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Transcribed Image Text:A pulley is attached to one end of a rough plank, which makes an angle of
34° with the horizontal. A box is held at rest on the plank by a string that is
attached to the box and passes over the pulley. A bucket of water is attached
to the other end of the string and hangs freely. The coefficient of static
friction between the plank and the box is 0.8. The box remains at rest but is
on the point of slipping up the plank. The bucket of water has mass 7.5 kg.
pulley
box
bucket of water
34°
Model the box and the bucket of water as particles, the string as a model
string and the pulley as a model pulley.
(a) By considering the forces acting on the bucket of water, find the
magnitude of the tension in the string (in newtons) in terms of g and
the magnitude of the acceleration due to gravity (in ms-2).
(b) State the four forces that act on the box and draw a force diagram
showing them, including the angles that show their directions.
(c) Take the unit vector i to be in the direction up the plank and the unit
vector j to be in the direction perpendicular to the plank and upwards.
Express the forces in component form, in terms of unknown magnitudes
where appropriate. Hence find the mass of the box (in kg) to two
significant figures.
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