Answer:
U = 102.8 J (100 J to two significant digits)
Explanation:
potential energy converted = 20(9.8)(1.8) = 352.8 J
kinetic energy at base of track = ½(20)5.0² = 250 J
energy (work) of friction 352.8 - 250 = 102.8 J
Answer:
(A) Angular speed 40 rad/sec
Rotation = 50 rad
(b) 37812.5 J
Explanation:
We have given moment of inertia of the wheel 
Initial angular velocity of the wheel 
Angular acceleration 
(a) We know that 
We have given t = 2 sec
So 
Now 
(b) After 3 sec 
We know that kinetic energy is given by 
To solve the problem, it is necessary to apply the concepts related to the kinematic equations of the description of angular movement.
The angular velocity can be described as

Where,
Final Angular Velocity
Initial Angular velocity
Angular acceleration
t = time
The relation between the tangential acceleration is given as,

where,
r = radius.
PART A ) Using our values and replacing at the previous equation we have that



Replacing the previous equation with our values we have,




The tangential velocity then would be,



Part B) To find the displacement as a function of angular velocity and angular acceleration regardless of time, we would use the equation

Replacing with our values and re-arrange to find 



That is equal in revolution to

The linear displacement of the system is,



The correct answer is: Option (A) 75 J
Explanation:
First, be careful with the units here. As you can see it is mentioned that there is a 50N box. It means that the weight (<em>mg</em>) of the box is given as the unit is <em>Newton</em>, not its mass (which is in kg).
As,
Potential-energy = mass * acceleration-due-to-gravity * height
PE = m*g*h --- (A)
In equation (A), mg is actually the weight of the box, which is given.
mg = 50N
h = height = 1.5m
Plug the values in equation (A):
PE = 50 * 1.5 = <em>75 J (Option A)</em>