Mechanics | Relativity Answers

Two waves 1 and 2 are present on a string:
y1 = ( 35 mm ) Sin[ ( 8.4m^-1 )x - ( 15.7s^-1 )t ]
y2 = ( 35 mm ) Sin[ ( 8.4m^-1 )x- ( 15.7s^-1)t ]

(i) Write the expression for the resultant wave, y = y1 + y2 in the form of wave function
for a standing wave. (ii) Determine the x coordinates of the first two antinodes, starting at
the origin and progressing towards + x direction. (iii) Determine the x coordinate of the
node that is between the antinodes of part (ii).

1.A harmonic wave on a rope is described by the expression
y(x,t)=(4.3 mm)sin[ (2pi/0.82 m)(x+ (12 m/s)t) ]
What are the wave’s wavelength, period, wave number, frequency, and direction of
propagation.
2.For the wave in qus 1 above, determine the displacement and acceleration of the
element of the rope located at x = 0.58m at the instant t = 0.41s.

Establish the differential equation for a system executing simple harmonic motion
(SHM). Show that, for SHM, the velocity and acceleration of the oscillating object is
proportional to w(0) and w^2(0), respectively, where w(0) is the natural angular frequency of
the object.
note : here w stands for omega

The displacement of a particle executing SHM is given by
x(t) = 6sin5(pi)t + 8cos5(pi)t
where x is in cm and t is in seconds. Calculate the amplitude, time period and initial
phase of the SHM. Also, obtain the expression for the velocity of the particle.

motorcycle is going along are banked road and he has to line, inwards making an angle of 21°49' with the vertical in order to keep his balance if path length is 1 km long find the speed of the cyclist?

A glass with a mass of 0.472 kg is dropped and has a speed of 2.7 m/s when it suddenly hits the hard dining room floor. Calculate the impulse force

A glove is dropped from a 40 m tall building and simultaneously a ball is thrown from the ground at the speed of 40 m/s. when and where do they meet??

Consider a 555 N cat burglar supported by a
cable as in the figure.Find the tension in the inclined cable.
Answer in units of N and also Find the tension in the horizontal cable.
Answer in units of N

Two men decide to use their cars to pull a
truck stuck in mud. They attach ropes and
one pulls with a force of 757 N at an angle
of 27◦ with respect to the direction in which
the truck is headed, while the other car pulls
with a force of 1177 N at an angle of 18◦ with
respect to the same direction What is the net forward force exerted on
the truck in the direction it is headed?
Answer in units of N

A ball dropped from the height of of 200
meters how much time or when it will take to
hit the surface? and what will be the final
velocity"