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Trajectory of a particle. A particle moves in a two-dimensional orbit defined byx(t) = ro0[1 + cos(omegat)] (1)y(t) = ro0[2 + sin(omegat)] (2)
(a) Sketch the trajectory. Find the velocity and acceleration (as vectors, and also their magnitudes), and draw the corresponding velocity and acceleration vectors along various points of your trajectory. Discuss the results physically - can you relate your finding to what you know from previous courses? Finally: what would you have to change if you want the motion to go the other way around?(c) Prove (in general, not just for the above situation) that if velocity, v(t), of any particle has constant magnitude, then its acceleration is orthogonal to v(t). Is this result valid/relevant for the trajectory discussed in part a?Hint There’s a nice trick here - consider the time derivative of |v(t)|^2=v.v
a ball with mass 2.5kg is moving in outer space with a velocity of 6.0 m/s horizontally, and a box of mass 4.5kg is moving with a velocity of 4.0m/s at an angle of 120 degrees from the horizontal
Copper wire (resistivity 1.7x10-8 italic capital omega space straight m , circular cross section with radius 2.34 mm) is used to form 2 thousand circular loops of wire in a solenoid
An astronaut on the Mars attaches a small brass ball to a 1.00- length of string and makes a simple pendulum. She times 13 complete swings in a time of 35.4 seconds. From this measurement she calculates the acceleration due to gravity on the Mars.
A student sits on a rotating stool holding two 3.0 kg objects. When his arms are extended horizontally, Find the new angular speed of the student
As a bar magnet moves toward a 150-turn coil, the magnetic field (which is perpendicular to the plane of the coil) changes from 0.25 T to 0.53 T in 0.3 s. what is the magnitude of the induced current in the coil
A 116 g Frisbee is 28 cm in diameter and has about half its mass spread uniformly in a disk, and the other half concentrated in the rim. What is the rotational inertia of the Frisbee
A rock of mass m = 1.0 kg is tied to a string of length L = 1.9 m and is twirled in a vertical circle. The speed v of the rock is constant; that is, it is the same at the top and the bottom of the circle. If the tension in the string is zero when the..
A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 18.0° below the horizontal. Find the length of time the car is in the air
A piece of Nichrome wire has a radius of 5.00 x10-4 m. It is used in a laboratory to make a heater that uses 2.00 102 W of power when connected to a voltage source of 120 V. Ignoring an effect of temperature on resistance, estimate the necessary l..
At an outdoor market, a bunch of bananas attached to the bottom of a vertical spring of force constant 16.0 N/m is set into oscillatory motion with an amplitude of 20.0 cm. What is the weight of the bananas in newtons
Find the peak magnetic field in an electromagnetic wave whose peak electric field is 200N/C
What is the tension in the rope that is lifting the lift and what is the tire's average angular acceleration during the 4.5 s time interval?
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