Mechanics | Relativity Answers

Balls A and B accelerate from rest towards each other at 2 m/s² and 3 m/s² respectively. Given that the initial distance between the balls is 1500 m, determine:

i. the time taken for the balls to meet.

ii. the distance covered by ball A when the balls meet.

iii. the distance travelled by ball B when the balls meet.

The power, P, produced by a wind turbine is given by:

P = ( ½) C𝜌Av³

where 𝜌 is the density of air [ML^-3 ], A is the cross-sectional area [L² ] of the blade and v is the velocity of air. Determine in MLT the dimensions of:

i. v³

ii. P

iii. C

find the expression for the depression of the free end of a cantilever when the weight of the beam is effective?

A 500 g bar of ice is initially at -25 °C. Calculate the amount of energy required to vapourize 25% of the substance at 100 °C.

The fission of uranium nuclei in a nuclear reactor produces high speed neutrons. Before a neutron can trigger additional fissions, it has to be slowed down by collisions with carbon nuclei in the moderator of the reactor. Suppose a neutron with mass of 1.0u travelling at 2.0x107m/s undergoes a head-on elastic collision with a carbon nucleus with mass of 12u initially at rest. Calculate the velocities of the neutron and carbon after the collision.

A rocket with an initial mass of 7.0x102kg is in outer space. Suppose that 3/4 of the initial mass is fuel and the final mass is 1/4 of the initial mass. The rocket ejects the mass with a relative speed of 3.0km/s and consumes the fuel at a constant rate in a total time of 90s. Calculate the final speed of the rocket when it starts from rest.

A heavy block is suspended from a vertical spring.

The elastic potential energy is stored in the spring is 4 J.

What is the spring constant if the elongation of the spring is 10 cm?

Express the moment of the couple acting on the pipe assembly shown in rectangular form. The force magnitude F = 100 N

A loaded crane has a total mass of 225 kg. If a 312-N force acting at an angle of 30 degrees to the ground is applied, how much is done in moving the crane 20 feet? What is the weight of the loaded crane?

The vector −→k and −→x in the figure has a magnitude of 10.0 [m−1 ] and 5.00 [m], respectively. The vector −→k makes an angle of 35.0 ◦ with respect to the yaxis while the vector −→x makes an angle of 15.0 ◦ with respect to the x-axis. What is the scalar product, −→k · −→x ?