Kinematics Definition and 1000 Threads

Homework Statement Two blocks slide on an incline of angle \theta . Block 1 has mass m1 and coefficient of kinetic friction μ1 with the surface, block 2 has mass m2 and coefficient of kinetic friction μ2. The gravitational acceleration is g. In terms of these parameters, under what condition...

A child is in danger of drowning in the river. The river has a current of 2.5 km/hr . The child is 0.6 km from the shore. A rescue boat with speed 20.0 km/hr (with respect to the water) ,located 0.8km downstream, sets off from the shore. What would be the optimum angle (shore -> boat ) to reach...

So basically i am confused about time 0 in terms of kinamatics graphs Lets say i throw a ball upwards so what does time t=0 represent, the time after which the ball is released or the time at which ball is about to be released? Secondly in projectile motion if i throw a ball horizontally at a...

Homework Statement An object is released from rest in the gravitational field of the Earth. Air resistance is negligible. How far does the object move during the fourth second of its motion? A. 15 m B. 25 m C. 35 m D. 45 m Homework Equations v = u + at s = ut + 1/2 at^2 v^2=u^+2as...

does mass affect the motion of the vertical upward, vertical motion down, free fall motion, and parabolic motion?

Homework Statement Two cars are 1.4 km apart and driving towards each other. One car starts from rest and accelerates uniformly at 1.2 m/s^2. The other car is driving at a constant speed of 18 m/s. When will the cars meet? Homework Equations d=vt d=ut + 1/2at^2 d=vt-1/2at^2 v^2 = u^2 + 2ad...

Homework Statement Your cousin has built a model rocket that she wishes to launch in your backyard. You're a little worried by this, and ask her for details. She tells you, when I launch the rocket straight upwards, the acceleration will be 3.5g = (3.5*9.8m/s^2) for 4.3 seconds, then burn out...

Homework Statement You are at a stoplight when you see a car approaching from behind at constant velocity. To avoid getting rear-ended, you accelerate forward with constant acceleration. Assume that you have managed to start at the last possible instant to avoid getting hit, as determined by...

Homework Statement Someone mistakenly threw away a lovely couch, and you decide to take it back to your apartment. You push it with a force of 350 Newtons and at 30 degrees below the horizontal at 2 m/s. The coefficents of friction are μs = 0.4 and μf = 0.3. What is the couch's mass? Homework...

Homework Statement Two stationary motorbikes at time 0s are separated by distance of 80m. Both motorbikes accelerate at a constant rate as the travel towards each other. Motorbike X accelerates at a rate of 4.6m/s2 . Motorbike Y accelerates at a rate of 2.4m/s2 . Calculate the amount of time...

Homework Statement A person is standing on an elevator initially at rest at the first floor of a high building. The elevator then begins to ascend to the sixth floor, which is a known distance h above the starting point. A plot of the acceleration as a function of time is shown in the figure...

I have collected data on a car accelerating down a straight track. I graphed it Position vs Time. Then I found the tangent slope at 5 points along the curve and plotted them as velocity. But then I linearized the position vs Time graph (position vs Time^2.) However, the slope of the velocity vs...

Homework Statement There are two particles. There are moving equally on two intersecting lines to intersection. On time t=0 is the distance of two particles d. The velocity of one particle relative to the other has a projection u in the direcion of d. In direction perpendicular to d is the...

Homework Statement 13.43 A child slides down the helical water slide AB. The description of motion in cylindrical coordinates is ##R=4m##, ##θ=ω^2t^2## and ##z=h[1-(\frac {ω^2t^2} {π})]##, where h=3m and ω=0.75rad/s. Compute the magnitudes of the velocity vector and acceleration vector when...

Homework Statement Captain American bails out of an airplane and falls 50 meters without friction. When the parachute opens, he decelerate at 2.0m/s2. He reaches the ground with a speed of 3.0 meters/sec. a.) How long is captain america in the air? do= d= vo= v=3m/s t= ? a= -9.8m/s2 ?? (this...

Homework Statement The engineer of a passenger train rounding a curve at 30m/s sights a slow-moving freight train 200m ahead on the same track traveling in the same direction with a constant velocity of 10m/s. The engineer of the passenger train immediately applies the brakes, causing a...

Homework Statement Luke Skywalker is making a diving run at the Death Star, approaching in his X-Wing at a rate of 500m/s. (The Death star is hollow, so it has almost no gravity.) Suddenly, at 800 meters from the Death Star, Luke fires his retro rockets. This creates a reverse acceleration of...

