Question

# A 8 kg block slides down a frictionless incline making an angle of 20◦ with the...

A 8 kg block slides down a frictionless incline making an angle of 20◦ with the horizontal. The acceleration of gravity is 9.81 m/s2 .

a) Find the work done by the gravitational force when the block slides 5.9 m (measured along the incline).

b) What is the total work done on the block?

c) What is the speed of the block after it has moved 5.9 m if it starts from rest?

d) What is its speed after 5.9 m if it starts with an initial speed of 1.6 m/s?

a) vertical height travelled by the block, h = d*sin(20)

= 5.9*sin(20)

= 2.02 m

so, Workdone by gravity, Wg = m*g*h

= 8*9.81*2.02

= 158 J

b) Total Workdone, Wnet = Wg (since Workdone by normal force is zero)

= 158 J

c) use Work-energy theorem,

Wnet = Kf - Ki

Wnet = (1/2)*m*vf^2 - 0

==> vf = sqrt(2*Wnet/m)

= sqrt(2*158/8)

= 6.28 m/s

d) Again use Work-energy theorem,

Wnet = Kf - Ki

Wnet = (1/2)*m*vf^2 - (1/2)*m*vi^2

==> vf = sqrt(2*Wnet/m + vi^2)

= sqrt(2*158/8 + 1.6^2)

= 6.49 m/s

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