The Atwood’s machine shown consists of two blocks of mass m1 and m2 that are connected by a light string that passes over a pull
ey of negligible friction and negligible mass. The block of mass m1 is a distance h1 above the ground, and the block of mass m2 is a distance h2 above the ground. m2 is larger than m1. The two-block system is released from rest. Which of the following claims correctly describes the outcome after the blocks are released from rest but before the block of m2 reaches the ground? Select two answers.
1 answer:
(A) For the system consisting of the two blocks, the change in the kinetic energy of the system is equal to work done by gravity on the system.
(D) For the system consisting of the two blocks, the pulley and the Earth, the change in the total mechanical energy of the system is zero.
<h3 /><h3>The given parameters:</h3>- Mass of block 1 = m1
- Mass of block 2, = m2
- Height of block 1 above the ground, = h1
- Height of block 2 above the ground = h2
The total initial mechanical energy of the two block system is calculated as follows;
When the block m2 reaches the ground the block m1 attains maximum height and the total mechanical energy at this point is given as;
Thus, we can conclude the following before the block m2 reaches the ground;
- For the system consisting of the two blocks, the pulley and the Earth, the change in the total mechanical energy of the system is zero.
- For the system consisting of the two blocks, the change in the kinetic energy of the system is equal to work done by gravity on the system.
Learn more about conservation of mechanical energy here: brainly.com/question/332163
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(a) See figure in attachment (please note that the image should be rotated by 90 degrees clockwise)
There are only two forces acting on the balloon, if we neglect air resistance:
- The weight of the balloon, labelled with W, whose magnitude is
where m is the mass of the balloon+the helium gas inside and g is the acceleration due to gravity, and whose direction is downward
- The Buoyant force, labelled with B, whose magnitude is
where is the air density, V is the volume of the balloon and g the acceleration due to gravity, and where the direction is upward
(b) 4159 N
The buoyant force is given by
where is the air density, V is the volume of the balloon and g the acceleration due to gravity.
In this case we have
is the air density
is the volume of the balloon
g = 9.8 m/s^2 is the acceleration due to gravity
So the buoyant force is
(c) 1524 N
The mass of the helium gas inside the balloon is
where is the helium density; so we the total mass of the balloon+helium gas inside is
So now we can find the weight of the balloon:
And so, the net force on the balloon is
(d) The balloon will rise
Explanation: we said that there are only two forces acting on the balloon: the buoyant force, upward, and the weight, downward. Since the magnitude of the buoyant force is larger than the magnitude of the weigth, this means that the net force on the balloon points upward, so according to Newton's second law, the balloon will have an acceleration pointing upward, so it will rise.
(e) 155 kg
The maximum additional mass that the balloon can support in equilibrium can be found by requiring that the buoyant force is equal to the new weight of the balloon:
where m' is the additional mass. Re-arranging the equation for m', we find
(f) The balloon and its load will accelerate upward.
If the mass of the load is less than the value calculated in the previous part (155 kg), the balloon will accelerate upward, because the buoyant force will still be larger than the weight of the balloon, so the net force will still be pointing upward.
(g) The decrease in air density as the altitude increases
As the balloon rises and goes higher, the density of the air in the atmosphere decreases. As a result, the buoyant force that pushes the balloon upward will decrease, according to the formula
So, at a certain altitude h, the buoyant force will be no longer greater than the weight of the balloon, therefore the net force will become zero and the balloon will no longer rise.
Answer:
v = 14 m/s
Explanation:
given,
radius of dip = 40 m
The passengers in a roller coaster car feel 50% heavier than their true weight.
Apparent weight
When the car is at the bottom, the weight will be acting downwards and the centripetal force will also be acting downward where as Normal force which is apparent weight will be acting in upward direction.
now,
v = 14 m/s