A34 kg block slides with an initial speed of 9 m/s up a
rampinclined at an angle of 10o with the horizontal.
thecoefficient of kinetic friction between the block and the ramp
is0.6. use energy conservation to find the distance the block
slidesbefore coming to rest.

5.4 m

Explanation:

mass, m = 34 kg

initial velocity, u = 9 m/s

final velocity, v = 0 m/s

coefficient of friction, μ = 0.6

Angle of inclination, θ = 10°

Let teh distance traveled before to come into rest is d.

According to the work energy theorem, the work done by all the forces is equal to the change in kinetic energy of the block.

Work done by the gravitational force = W1 = -  mg Sinθ x d  

Work done by the frictional force = W2 = - μ N = - μ mg Cosθ x d

negative sign shows that the direction of force and the direction of displacement is opposite to each other.

Total work done W = W1 + w2

W = - 34 x 9.8 x Sin 10 x d - 0.6 x 34 x 9.8 x cos 10 x d

W = - 254.86 d

Change in kinetic energy = 0.5 x m (v^2 - u^2)

                                         = 0.5 x 34 (0 - 81) = - 1377

So, W = change in KE

- 254.86 d = - 1377

d = 5.4 m

kepler used the data from tycho blahe (his mentor) to construct the laws of planetary motion.