Mechanics | Relativity Answers

The length of the mercury column in a non-calibrated mercury thermometer is 5.5 cm

when its bulb is immersed in melting ice and 24.5 cm when the bulb is in the steam above

boiling water at sea level.

Determine the:

i. temperature for a length of 14 cm

ii. length for a temperature of 75 ℃

iii. length that would correspond to a temperature of – 6 ℃

A. An airliner must reach a speed of 110 m/s to take off. If the available runway is 2.4 km

and the aircraft accelerates uniformly from rest at one end, what minimum acceleration

must be available if it is to take off?

B. A speeding motorist driving a car, passes a traffic police officer on a stationary

motorcycle. The police officer immediately gives chase: his uniform acceleration is

4ms-2

, and by the time he draws level with the speeding car, the police officer is

travelling at 30ms-1

.

i. How long did it take for the police officer to catch the car?

ii. If the speeding motorist continued to travel at a steady speed during the

chase, what was his speed?

C. A stone is thrown vertically upwards with a speed of 24.0 ms-1

. Using g = 9.8 ms-2

and

ignoring air resistance:

i. How much time is required to reach this height?

ii. Why are there two answers to (ii.)?

iii. Sketch the velocity-time graph for the stone, from it is released until it

returns to the thrower.

A train of mass 200kN has a frictional resistance of 5N per kN. The speed of the

train, at the top of an inclined of 1 in 80 is 45 km/h. Find the speed of the train after

running down the incline for 1km.

A. An object of mass m is placed on an inclined plane with a rough surface. Derive an

equation of the acceleration of the object sliding down the incline. [Be sure to

include an appropriate diagram highlighting the relevant forces] (10 marks)

B. A train of mass 200kN has a frictional resistance of 5N per kN. The speed of the

train, at the top of an inclined of 1 in 80 is 45 km/h. Find the speed of the train after

running down the incline for 1km. (10 marks)

A student builds and calibrates an accelerometer, which she uses to determine the speed of her

car around a certain unbanked highway curve. The accelerometer is a

plumb bob with a protractor that she attaches to the roof of her car. A friend riding in the car

with her observes that the plumb bob hangs at an angle of 15.0° from the vertical

when the car has a speed of 23.0 m/s.

A. What is the radius of the curve? (8 marks)

B. What is the centripetal acceleration of the car rounding the curve? (7 marks)

C. What is the speed of the car if the plumb bob deflection is 9.00° while

rounding the same curve? (5 marks)

A body of mass 25kg falls on the ground from a height of 19.6m. The body penetrates into the

ground. Assume the resistance by the ground to penetrate is constant and equal to 4998N.

Take g = 9.8m/s2

.

A. Find the final velocity of the body just before it hits the ground. (8 marks)

B. Calculate the retardation (acceleration) when the body is penetrating the ground.

(7 marks)

C. Find the distance through which the body will penetrate into the ground.

(5 marks)

An object of mass m is placed on an inclined plane with a rough surface. Derive an equation of the acceleration of the object sliding down the incline. [Be sure to include an appropriate diagram highlighting the relevant forces] 

An airliner must reach a speed of 110 m/s to take off. If the available runway is 2.4 km and the aircraft accelerates uniformly from rest at one end, what minimum acceleration must be available if it is to take off?

The equation of motion for a particular mass m suspended from a spring of constant k, is:

x=0.40cos(0.70t-0.30)

where x is the displacement of mass from its rest position, t is the time and the phase angle is in radians

From this equation find:

a)The amplitude

b)The frequency of vibration

c)The period

d)The phase angle in degrees

e)The ratio k/m for the spring

A body A of mass 2M is placed on a smooth horizontal surface and a small block B of mass M is placed at the top of the body, starting from rest, block B slides down on smooth surface of A, at instance when block B leaves A, the speed v of A