Newton's First law implicitly defines what a force is by describing what happens in the absence of forces.
In the absence of forces and when viewed from an inertial reference frame an object at rest will remain at rest and an object in motion will maintain its motion at a constant velocity...
Also keep in mind, that a continuous function is not necessarily differentiable at a point x. Case in point: f(x) = | x | at x = 0
Here we see that f(x) satisfies the 3 conditions necessary for continuity:
1. f(0) is defined
2. \lim_{x\rightarrow 0} | x | exists
3...
This is a brief explanation. If you need a more detailed mathematical solution, just let me know.
There are different types of energy (i.e. spring potential, kinetic, gravitational potential, potential chemical energy). Let's assume the fuel used by this space taxi is stored chemical...
D is correct, but I think you are making it more difficult that it actually is. The given kinematic equation only has one unknown, v02. Just isolate the variable and take the square root of both sides.
Your question appears a little vague. Generally, the spring constant is implied by the variable k (dimensions N/m) and x is the displacement of the spring (in meters) from its equilibrium point. In general, the force Fs of the spring is given by:
Fs = -kx
The negative implies the force...
The force applied by the worker is constant and along the direction of displacement and the force done by friction is opposite the direction of displacement so we can use the relation
W = Fd
The net work is the sum of all the works (watch your signs!).
Excellent work so far, but you need to finish the problem. You have calculated the net acceleration acting on the elevator. From the problem, we see the elevator undergoes constant accleration through a displacement of 3m. Kinematically, is there an equation that we can use that gives the...
Let's see, we are given explicitly the maximum height of the object as 80 meters. If we make the assumption the object is close to a flat Earth approximation, then the acceleration acting on the object is -g. Implicitly, we can that if the object just goes the minimum height of 80 meters, then...
Assume the car wheels rest on a horizontal surface and rotate without slipping for simplifcation.
When a tire rotates on a surface (without slipping), the point of the tire that is in contact with the surface remains stationary (otherwise it would slip). The point wants to move one...
Kinematic equations can be applied to translational motion with constant acceleration. The same works in rotational dynamics. In fact, the equations for both types of motion share a common format with different variables. Given an initial and final angular speed during some time interval...
I believe this to be mathematically similar. But to be sure, let's show it to be so...
Let's assume the object rotates around the y-axis then translate this according to the parallel axis theorem.
Since the aor is the y-axis, the moment of inertia of the system includes the "arms" that...
I believe I erred in posting the equations from copy / paste. The posted equation has been corrected to the appropriate value:
Total I = 1/3 ML^2 + 1/12 ML^2 + M(L/2)^2 + M(L/2)^2
This is the equation I used to reduce to the 11/12 ML^2 and was told the answer was incorrect.
Some textbooks classify this type of a problem as a perfectly inelastic collision. For this type of collision, two objects, intially separate, collide and stick together. The momentum of the system is conserved, but the kinetic energy of the system isn't. In fact, it can't be conserved for...
I'm a physics major with a quick HW question for a Calc-based physics class. I'll present the problem along with my work. Any help would be appreciated:
HW Problem:
Consider 3 uniform thin rods all perpendicular to one another in such a manner that they align with the x, y, and z axii...