Brick A is on an incline that makes an angle of 30.0º above the horizontal. It i
ID: 2024403 • Letter: B
Question
Brick A is on an incline that makes an angle of 30.0º above thehorizontal. It is attached via a cord over a frictionless pulley at the top
of the incline to a second brick, B, that is hanging vertical above the
ground. Brick B hangs a distance of 2.0 m above the groundThe
mass of A is 2.60 kg and the mass of B is 2.20 kg. The
coefficient of friction between A and the incline is µk = 0.180.
A) Draw the free-body diagrams for all the forces acting on bodies A
and B and write the net force equations for both bricks.
B) Solve for the acceleration of brick B and for the time for B to hit
the ground.
Explanation / Answer
A) free body of A
mg sin30 acts along the incline downwards
tension T and friction force Kmg cos acts upwards along the incline
let the acceleration 'a' be a upwards
free body of B
m'g acts downwards and acceleration 'a' is downwards
tension T acts upwards
B) from free body of A
T + kmg cos - mgsin = ma
T + 0.18*2.60*10 (3/2) - 2.60*10(1/2) = 2.6 a
T -8.947 = 2.6 a --------------EQ1
from free body of B
m'g - T = m'a
2.2(10) - T = 2.2 a -----------EQ2
adding the two equations
22 - 8.947 = 4.8 a
a = 2.72 downwards for block B
using s = ut + 1/2 at2
2 = 0 + 1/2 *2.72 t2
t = 1.212 sec
the answers are approximaton coz g is approximated to 10 for easy calculation
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