Question

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?

Answer #1

**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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