Answer:
3.9 m
Explanation:
The principle of work and energy
ΔE = W Formula (1)
where:
ΔE: mechanical energy change (J)
W : work of the non-conservative forces (J)
ΔE = Ef - E₀
Ef : final mechanical energy
E₀ : initial mechanical energy
Ef = K f+ Uf
E₀ = K₀ + U₀
K =(1/2 )mv² : Kinetic energy (J)
U = mgh :Potential energy (J)
m: mass (kg)
v : speed (m/s)
h: hight (m)
Known data
m = 1 kg : mass of the block
v₀ = mg(h).0 m/s Initial speed of the block
vf = 0 = Final speed of the block
θ =40° :angle θ of the ramp with respect to the horizontal direction
μk=0 : coefficient of kinetic friction
g = 9.8 m/s² : acceleration due to gravity
Problem development
W = 0 , Because the friction force (non-conservative force ) is zero
Principle of work and energy to the Block:
ΔE = W
Ef - E₀ = 0 Equation (1)
Ef = K f+ Uf =(1/2 )m(0)² + mg(h)= mg(h) (Joules)
E₀ = K₀ + U₀ = (1/2 )m(7)² + mg(0) = 24.5m (Joules)
In the equation (1) :
Ef = E₀
mg(h) = 24.5m
We divided by m both sides of the equation
g(h) = 24.5
h = 24.5 / g
h = 24.5 / 9.8
h = 2.5 m
We apply trigonometry at the ramp to calculate how far up the ramp (d) does the block slide before coming momentarily to rest :
sinθ = h/d
d = h / sinθ
d = 2.5 m / sin40°
d = 3.9 m
