Mechanics | Relativity Answers

A block of unknown mass is attached to a
spring of spring constant 9.6 N/m and undergoes simple harmonic motion with an amplitude of 14.8 cm. When the mass is halfway
between its equilibrium position and the end-point, its speed is measured to be 32.7 cm/s.
Calculate the mass of the block.
Answer in units of kg.

A visitor to a lighthouse wishes to determine
the height of the tower. She ties a spool
of thread to a small rock to make a simple
pendulum, which she hangs down the center
of a spiral staircase of the tower. The period
of oscillation is 10.8 s.
The acceleration of gravity is 9.8 m/s2 .
What is the height of the tower?
Answer in units of m.

A vehicle of mass 710 kg accelerates uniformly from rest to a velocity of 65 kmh -1 in 12 seconds whilst ascending a 15% gradient. The frictional resistance to motion is 0.5kN. Making use of D’ Alembert’s principle, determine:

i) The tractive effort between the wheels and the road surface.
ii) The work done in ascending the slope.
iii) The average power developed by the engine.

Find the work done by pushing a mass of 700 kg through a distance of 4.5m along a surface if the coefficient of friction is 0.2. Assume the force is applied horizontally.

When a falling meteor is at a distance 4.19 times the radius of the Earth above the Earth’s surface, what is its free fall acceleration? The acceleration of gravity is 9.8 m/s2, the universal gravitational constant is 6.67259×10−11 N · m2/kg2, and the Earth’s radius is 6.37 × 106 m. Answer in units of m/s2.

For constant acceleration write an equation relating the final velocity and time to the initial velocity and time

A water tank contains water upto 20 cm high.&
Calculate the pressure exerted by water at the bottom of the tank.

A piece of ice is gently placed on the surface of water filled in a glass tumbler, so the water rises to the brim.
What will happen to the level of water when the ice melts? Will the water overflow? If not, explain with reason.

A juggler throws a ball from height of 0.950 m with a vertical velocity of +3.50 m/s and misses it on the way down. What is its velocity when it hits the ground?

The displacement vector for a 15.0 second interval of a jet airplane's flight is (2850, −2430) m. (a) What is the magnitude of the average velocity? (b) At what angle, measured from the positive x axis, did the airplane fly during this time interval? Express the angle as a number between −180° and +180°