Mechanics | Relativity Answers

A common technique used to measure the
force constant k of a spring is the following:
Hang the spring vertically, then allow a
mass m to stretch it a distance d from the
equilibrium position under the action of the
“load” m g.Find the spring constant k if the spring
is stretched a distance 82 m by a suspended
weight of 64 N. The acceleration of gravity is
9.8 m/s2. Answer in units of N/m.

Imagine that you want to shoot an apple hanging in a branch with an arrow. You aim the arrow and at the exact time you shoot it, the apple falls from the branch. Will it hit? It should still hit the apple if the air resistance ( wind) is negligible that day. Why will the projectile always hit the falling object it is aimed at if it is fired at the same time the object starts to fall? Think about this problem in terms of projectile motion.

A fireman standing on a 13 m high ladder
operates a water hose with a round nozzle of
diameter 2.53 inch. The lower end of the hose
(13 m below the nozzle) is connected to the
pump outlet of diameter 3.61 inch. The gauge
pressure of the water at the pump is
P
(gauge)
pump = P
(abs)
pump − Patm
= 31.5 PSI = 217.185 kPa .
Calculate the speed of the water jet emerging from the nozzle. Assume that water is an
incompressible liquid of density 1000 kg/m3
and negligible viscosity. The acceleration of
gravity is 9.8 m/s
2
.
Answer in units of m/s.

A 5.00 m, 0.732 kg wire is used to support two identical, uniform 235 N posts of equal lengths at an angle of 57.0 degrees above the horizontal. Assume the wire is horizontal. A strong wind is blowing, causing the wire to oscillate in its fundamental (first harmonic) mode.
a) What is the wavelength of the fundamental mode?
b) What is the wave speed of the transverse waves on the wire that are combining to yield the fundamental standing wave pattern that is observed? (Hint: The posts are in equilibrium; calculate the torque about the pivots of the beams to determine the tension in the wire.)
c) What would be the frequency of the fifth harmonic?

A ball of mass 2 kg is projected up in the air from ground level with a speed 20 ms-1. it experiences constant air resistance R. It returns ground level with a speed of 15 ms-1 find R

A 5.5-kg rifle fires an 11 g bullet with a velocity of 1000 m/s. Question: what is the recoil velocity of the rifle

Kinematics
A dust particle kicked by Neil Armstrong on the moon leaves the lunar surface travelling at 2.0 m/s upwards. It moves upwards to a maximum height and then begins to falling back downwards. When it return to neils waist height on its descent( a height of 120cm above the lunar surface) it is falling at 33 cm/s

Determine the acceleration
Maximum height
And how long it takes from being kicked upwards to reach neils waist height on its descent

A man traveling in a train noticed that he passes a telegraphy Pole every 5secs he knows that the pole are 125m apart what speed does he deduce that the train is traveling in kmh

A pile driver drives a stake into the ground.the mass of the pile is 2500kg and it is dropped through a height of 10m on each stroke.the resisting force of the ground for this stake is e ×108N. how far is h stake driver on each stroke

A brick falls a distance Ah, with a potential energy change of Delta U g =|mg| Delta h . If no work is done on the earth-brick system, what is the change in the brick's kinetic energy , AK?