Motion Definition and 999 Threads

First, I tried solving for the total time of flight, which I got as 100 = 5cos25*t --> t=22 s Since we know the height at which the object lands, but not at which it is launched, I tried setting up the equation as: yf = 40 - y0 = y0 + 5sin25*(22) - 1/2(9.8)(22)^2 However, I got y0 = 1183 m...

Homework Statement: The particle is moving in circular orbit such a way that the net force (F) is always towards the point p (point p is on the circumference of circle). Find the variation of force F with respect to r. i.e find the value of n in the expression F=kr^n Homework Equations: F=kr^n...

a) Describe the motion of the spool: it will roll down the plane, rotating counter clockwise. I am confused when setting up equation of torque. If I take center of the spool as pivot, only the tension of thread produces torque but the direction will be clockwise and it makes the spool will move...

Fn= normal force W=mg W=(65)(9.8)= 637N Fn-637= -(65)(0.2*9.8) Fn= 509.6N I got the weight of the woman in the elevator, but I have trouble finding what the scale reads in kg. I was given the solution which read: a = (g-0.2g)= 0.8g W= 0.8g*509.6N= 52kg. My questions 1. why do I have to...

A Uniform rod AB of length 7m is undergoing combined motion such that, at some instant, velocities at top most point A is perpendicular to the rod and magnitude is 11 m/s. The mid point/ centre of mass ,say C, has a velocity of 3 m/s and is also perpendicular to the rod. If both the velocities...

Well, ##r(t)## in ##A## is just a vector ##(0;y)## because is tangent to the trajectory. Then, from the perspective of ##B## the particle moves in an uniform circular motion. Is this right? The velocity from ##B## must be ##\omega##, right? And what about acceleration?

Well, first I tried to understand the relation between the velocities and accelerations of both bodies and I got that the velocity of ##B## is half the velocity of ##A##. This is because a change in length of the cord "that touches ##A##" must be equal to the change in length of the two cords...

As the problem asks for the spaceship's perspective, I know that I should take ##\vec v_S=0## and ##\vec v_M=24.1-19.3## because the motion is relative to the spaceship. Then, the relative velocity of Mars and ##SM## should have the same direction. If they have the same direction, that angle...

The first doubt that comes to my mind is "I have to determine the acceleration with respect to what?", because the problem doesn't tell. Then, I have some problems when having to plug the data in the formula of acceleration. ##\vec a_B=0## because the origin isn't accelerated, ##\vec{\dot...

This problem arose in modeling camera focusing movement, such as a control system might do. It assumes a simple (thin) lens, rays close to the optical axis, and monochromatic light. While most camera lenses are not simple, this is a first approximation. Camera lenses project an image of a...

The final answer should have a negative b^2⋅r(dot)^2⋅r term but I have no idea how that term would become negative. Also I know for a fact that my Lagrangian is correct.

I start out by substituting rcos(Θ) and rsin(Θ) for x and y respectively. This gives me z=(b/2)r^2. The Lagrangian of this system is (1/2)m(rdot^2+r^2⋅Θdot^2+zdot^2)-mgz. (rdot and such is the time derivative of said variable). I then find the time derivative of z, giving me zdot=br⋅rdot and...

My working: ##s=\int v## ##v= \sqrt{\frac{a_{c}}{r}}=\sqrt{\frac{a_{c}}{\frac{4}{2t+2}}}## ##s= \int_{0}^{2} \sqrt{\frac{2}{\frac{4}{2t+2}}}## My final answer seems to be wrong. Any ideas? Cheers

The particle is moving under a force field with the potential energy equation described above. I find it logical that Newton's Laws can be used as in the question itself it is stated that the velocity is quite small and we could approximate its subsequent motion via the notions of Classical...

According to the semiclassical approximation, in response to a constant electric field I would get a periodic motion of the electron, like this: The sinusoidal type function is the velocity, while the function that goes to infinity is the effective mass. Thus I was wondering, since ##v## also...

Well, I tried decomposing velocity into its components on the radial and angular axis. But I have problems with the angles because in some parts of the trajectory the velocity is on the angular coordinate, but in other parts it isn't. I mean, I can't say ##V=V e_\theta## because it's not always...

