(a) (i) Define uniform acceleration. (ii) Write an equation that relates linear velocity, angular velocity...
(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 30 N 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 and 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 30° to the horizontal. If the crate slides down with a constant speed, calculate the:
(i) co-efficient of kinetic friction;
(ii) magnitude of the frictional force acting on the crate. [ g = 10 ms\(^{-2}\)]
Explanation
(i) Uniform acceleration is a constant time rate of increase in velocity.
(ii) Linear velocity = angular velocity x radius of path V = \(\omega\)r
(b) Scale: 1 cm to 5 N
30N = 6cm and 40N = 8cm
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(c) A floating ship is balanced by its weight and the upthrust on it. Hence when off-loaded the upthrust becomes greater than the weight of the ship, therefore when refilled with sand and water, equilibrium is restored for stability.
d)(i) \(\mu = tan \theta = tan 30^o = 0.5774\)
(ii) F = \(\mu g cos \theta\) = 0.5774 x 20 x 10 x Cos 30\(^o\) = 100N