Homework Statement 13.34 The curved portion of the cloverleaf highway interchange is defined by ##R^2=b^2sin2θ##, 0<=θ<=90deg. If a car travels along the curve at the constant speed v0, determine its acceleration at A Homework EquationsThe Attempt at a Solution [/B] Is this wrong?

Homework Statement 13.30 The colar B slides along a guide rod that has the shape of the spiral R = bθ. A pin on the collar slides in the slotted arm OC. If the speed of the collar is constant at v0, determine the angular speed ##\dot θ## of the arm OC in terms of v0, b, and θ. Homework...

Homework Statement 13.29 The colar B slides along a guide rod that has the shape of the spiral R = bθ. A pin on the collar slides in the slotted arm OC. If OC is rotating at the constant angular speed ##\dot θ = ω##, determine the magnitude of the acceleration of the collar when it is a A...

Homework Statement 13.25 The rod OB rotates counterclockwise about O at the constant angular speed of 45 rev/min while the collar A slides toward B with the constant speed 0.6 m/s, measured relative to the rod. When collar A is in the position R = 0.24m, θ = 0, calculate (a) its velocity...

Homework Statement If vector a is added to vector b, the result is the vector c = (7.00, 3.00). If b is subtracted from a, the result is the vector d = (−4.50, 9.25). what is the magnitude of a? what is the magnitude of b? Homework EquationsThe Attempt at a Solution a + b = (7.00, 3.00)c...

If I'm driving a car and I have changed my dierction of motion without changing the speed, in this case how to calculate the acceleration of the car in a particular time? I'm not talking about circular motion.

Homework Statement 13.24 A particle travels along a plane curve. At a certain instant, the polar components of the velocity and acceleration are vR=90mm/s, vθ=60mm/s, aR=-50mm/s2, and aθ=20mm/s2. Determine the component of acceleration that is tangent to the path of the particle at this...

Homework Statement This is Pytels Dynamics 2nd edition problem 13.16 13.16. Pen P of the flatbed plotter traces the curve y=x3/80000, where x and y are measured in mm. When x=200mm, the speed of slider A is 60 mm/s. For this position, calculate (a) the speed of P; and (b) the normal component...

Homework Statement A sniper standing on a 70 meter-tall tower fires his rifle at 30 degrees upwards with the initial velocity of 1000 m/s. What is the range of the bullet and how much time will pass before it hits the ground? Assume no air-resistance. 2. The attempt at a solution I divided...

1. Homework Statement It's an auto closing gate. Two parts of the gate are identical. I had given to find the time taken to close the gate. The distance to close point (P) of the gate from closed event of the gate is given as "a". Sorry for my bad English. What i need to know is how the two...

Homework Statement Pytel Dynamics Problem 13.4 13.4 The particle passespoint O at the speed of 2.4 m/s. Between O and B, the speed changes at the rate of 2.2√v m/s2, where v is the speed in m/s. Determine the magnitude of the acceleration when the particle is (a) just to the left of pont A...

I am not sure how to approach a problem involving the friction coefficient when only given initial velocity, final velocity, and distance traveled. I could combine the friction and kinematic equations, but I am only familiar with doing that for one velocity... Here is the specific problem I had...

If a rigid link pin joint-fixed on ground and is rotating freely about the same point with uniform ang. vel., can we say the vector form of angular vel. (omega) is nothing but moment of the tangential (perpendicular) vel. at the other end?

Homework Statement A projectile launched at A with an initial velocity of 24 m/s at the angle θ=60deg, impacts the vertical wall at B. Neglecting air resistance, calculate the height h Homework EquationsThe Attempt at a Solution Here is my solution As you can see to find height h I assumed...

So I recently developed an interest in quad-rotors and was getting stated with its dynamics. I am particularly intrigued by the yaw motion of a quad-copter which comes into effect as a result of torques of the motors. When the motor torques are variable, we observe the yaw motion as result of a...

Can someone check if I'm doing this problem correctly? Please tell me if I did anything wrong. 1. Homework Statement A 12 g bullet passes horizontally through a 15 cm tall, 20 cm long .5 kg block which is initially at rest on a 1 meter tall table’s edge. The bullet is initially moving 230 m s...

Homework Statement Homework EquationsThe Attempt at a Solution The two particles are supposed to move along the same line. And the two radius vector could be anything. Is this correct?

