Answer:
d) The total mechanical energy is constant.
Explanation:
The total mechanical energy of a pendulum is given by:
where
KE is the kinetic energy (the energy of motion), given by
where
m is the mass of the pendulum
v is its speed
PE is the potential energy of the pendulum (the energy due to its position), given by
where
g is the acceleration due to gravity
h is the height of the pendulum relative to the ground
In absence of air resistance, the total mechanical energy of the pendulum is constant. This means that there is a continuous conversion of energy between kinetic and potential. In particular:
- When the pendulum is at its highest position (maximum displacement), the potential energy is maximum while the kinetic energy is minimum)
- When the pendulum crosses its equilibrium position, the kinetic energy is maximum (maximum speed) while the potential energy is minimum
Answer:
The change in temperature of 576.9°C will produce an elongation of 9 inches per feet in steel.
Explanation:
The formula for linear expansion of a material is:
ΔL = αLΔT
where, ΔL = change in length
L = Original length
ΔT = Change in temperature
α = coefficient of linear expansion
For steel, α = 13 x 10^-6 /°C
L = 100 ft
ΔL = (9 in)(1 ft/12 in) = 0.75 ft
Therefore,
0.75 ft = (13 x 10^-6 /°C)(100 ft)ΔT
<u>ΔT = 576.9°C</u>
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Answer
given,
length of the track = 200 m
speed of runner 1 = 6.20 m/s
speed of the runner 2 = 5.5 m/s
distance covered by the fastest runner, d = 6.2 t
distance covered by the slow runner,d = 5.50 t + 200
time taken to overtake for the first time
6.2 t = 5.50 t + 200
0.7 t = 200
t = 285.7 s
distance covered from the starting point
d = 6.2 t
d = 6.2 x 285.7
d = 1771.43 m
for next overtaking time taken will be double
t' = 258.7 x 2 = 571.4 s
distance travel by the runner from the starting point
d' = 6.2 t'
d' = 6.2 x 571.4
d' = 3542.68 m