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Answer:
At t = 4.2 s
Angular velocity: 6. 17 rad /s
The number of revolutions: 2.06
Explanation:
First, we consider all the forces acting on the pulley.
There is only one force acting on the pulley, and that is due to the 1.5 kg mass attached to it.
Therefore, the torque on the pulley is
where m is the mass of the block, g is the acceleration due to gravity, and R is the radius of the pulley.
Now we also know that the torque is related to angular acceleration α by
therefore, equating this to the above equation gives
solving for alpha gives
Now putting in m = 1.5 kg, g = 9.8 m/s^2, R = 20 cm = 0.20 m, and I = 2 kg m^2 gives
Now that we have the value of the angular acceleration in hand, we can use the kinematics equations for the rotational motion to find the angular velocity and the number of revolutions at t = 4.2 s.
The first kinematic equation we use is
since the pulley starts from rest ω0 = 0 and theta = 0; therefore, we have
Therefore, ar t = 4.2 s, the above gives
So how many revolutions is this?
To find out we just divide by 2 pi:
Or about 2 revolutions.
Now to find the angular velocity at t = 4.2 s, we use another rotational kinematics equation:
Since the pulley starts from rest, ω0 = 0. The change in angle Δθ we calculated above is 12.97. The value of alpha we already know to be 1.47; therefore, the above becomes:
Hence, the angular velocity at t = 4.2 w is 6. 17 rad / s
To summerise:
at t = 4.2 s
Angular velocity: 6. 17 rad /s
The number of revolutions: 2.06
Answer:
The final temperature of both objects is 400 K
Explanation:
The quantity of heat transferred per unit mass is given by;
Q = cΔT
where;
c is the specific heat capacity
ΔT is the change in temperature
The heat transferred by the object A per unit mass is given by;
Q(A) = caΔT
where;
ca is the specific heat capacity of object A
The heat transferred by the object B per unit mass is given by;
Q(B) = cbΔT
where;
cb is the specific heat capacity of object B
The heat lost by object B is equal to heat gained by object A
Q(A) = -Q(B)
But heat capacity of object B is twice that of object A
The final temperature of the two objects is given by
But heat capacity of object B is twice that of object A
Therefore, the final temperature of both objects is 400 K.
Answer:
<em>The current is 11 Amperes</em>
Explanation:
<u>Electric Current</u>
The electric current is defined as a stream of charged particles that move through a conductive path.
The current intensity can be calculated as:
Where:
Q = Electric charge
t = Time taken by the charge to move through the conductor
The current intensity is often measured in Amperes.
The charge passing through a point in a circuit is Q= 55 c during t=5 seconds, thus the current intensity is:
I = 11 Amp
The current is 11 Amperes
Answer:
Fc = 123 Newton
Explanation:
Net force can be defined as the vector sum of all the forces acting on a body or an object i.e the sum of all forces acting simultaneously on a body or an object.
Mathematically, net force is given by the formula;
Where;
Fnet is the net force.
Fapp is the applied force.
Fg is the force due to gravitation.
Given the following data;
Normal force = 25N
Mass = 10kg
To find the centripetal force;
From the net force, we have the following formula;
Fc = N + mg
Where;
Fc is the centripetal force.
N is the normal force.
mg is the the weight of the object.
Substituting into the formula, we have;
Fc = 25 + 10(9.8)
Fc = 25 + 98
Fc = 123 Newton