Classical Mechanics Answers

Which of the following is an accurate statement?
1 : The magnitude of a vector can be zero even though one of its components is not zero.
2 : It is possible to add a scalar quantity to a vector.
3 : Even though two vectors have unequal magnitudes, it is possible that their vector sum is zero.
4 : Rotating a vector about an axis passing through the tip of the vector does not change the vector.
5 : The magnitude of a vector is independent of the coordinate system used.

A particle of mass 3 units moves in xy plane under influence of a force field having potential V equal to 12x(3y-4x).The particle starts at time t=0 from rest and the point with position vector 10i-10j. 1.set up differential equations and conditions describing the motion 2.solve the equations in (1) 3.find the position at any time 4.Find the velocity at any time

A uniform solid disk of mass M=10 kg and radius R=0.4 m is initially at rest. The disk can rotate freely about a fixed frictionless axle passing through the center of the disk and perpendicular to the disk. Two forces of magnitude F1=2 N and F2=1 N are applied tangentially to the disk, as shown in the figure below. The moment of inertia of a disk is given as I=½MR2.
(a) Calculate the magnitude of the nettorque dueto the two forces shown.
(b)Calculate the magnitude of the resulting angular acceleration.
(c) How long does it take the disk to complete one revolution?

"life cannot exist without plasma".discuss this in detail

A boy can throw a ball obliquely to a maximum horizontal distance 'X' while standing on the ground.If he throws the same ball from the top of a tower of height ' X ' at an angle of 45° above the horizontal from the foot of the tower the ball hits the ground at a distance (Assume same initial speed)

A 1kg mass slides down several frictionless inclines - each incline angle decreases by 1 degree for each 1-meter segment travelled. When the mass reaches the 0-degree incline, determine the total time travel time, the total height the mass falls and velocity.

In Fig. 2, a block of mass m lies on a horizontal frictionless surface and is attached to one end of a horizontal spring (spring constant k) whose other end is fixed. The block is initially at rest at the position where the spring is unstretched (x = 0) when a constant horizontal force F in the positive direction of the x axis is applied to it. A plot of the resulting kinetic energy of the block versus its position x is shown in Fig. 7-36. The scale of the figure’s vertical axis is set by Ks = 4.0 J. (a) What is the magnitude of F ? (b) What is the value of k?

A car’s suspension is being tested, made from a single spring of stiffness k = 150 kNm-1. The suspension is attached to a testing system which can compress and extend the suspension many times a second given a certain input . An accelerometer is placed at the bottom of the spring.The system is tested in a lab under two different conditions for which you are asked to calculate different parameters.
A) The acceleration picked up by the sensor matches the following equation:

an elastic material has a length of 36cm when a load of 40N is hung on it and a length of 45cm when a load of 60N is hung on it. what is the original length of the screen?

A. Particle moving in a circle of diameter 5 m .what is displacement when it covers one and half revolution