Mechanics | Relativity Answers

The soccer ball is kicked at 33° from the edge of the building with an initial velocity of 17 m/s and lands 61 meters away from the wall. How tall is the building that the child is standing on?

For surface waves in shallow water, the frequency and wavelength are connected through
the relation
3
2
ρλ
π
=
S
f
where S and ρ respectively denote surface tension and density of water. Calculate the
group velocity of waves. How is it related to phase velocity?

10. a) At what angular speed must a centrifuge rotate if a particle placed 7.0 cm from its axis of
rotation is to experience an acceleration of 1000g? (Take g = 10 ms−2
) (5)
b) Explain why hurricanes spin counter clockwise in the Northern hemisphere and
clockwise in the Southern hemisphere.

The potential energy (in J) of a system in one dimension is given by:

2 3 U (x) = 5 − x + 3x − 2x
What is the work done in moving a particle in this potential from x = 1 m to x = 2 m? What
is the force on a particle in this potential at x = 1 m and x = 2 m? Locate the points of stable
and unstable equilibrium for this system.

Three point masses of 3 kg each have the following position vectors:
r i k r j k r i j mˆ 3 mˆ
; ( ) 3( )1 m ˆ 3 mˆ
( ) 4 mˆ m ˆ
( ) 2( 3 )
2 2 2
1 2 3
t = t + t + t ; t = t + t = t − + t
r r r
Determine the velocity and acceleration of the centre of mass of the system.

A coin with a diameter of 2.5 cm is dropped on edge onto a horizontal surface. The coin starts out with an initial angular speed of 23 rad/s and rolls in a straight line without slipping. The rotation slows with an angular acceleration of magnitude 2.1 rad/s$^2$. How far does the coin roll before it stops?

Two blocks of masses 1kg and 2kg are in contact liying on a horizontal smooth surface. The blocks are pushed by the force of 6N. IF THE BLOCKS ARE ALWAYS IN CONTACT, WHAT IS THE FORCE AT THEIR COMMON CONTACT {IF FORCE APPLIED AT 1KG BLOCK}?

A cart is moving horizontally along a straight line with constant speed of 30 m/s. A projectile is fired from the moving cart in such a way that it will return to the cart after the cart has moved 80 m. At what speed (relative to the cart) and at what angle (to the horizontal) must the projectile be fired?

A particular spring stretches 20 cm when a 500g mass is hung from it. Suppose a 2.0kg mass is attached to the string and it is displaced 40 cm from equilibrium position and released. Find the speed of the mass when x = 10 cm.

What are the conditions for the mechanical equilibrium of a rigid body?
A ladder is placed against a wall making an angle θ with the floor. The wall is frictionless
but the coefficients of static and kinetic friction for the floor are µs and µk,
respectively.
Obtain an expression for the smallest value of θ for the ladder to not slip.