Classical Mechanics Answers

In an experiment using a linear air track a 0.5kg rider travelling to the right at 2m/s collides with a stationary rider of mass 1kg find the velocities of the two riders after collision if it is perfectly elastic

2.3 The width of a confidence interval is a measure of its precision. The narrower the confidence interval, the more precise is the interval estimate, and vice versa. Describe any three aspects that influence the precision of the width of a confidence interval of a single population mean. 

A drain has a rectangular profile. W is the width of the drain in meters, and

D is the depth of the water in meters.

In the case that the depth is much less than the width the amount of water that flows per second through a rectangular drain is given by the following formula:

Q = (A/n)*(D^2/3)*(S^1/2) ------------- (1)

In which:

- Q is the volume of water that

flows per second through the

drain (in m3/s);

- A = W×D, the cross-sectional

area of the drain up to the level

of the water (in m2)

- n is a parameter describing the

resistance to the flow of water;

- S is the gradient of the river

(in m/m).

Use formula 1 to derive the units of n.

The following data relate to a four-link mechanism :

2.

  Link Length Mass

AB 60mm 0.2kg BC 200mm 0.4kg CD 100mm 0.6kg AD 140mm

MOI about an axis through centre of mass

80 kg. mm2 1600 kg. mm2 400 kg. mm2

          AD is the fixed link. The centres of mass for the links BC and CD lie at their mid-point whereas the centre of mass for link AB lies at A. Find the drive torque on the link AB at the instant when it rotates at an angular velocity of 47.5 rad s counter clockwise and angle DAI is 135 degree. Neglect gravity effects.

Note : All figures must be drawn with proper dimensions (reducing scale may be used) a

A winding drum with a mass 400 kg and a 2 m effective diameter raises a cage of mass 800 kg by a light rope. The radius of gyration of the drum is of 1 m. A balance mass of 500 kg is also used as a counterweight. The resistance to the motion of both cage and balance mass is 0.5 N / kg. The drum is driven by an electric motor through a reduction gear system with a ratio of 4:1. If the cage must accelerate upwards at 2 m/s2 , calculate the torque on the motor if the efficiency is 75%. 

A boy throws a ball straight into the air. It reaches the highest point of its flight in 4 seconds. How fast was the ball going when it left the boy’s hand?