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

given data:

determine the horse power (h.p) = ?

force applied to move the box(f) = 10 pounds,

box lifted from a distance         (d) = 3 feet

time taken to lift                         (t) = 10 sec,

the horse power is defined as amount of work required to move a load. the horse power is equal to 550 foot-pound per second

                  1 h.p   = 550 foot-pound/second

it can also be defined as the the load that need to be move a body for certain distance in a certain amount of time.

mathematically,

                      h.p = (force × distance)/ time

                            = (10 × 3)/ 10

                            = 30/10

                            = 3 foot -pound/sec

hence, the horse power is needed to move the box is 3 foot-pound/second

important note: 1 h.p = 550 foot-pound/second = 746 watts