A heavy copper ball of mass 2 kg is dropped from a fiftieth-floor apartment window. Another one with mass 1 kg is dropped immedi
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Hi there!
We know that:
U = Potential Energy (J)
K = Kinetic Energy (J)
E = Total Energy (J)
At 10m, the total amount of energy is equivalent to:
U + K = 50 + 50 = 100 J
To find the highest point the object can travel, K = 0 J and U is at a maximum of 100 J, so:
100J = mgh
We know at 10m U = 50J, so we can solve for mass. Let g = 10 m/s².
50J = 10(10)m
m = 1/2 kg
Now, solve for height given that E = 100 J:
100J = 1/2(10)h
100J = 5h
<u>h = 20 meters</u>
a) Constant
b) Constant
Explanation:
a)
We can answer this question by using the equivalent of Newton's second law of motion of rotational motion, which can be written as:
(1)
where
is the net torque acting on the object in rotation
I is the moment of inertia of the object
is the angular acceleration
The angular acceleration is the rate of change of the angular velocity, so it can be written as
where
is the change in angular velocity
is the time interval
So we can rewrite eq.(1) as
In this problem, we are told that at a given instant, the object has an angular acceleration due to the presence of torques, so there is a non-zero change in angular velocity.
Then, additional torques are applied, so that the net torque suddenly equal to zero, so:
From the previous equation, this implies that
Which means that the angular velocity at that instant does not change anymore.
b)
In this second case instead, all the torques are suddenly removed.
This also means that the net torque becomes zero as well:
Therefore, this means that
So also in this case, there is no change in angular velocity: this means that the angular velocity of the object will remain constant.
So cases (a) and (b) are basically the same situation, as the net torque is zero in both cases, so the object acts in the same way.
Answer:
h=12.41m
Explanation:
N=392
r=0.6m
w=24 rad/s
So the weight of the wheel is the force N divide on the gravity and also can find momentum of inertia to determine the kinetic energy at motion
moment of inertia
Kinetic energy of the rotation motion
Kinetic energy translational
Total kinetic energy
Now the work done by the friction is acting at the motion so the kinetic energy and the work of motion give the potential work so there we can find height