Answer:
22.47 %
Explanation:
v 1 = 328 m/s, v 2 = 363 m/s
We know that the velocity of a wave in a stretch string is directly proportional to the square root of the tension in the string.
Percentage increase in the tension
= \left ( \frac{1}{0.8165}-1 \right )\times 100
= 22.47 %
Given:
k = 100 lb/ft, m = 1 lb / (32.2 ft/s) = 0.03106 slugs
Solution:
F = -kx
mx" = -kx
x" + (k/m)x = 0
characteristic equation:
r^2 + k/m = 0
r = i*sqrt(k/m)
x = Asin(sqrt(k/m)t) + Bcos(sqrt(k/m)t)
ω = sqrt(k/m)
2π/T = sqrt(k/m)
T = 2π*sqrt(m/k)
T = 2π*sqrt(0.03106 slugs / 100 lb/ft)
T = 0.1107 s (period)
x(0) = 1/12 ft = 0.08333 ft
x'(0) = 0
1/12 = Asin(0) + Bcos(0)
B = 1/12 = 0.08333 ft
x' = Aω*cos(ωt) - Bω*sin(ωt)
0 = Aω*cos(0) - (1/12)ω*sin(0)
0 = Aω
A = 0
So B would be the amplitude. Therefore, the equation of motion would be x
= 0.08333*cos[(2π/0.1107)t]
i. 1,350 calories
j. 992 calories
k. 235.6 calories
2. Calories of energy into water = (amount of water, in grams) x (change in the water's temperature, in °C)
3.a. 840 calories
3.b. 840 calories
4. 80°C
Answer:
The answer ro this question is fear of failure
Answer:
a) 8 cents
b) 25.6 cents
c) 2.4 cents
Explanation:
Given:
Cost of electricity = 8 cents/kWh
Total cost = Wattage ×Time × Electricity cost
a) cost of running a lamp of 100 W for 10 h will be
Energy consumed = 100 W ×10 h = 1000 Wh or 1 kWh [1 kW = 1000 W]
Total cost = Energy consumed × electricity cost
⇒Total cost = 1 kWh × 8 cents/kWh = 8 cents
b) cost of running a TV of 400 W for 8 h will be
Energy consumed = 400 W × 8 h = 3200 Wh or 3.2 kWh
Total cost = Energy consumed × electricity cost
⇒Total cost = 3.2 kWh × 8 cents/kWh = 25.6 cents
c) cost of running a microwave of 1200 W for 15 min will be
Energy consumed = 1200 W × = 300 Wh or 0.3 kWh [1h = 60 min]
Total cost = Energy consumed × electricity cost
⇒Total cost = 0.3 kWh × 8 cents/kWh = 2.4 cents