Mechanics | Relativity Answers

An electric fan is turning at 3.0 rev/s when it is turned off, it coasts to rest in 18s. Assuming the deceleration is uniform, how many revolutions did it turn through while coming to rest?

A large 3kg object hangs from a rope wound on a 40 kg wheel. The wheel has an actual radius of 0.75m and a radius of gyration of 0.60m. Find the angular acceleration and the distance through which the weight will fall in the first 10s.

a ball thrown upwards returns to the ground with the initial speed of u. the ball is at a height of 80 m at two times, the time interval being 6 s. find u by assuming g=10 m/s

Find, by the Fourier-series method, the steady-state solution for an undamped harmonic oscillator subject to a force having the form of a rectified sin-wave: F(t)=F₀|sinω₀t|, where ω₀ is the natural frequency of the oscillator.

A cyclist accelerates at a rate of 6.6m/s/s. How long will it take the cyclist to reach a speed of 14m/s from rest?

A ball thrown down from a balcony lands in 0.7 s on the ground at a speed of 23 m/s. Find:

a) the initial speed;


b) the height from which it was thrown;


c) the time to land if it were thrown up from the balcony with the same initial speed.

A truck starts from rest and accelerates at 0.7m/s2. 5 s later, a car accelerates from rest at the same starting point with an acceleration of 2.2m/s2.

a) Where and when does the car catch the truck?
_____ m from the starting point
at _____ seconds from the moment the truck started to accelerate.

b) What are their velocities when they meet?
The truck :
The car :

If 50 g is suspended at 15 , and 75 g is suspended at 135 , what mass must
be suspended at what angle to balance these two forces?

A simple pendulum of length l is suspended from a hook mounted on a slanted wall. The
wall makes a small angle theta with the vertical. The pendulum is displaced from the vertical
by a small angle phi(phi>theta)  and released. Assuming that the collision of the bob is elastic,
the time period of oscillation is

Obtain the expectational value of the potential energy v(x) = 1/2 mw^2x^2 of the one dimensional harmonic oscillator in the first excited state Ψ1(x) = 2(a/2√2)^1/2 axe^-a^2x^2/2