My workings: ##D(t) = Asin\omega t## ##v(t) = \frac{\text{dD}}{\text{dt}}=Acos(\omega t)\omega## ##v(t) =Acos(\omega t)\omega## When displacement half of amplitude, ## Asin\omega t## = 0.5##A## ## sin\omega t## = 0.5 ##v(t) =Acos(\omega t)\omega## ##v(t) =\omega (0.5Asin\omega t)cos \omega t ##...

I think my approach is quite wrong, still I gave it a shot: First I know that ##v_A=13.3 m/s=r\omega=60\omega \rightarrow \omega=0.2 \frac{rad}{s}## Then $$\vec a_A=-r\omega^2 e_r=-2.4 e_r$$ But ##e_r=\cos{\theta}i+\sin{\theta}j## and substituing the latter in the acceleration equation I have...

Do virtual particles travel at the speed of light, or do they have 'virtual rest mass'?

I know the ans comes out to be mgsintheeta/3 by using f=ma and the torque eqn but my question is as stated in the question the cylinder is in pure rolling hence friction should only try to oppose mgsintheeta so that the accelration does not change hence v remains equal to rw so why is the ans...

The below attempt will look messy, but I'm really kind of stuck as how to proceed on here. Thanks for any advice.

For the non-circular object of mass m: From Newtons second law we get that F-N-T=ma where N is the force that the cylinder acts on the object. Replacing numbers: 13-N=2a. For the cylinder: From Στ=Τa(ang) we get that T'= 1/2ma or T'=a. Where T' is the friction that acts on the cylinder and we...

Hi, I have a question regarding a pendulum and it's motion/momentum given the axis it moves around. In the below picture, there are two version of a pendulum with a weight at the bottom. It moves in and out of the screen, around an axis resting on two nails (red). My question is, how does the...

I tried getting the velocity of a which by using constraint came out to be 3 and by using the eqn for vcom i got the ans as 3.5 i just want to confirm is this the correct answer

Hi everyone. Do correct me if I am thinking wrongly. So to find angular velocity, won't I just have to integrate angular acc = 2t, which means angular velocity = t^2? Hence, won't the answer be 3^2=9? The answer seems to be 5.43 :/ Thanks

Hi guys! I am currently learning about fluid dynamics, and I am stuck on a certain equation derivation. It's about sinking motion which considers only gravity force, buoyant force, and viscous resistance. The link attached has the details...

A swing is suspended from a non-horizontal tree branch. Points C and D are fixed in space. All 4 line segments in the diagram have constant distance. After some initial "kick" imparts energy to the system the only force acting externally on the system is gravity. Is it possible to predict the...

Solving the relevant equation tan-1(30/7) = 76.865977693604 = 77 Just need confirmation or a correction since I am very new to physics in general

At the moment of throwing the ball the ball will have a vertical vel of 4 and horizontal of 3 wrt to elevator so as seen from inside the elevator the ball will behave like a projectile where g(eff) = 8 and with time period 1 sec hence range will be the displacement which should be 3 m but ans...

11.1 Parametric equations and a parameter interval for the motion of a particle in the xy-plane given. Identify the paritcals path by finding a Cartestian equation for it $x=2\cos t, \quad 2 \sin t, \quad \pi\le t \le 2\pi$ (a) Identify the particles path by finding a Cartesian Equation the...

Consider the example of flashing light in spaceship. The observer in the spaceshipe and the observer in the Earth measure different times. Both observers could argue that the clock of the other tick slower(motion is relative). But is anyone right ? I mean the one will measure proper time...

So ##T+U=\frac{1}{2}m(\dot{x}^{2}+\dot{y}^{2})-mgy=constant##. If I derive this with respect to ##t## $$\dot{x}\ddot{x}+\dot{y}\ddot{y}-g\dot{y}=0$$ Then I use ##\dot{y}=\dot{x}\frac{dy}{dx},\ddot{y}=\ddot{x}\frac{dy}{dx}+\dot{x}^{2}\frac{d^{2}y}{dx^{2}}## to get...

