Answer:
Explanation:
Given that,
Heat measured, Q = 81500 J
Mass of water, m = 0.5 kg
The specific heat of water is 4,184 J/kg °C
We need to find the change in temperature. The heat measured is given by :
Where
is the change in temperature
So, the change in temperature is .
Answer:
Explanation:
stiffness k = 160
m = 10
angular frequency ω =
=
= 4
ω = 4
Let x = 4 - A sinωt
when t = 0
x = 4 in
when t = 2 s , x = - 4
- 4 = 4 - A sinωt
8 = A sin 4 x 2
8 = A sin8
A = 8 / sin 8
= 8 / .989
= 8.09 in .
x = 4 - A sinωt
dx / dt = - Aω cosωt
v = - Aω cosωt
for t = 0
v = - Aω
= - 8.09 x 4
= - 32.36 in / s
initial velocity v = - 32.36 in /s
displacement x for t = 4s
x = 4 - 8.09 sin 4 x 4
= 4 - 8.09 sin 16
= 4 - 8.09 x - .2879
= 4 + 2.33
= 6.33 in.
c ) Amplitude of vibration A = 8.09 in .as calculated above .
To solve this problem we use the general kinetic equations.
We need to know the time it takes for the car to reach 130 meters.
In this way we have to:
Where
= initial position
= initial velocity
= acceleration
= time
= position as a function of time
.
We use the quadratic formula to solve the equation.
t = 6.63 s and t = -17.1 s
We take the positive solution. This means that the car takes 6.63 s to reach 130 meters.
Then we use the following equation to find the final velocity:
Where:
= final speed
The final speed of the car is 27.25 m/s