Homework Statement Homework Equations vav = total distance traveled/ total time taken The Attempt at a Solution I have a problem in part c . How am I supposed to solve it? Is there any standard way to solve it?

Homework Statement An Airbus 380 needs to reach the velocity of 280 kmh^-1 before it takes off. The maximum acceleration the plain reaches in the runway is 0.95 ms^-2. Verify THAT the plane can use an airport with this runways. Runway 1: 3805 meters (SSW-NNE) Runway 2: 2400 meters (S-N)...

Let's imagine that we fire a cannon located on a platform high above the ground and we want to compute the time after which the horizontal velocity of the cannonball will be zero. Let's assume that we shoot at 0 degree angle. 1. Air resistance force F = C_d \frac{\rho v^2}{2}S 2. Assuming that...

Imagine such situation: There is a sniper who fires his rifle, the bullet travels at the initial speed of, say, 1400 m/s. His target is standing 2000 meters away and the wind is blowing at 30 m/s opposing the bullet's motion. Let's assume that the bullet is fired in a straight lane and it may...

I would greatly appreciate it if someone can clarify the conditions on when to use to each of the kinematics equations, because I end up with the wrong answer for using the wrong equations of the 3. 1. vf = vi + at When can I use this and when cannot? 2. vf^2 = vi^2 + 2a(xf-xi) When can I use...

Can there be a system that utilizes mechanical energy to produce kinetic energy, but "storing" the mechanical energy to be used at a different time for kinetic energy? Like a bike where you pedal but don't move; that mechanical energy is waiting to be "released" by some mechanism *** exclude...

Homework Statement In a 2-body scattering event, A + B → C + D, it is convenient to introduce the Mandelstam variables, s ≡ −(PA + PB)2 , t ≡ −(PA − PC) 2 , u ≡ −(PA − PD) 2 , where PA,...,D are the 4-momenta of the particles A, . . . , D respectively, (· · ·) 2 = (· · ·) · (· · ·) denotes a...

Homework Statement An elevator ascends from the ground with uniform speed. At time ##T_1## a boy drops a marble through the floor. The marble falls with uniform acceleration ##9.8## m/s^2 and hits the ground ##T_2## seconds later. Fiind the height of the elevator at time ##T_1##. Clue : if...

Homework Statement A body X moving with a velocity v makes an elastic collision with a stationary body Y of equal mass on a smooth horizontal surface. Which statement gives the velocities of the two bodies after the collision? (multiple choice question)The Attempt at a Solution The answer...

Homework Statement Two cars are traveling in a straight line, in the same direction, along a multi-lane highway in adjacent lanes. Car A starts 100 m behind Car B and both cars are initially traveling with a velocity of 20 m s−1 . Car B maintains a constant velocity but Car A begins to...

Homework Statement Homework Equations This would be the part I think I'm missing The Attempt at a Solution In the fourth line, Ix, where is the justification for multiplying 1/3 by the first term? I believe they are using the center of inertia of a rod, which is mr2 and the first term...

Homework Statement I have a rotating platform that spins as a mass attached to a wheel rotates the larger platform. The mass accelerates to the ground which spins the platform essentially. I am trying to calculate the moment of inertia of another mass which will be attached to the rotating...

Homework Statement Homework Equations The equations are all given The Attempt at a Solution This isn't really a homework question... it's solved, but I'm having a hard time following it. I don't understand where the first term: -a(kaθ) comes from. I can see it's the moment relation...

Homework Statement An 7.80-cm-diameter, 400 g solid sphere is released from rest at the top of a 1.70-m-long, 20.0 degree incline. It rolls, without slipping, to the bottom Homework Equations I=2/5 Mr^2 K = 1/2 m*v^2 Kroll = 1/2 Iw2 mgh=K+Kroll The Attempt at a Solution Using the above energy...

Homework Statement I'm having some issues with the following exercise: The graph below represents the marking of a vehicle speedometer in funtion of time. Elaborate the corresponding graphs of acceleration and space traveled in function of time. What is the average acceleration of the vehicle...

Homework Statement I think I made a mistake somewhere.. Homework Equations T = Jα T = F*R The Attempt at a Solution A) I started with T = Jα Since there is no slip, αm = αL Thus: Tm / Jm = TL / JL Plugging in, we find TL = Tm * JL / Jm = 2560 Now use T = F*R. Tm = Fm * Rm Plugging in...