Does the block move along the pink dotted lines as attached in the figure below? I tried to draw the FBD of the small block ##m ## at the lowermost point which is also attached below.(The direction of ## v_0 ## is actually tangential) Is the figure above correct? If not, why?

u=5m/s t=5sec the height will be the displacement s=ut - (1/2)gt^2 s=5*5-0.5*10* 25 s=-100m But the answer is 273.6m

This is just a conceptual question. I get that when a car is turning on an unbanked curve, the friction provides the centripetal force. I don't understand why this is though. I thought friction is supposed to oppose the direction of motion. But that would imply that the direction...

I think this question is important so posting it here. To cut a long story short there is a person in our country who is totally anti-science and anti-Western citilization. He says science is a big lie. < remainder of post deleted by moderator >

I can do the problem if the centre is fixed. The steps are: 1) Assuming tension in the string is zero at the top most position, we calculate the velocity at top most position by mv2/R = mg 2)Now, we simply apply mechanical energy conservation when the ball is at the top and bottom positions...

Could anyone please help me out with the second part of this question: I've got the first part, u = √(5ga) Here's my diagram for the second part: Distance traveled is from bottom of sphere to peg is 2πa/3 which means angle traveled is 2π/3. So the particlee is going to travel 2π/3 radians...

So here is what is going on in my mind: We have a turn that is 400m away from the center of the turn. The faster the car goes, the harder it is for it to maintain its radius. We have a component of the normal force that points towards the center, and static friction which does the same. I...

Hi all, I have attached an image of a page out of the book I am using for context. The blue arrow in Figure 12-3 describes the motion of the particle. I figured the net force would need to be in the same direction, but apparently the net force opposes the motion. So, in Figure 12-3 the pressure...

I refer to the second paragraph of 1916's book, "Die Grundlage der allgemeinen Relativitätstheorie", translated here. First issue There are two distant stellar bodies, with unchanging shapes: S₁ (spherical) and S₂ (ellipsoidal), made of the same amount and kind of matter. Their centres of mass...

Perpetual motion is fundamentally impossible. But almost perpetual motion is possible. The list of toys or devices designed to run for a very long time is short: crookes radiometer (photons, cheap), the drinking bird (heat engine, cheap), the Atmos clock (temperature, expensive), Beverly Clock...

I have attached below the solution provided by the textbook. I understand the whole solution, except when they divide the horizontal component and the vertical component and equate it to the tangent of 30. What seems strange to me is that, while initially the equation for the vertical component...

It was always my understanding that a Pendulum has equal time at different swing heights and teachers teach that but in fact, it is not true. I downloaded the LabinApp Pendulum Amplitude Demo App and it shows a slightly different time as you drop higher and higher. My question is why don't they...

what I know d=35.75 t=? what am I meant to do with this problem? I'll add more to this area once I know some more. thanks. Is the leafs velocity considered inital? if so I know Vi

What I know for Number 1. t=2.7s d=? Vi=0m/s^-1 a=9.8m/s^-2 Vf=? Equation to use? Vf=Vi+at= 0+9.8m/s^-2x2.3= 26.46m/s So for number one the final velocity is 26.46m/s d = 0.5 * g * t2 = 0.5x9.8x2.7^2=35.721 Number 2 I know t=2.3s d=35.721 vi? Vf? a=9.8? what formula do...

All i could think is that the z component of velocity will remain unchnged as there is no force in that direction.And for the x and y component can we imagine the helical motion as a superposition of a circle and a straight line.So for x and y component can we solve for a particle moving in a...

I have a solution, However Cant understand 1 point.Now, This is the solution: ##N_2 l cos\theta + \frac 1 2 F_g l cos\theta - f_2 l sin\theta = 0## ## N_2(1 - \mu tan\theta) + \frac 1 2 F_g = 0## This is the the point that I don't like - yes it is less that 0, but it's even less that...

Not sure how to go about it

What exactly is this equation telling me? How can I use it to work out the Equations of Motion given an equation of potential energy? Won't I have to solve a PDE? I'm extremely sorry if this question comes off ignorant.