ = P/A
⇒ σ = (24624000 N)/(0.216 m²) = 114000000 Pa = 114 MPa > 80 MPa
So σ > σmax we use σmax
⇒ P = σmax*A = (80*10⁶ Pa)*(0.216 m²) = 17280000 N = 17.28*10⁶ N
Answer:
51.96 m/s^-1
Explanation:
a) see the attachment
b) As we know the velocity of the projectile has two component, horizontal velocity v_ox. and vertical velocity v_oy as shown in the figure. At the highest point of the trajectory, the projectile has only horizontal velocity and vertical velocity is zero. Therefore at the highest point of the trajectory, the velocity of the projectile will be
v_ox=v_o*cosФ
=60*cos (30)
= 51.96 m/s^-1
Answer:
26b) 66.7%
27) 500 N
Explanation:
26.a) In a two pulley system, the load is attached to one of the pulleys. The other pulley is attached to a fixed surface, as well as one end of the rope. The other end of the rope goes around moving pulley, then around the fixed pulley.
26.b) Mechanical advantage is the ratio between the forces:
MA = load force / effort force
Efficiency is the ratio between the work:
e = work done on load / work done by effort
Work is force times distance.
e = (F load × d load) / (F effort × d effort)
Rearranging:
e = (F load / F effort) × (d load / d effort)
e = MA × (d load / d effort)
In a two pulley system, the load moves half the distance of the effort. So the efficiency is:
e = (4/3) × (1/2)
e = 2/3
e = 66.7%
27) In a three pulley system, the load moves a third of the distance of the effort.
e = (F load / F effort) × (d load / d effort)
0.40 = (600 N / F) × (1/3)
F = 500 N