The problem itself is easy. My question is regarding the proper use of inequality symbols.
I only need to do the first part to show where I am having the issue.
The forces I need to consider are the coaster car's weight ##W = mg## and the reaction ##A## of the tracks acting on it. With the...
After 3,32 seconds, vt should have varied by 0,695*3,32. I have done a previous exercise where you only needed to calculate the radial acceleration in this scenario. There, I took the vt after the given time, squared it and then divided with the radius. I remember clearing that one, so in this...
i think that the light sphere will go up higher(will have bigger acceleration) because there has to be a balance between the mass and the acceleration as long as the force is the same,
for example if you push a heavy object and with the same force pushed another light object the light object...
We know that ##v = \omega r## where ##r = R_{\text{E}} + h##. To compensate for the motion, the plane must fly along the equator at the same speed as the Earth but in the opposite direction, i.e. from east to west, so
$$\vec{v} = -\vec{ v}_{\text{E}}$$
$$v_{\text{E}} = \omega_{\text{E}}...
Hi
I'm having trouble to understand the centripetal force in a rotating rod with a mass in its end.
When ##90°<\theta<270°##, the centripetal acceleration is produced by the tension, which counteracts the radial component of the weight.
But what happens when ##\theta<90°## or ##\theta>270°##...
Homework Statement
A solid body begins to rotate around a fixed axis with angular acceleration ##\beta=\beta_0\cosφ##, where ##\beta_0## is a constant vector, ##φ##, is the angle of rotation of the body from initial position. Determine the angular velocity of this body as a function of the...
Homework Statement
This isn't really a homework but a project I'm doing that's due soon. In our multivariable calculus class, we're creating a 3D roller coaster, and I need to explain the physics behind the roller coasters.
For a roller coaster loop, if it were perfectly circular, we would...
Homework Statement
A light rod ##AB## of length ##2a## has a particle ##P## of mass ##m## attached to ##B##. The rod is rotating in a vertical plane about a fixed smooth horizontal axis through ##A##. Given that the greatest tension in the rod is ##\frac {9mg}{8}##, find, to the nearest degree...
Homework Statement
A ##5 ~kg## mass performs circular motion at the end of a light, inextensible string of length ##3~m##. If the speed of the mass is ##2 ~ms^{-1} ## when the string is horizontal, what is its speed at the bottom of the circle?
(assume ##g=10~ms^{-1}##) (Ans: ##8~ms^{-1}##)...
I am trying to work out the velocity of the ball in a loop in terms of theta from the horizontal (like a unit circle) as it loses contact with the track. And having a lot of trouble understanding this equation
m*g*sin(theta) = m*v2/r
and this explanation:
The ball will leave the rail when...
Homework Statement
A bead slides under the influence of gravity on the frictionless interior surface of the paraboloid of revolution z = (x^2+y^2)/2a = r^2/2a Find the speed v_0 at which the bead will move in a horizontal circle of radius r_0 Find the frequency of small radial...
Am I trying to solve a simple equation, but get stuck at the basic. I have have a spring with a cube attached to it (1kg). When I pull it with 5N, the spring extends to 50mm =amplitude, (Hooks law) the koefitient is 120. The determined absortion coeffitient is 0,2^-1s. I tried to get the...
Homework Statement
A new car is tested on a 300-m-diameter track. If the car speeds up at a steady 1.3 m/s^2 , how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration?
c = 300 m
a_t = 1.3 m/s^2
2. Relevant formulas
a_c = v^2 / r...
Assume an object accelerating at a certain value dV/dt. If this object was traveling in a circular motion the centripetal force would increase as the object moves faster.
To maintain centripetal acceleration constant while the object is accelerating (in its forward motion dV/dt) I think it...
friction is causes the circular motion in the car around a curve, and if we draw free body diagram we will see the friction force must be opposite the car motion so the force of friction not toward to the center of the curve ,so the force of friction must be not the centripetal force ,mustn't it?
Homework Statement
The system shown is initially at rest when the bent bar starts to rotate about the vertical axis AB with constant angular acceleration a 0 = 3 rad/ s2 . The coefficient of static friction between the collar of mass m = 2 kg and the bent bar is f.Ls = 0.35, and the collar is...
Homework Statement
A ball rolls down a ramp which forms a quarter circle of radius 0.5m. The ball weighs 25g. The bottom of the ramp is 1.5m above the floor. Assume no friction between the ball and the ramp. Assume no air resistance.
what is the force exerted by the ramp on the ball?
whatis...
When a mass is in a circular motion and suddenly gets released by its centripetal force, it will continue traveling in a straight path (tangent to the circle and perpendicular to the radius in the moment of release) if no other forces acting.
So let’s make a case: We have a space centrifuge...