### Question 8

(a) (i) Define uniform acceleration

(ii) Write an equation that relates linear velocity, angular velocity and radius of

path in circular motion.

(b) Two forces 30N and 40 N act at right angles to each other. Determine by scale drawing, the magnitude and direction of the resultant force, using a scale of 1 cm to 5 N.

(c) Explain why ships are usually refilled with sand water after they have been emptied of their cargo.

(d) A crate of drinks of mass 20 kg is placed on a plane inclined at 30o to the horizontal. If the crate slides down with a constant speed, calculate the:

### Observation

Part (a)(i). Most candidates were unable to differentiate between uniform acceleration and acceleration. Some defined uniform acceleration as __change__ in velocity instead of __increase__ in velocity which renders it incorrect. Some defined it as __rate__ of change instead of __time rate__ of __increase__ in velocity.

(ii) Most candidates were able to write the equation relating **v,w** and r correctly.

Part (b). Though a popular question among the candidates, only few were able to use scale drawing to determine the magnitude and direction of the resultant of the two forces. Some used calculation method in disregard to the given instruction.

Part (c). Many candidates could not give a good account of themselves. Some candidates even wrote that it is to prevent the ship from sinking, which was totally wrong.

Part (d): Many candidates responded fairly to thequestion. Some candidates simply used F = mg sin . Many candidates lost valuable marks because of the way they presented he work. Probably the answer was dictated to the candidates. For example some candidates wrote.

F = cos tita instead of tan.

A good number of the candidates were able to calculate the coefficient of kinetic friction using = tan.

The expected answers are:

8. (a)(i) __Uniform acceleration__.

Constant time rate of increase in velocity

OR

Velocity of the body increases by equal amounts in equal time intervals

(ii) linear velocity = angular velocity x radius of path

OR

v = ωr

(b)

≈ 37o 1o

**Note:** If a different method or scale is used, score 0.

** **

(c) A floating ship is balanced by its weight and the up thrust on it. When off- loaded, the upthrust becomes greater than the weight of the ship but when refilled with sand and water, equilibrium is restored for stability

** **

(d)(i) µ = tan

= tan 30 ** **

= 0.5774

(ii) F = µ mgcos

= 0.5774 x 20 x 10 x cos 30

= 100.0N

OR

F = mg sin

= 20 x 10 x sin 30