Theory question 118
Dynamics(a) An object is thrown up a smooth plane inclined at an angle of 30° to the horizontal. If the plane is 15m long and the object comes to rest at the top, find the (i) initial speed of the object (ii) time taken to reach the top.
(b) Force of magnitudes 5N, 5√3 N, 10N, 5√3 and 5N act on a body P, of mass 5kg as shown in the diagram. Find the (i) magnitude of the resultant force; (ii) acceleration of the body.
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(a) Retardation = g sin 30° = 10 × ½ = 5 ms−2 (taking g = 10)
(i) 0 = u2 − 2(5)(15), u = √150 ≈ 12.2 ms−1
(ii) t = u/5 = 2.45 s
(b) Forces at 60°, 30°, 0°, −30°, −60° to the 10N direction: components across cancel
Along: 10 + 2(5√3 cos 30°) + 2(5 cos 60°) = 10 + 15 + 5 = 30 N
(i) Resultant = 30 N along the 10N force
(ii) a = F/m = 30/5 = 6 ms−2
On a smooth slope the only retarding force is the weight component mg sin θ.