The gas in the balloon has a mass of 0.032 kg. The balloon has a volume of 0.025 m3. Calculate the density of the gas in the bal
1 answer:
You might be interested in
Average velocity is defined as the ratio in change in position to change in time,
v[ave] = ∆x/∆t
which on its own doesn't have anything to do with acceleration.
<u>If acceleration is constant</u>, the average velocity is the literal average of the initial and final velocities,
v[ave] = (v[final] + v[initial]) / 2
If this constant acceleration has magnitude a, the final velocity can be expressed in terms of the initial velocity by
v[final] = v[initial] + a*t
and plugging this into the previous equation gives
v[ave] = (v[initial] + a*t + v[initial])/2
v[ave] = v[initial] + 1/2*a*t
If the body in consideration is <u>initially at rest</u>, then
v[ave] = 1/2*a*t
which might be the relation you're looking for. But bear in mind the conditions I've underlined.
<u>If acceleration is not constant and changes over time</u>, so that the acceleration is some function of time a(t), then you can determine the velocity function v(t) by using the fundamental theorem of calculus. You need to know a particular velocity for some time to completely characterize v(t), though. For example, if you're given the initial velocity v[initial] = v(0), then
or if you know any other velocity for some time t₀ > 0,
Answer:
Explanation:
Mass of the bucket, m = 23 kg
Radius of the pulley, r = 0.050 m
The bucket is released from rest, u = 0 m/s
The time taken to fall, t = 2 s
Speed, v = 8.0 m/s
Moment of Inertia of the pulley, I = ?
Using the equation of motion:
v = u + at
8 = 0 + 2a
a = 8/2
a = 4 m/s²
The relationship between the linear and angular accelerations is given by the equation:
Angular acceleration,
Since the bucket is falling, it can be modeled by the equation:
mg - T = ma
T = mg - ma = m(g-a)
T = 23(9.8 - 4)
The tension, T = 133.4 N
The equation for the pulley can be modeled by: