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# (Solved): Question 2 ( 35 marks) The force F, acting in a constant direction on the block of mass M, has a m ...

Question 2 ( 35 marks) The force

F

, acting in a constant direction on the block of mass

M

, has a magnitude which varies with the position

x

of the block. When

x=0

, the block is moving to the right at speed

v_(0)

. The coefficient of kinetic friction between the block and surface is

\mu _(k)

, as shown in Figure 2. (Hint: use work and energy principle) Given:

M=20kg,c=3 v_(1)=5(m)/(s),d=4 v_(0)=2(m)/(s),k=50(N)/(m)2 \mu _(k)=0.3,g=9.81(m)/(s)2

a) Draw free body diagram for the system. (5 marks) b) Prove that

N_(B)=Mg+((c)/(\sqrt(c^(2)+d^(2))))kx^(2)

. (5 marks) c) Determine how far the block slides before its velocity becomes

v_(1)

. (10 marks) d) Determine the speed of the block after it slides a distance

s=3m

. (10 marks) e) What happen if we consider static friction in the system. (5 marks)

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