Question

A 3.5 kg block slides along a frictionless horizontal with a speed of 2.5 m/s. After sliding a distance of 5 m, the block makes a smooth transition to a frictionless ramp inclined at an angle of 50â—¦ to the horizontal. The acceleration of gravity is 9.81 m/s 2 .

Answer 1

L = 0.416 m

Step-by-step explanation:

In this exercise to calculate the distance traveled in the branch that climbs the block we can use the concepts of energy

Starting point Flat part

Em₀ = K = ½ m v²

Final point. Highest part of the ramp

`Em_(f)` = U = m g h

As there is no friction the mechanical energy is conserved

Em₀ =
`Em_(f)`

½ m v² = m g h

h = v² / 2g

h = 2.5 2/2 9.8

h = 0.3189 m

The distance traveled can be found with trigonometry

sin 50 = h / L

L = h / sin 50

L = 0.3189 / sin50

L = 0.416 m