Mechanics | Relativity Answers

Cow 1: 400 kg and going 3 m/s. Cow 2: 500 kg and going 2 m/s Two cows collide with different masses and velocities and jet off 40 degrees to the right of original direction and 50 degrees to the left of original direction. Find the velocity of each cow.

A girl is sitting with her dog at the left end of a boat of length 10.0 m. The mass of the
girl, her dog and the boat are 60.0 kg, 30.0 kg and 100.0 kg respectively. The boat is at
rest in the middle of the lake. Calculate the centre of mass of the system. If the dog
moves to the other end of the boat, the girl staying at the same place, how far and in
what direction does the boat move?

A wheel 2.0 m in diameter lies in the vertical plane and rotates about its central axis
with a constant angular acceleration of 4.0 rad s−2
. The wheel starts at rest at t = 0 and
the radius vector of a point A on the wheel makes an angle of 60º with the horizontal at
this instant. Calculate the angular speed of the wheel, the angular position of the point A
and the total acceleration at t = 2.0s.

Wheels on a bicycle have a radius of 0.50 m. If the bicycle is traveling at a speed of 4.0 m/s, what is the period of rotation of its wheels?

A crate of mass 30.0 kg pulled by a force of 180 N up an inclined plane which makes is an angle of 30 with the The coefficient of kinetic friction between the plane and the crate is horizon. its speed after it has Hk 0.225. If the crates starts from rest, calculate been pulled 15.0 m. Draw the free body diagram.

Simple harmonic motion is the nature state of oscillation of stable system?

a) What should be the angular velocity of the earth such that a person of mass 80 kg
standing on the earth at the equator would actually fly off the earth?
b) A ball of mass 60g is moving due south with a speed of 50 ms−1 at latitude 30ºN.
Calculate the magnitude and direction of the coriolis force on the ball. Compare the
magnitude of this force to the weight of the ball.

A horizontal rod with a mass of 10 kg and length 12 m is hinged to a wall at one end
and supported by a cable which makes an angle of 30º with the rod at its other end.
Calculate the tension in the cable and the force exerted by the hinge.

A student is pushing a 35 kg desk across a floor at a constant speed of 4 m/s. How much work, to the nearest whole joule, must the student do on the desk to change the speed to 6 m/s?

What is the effect of damping in an oscillatory system? Differentiate between heavy
and critical damping. Show that the displacement of a weakly damped oscillator is
given by
x(t) = a exp(−bt) cos(w t − φ)
where symbols have their usual meanings