A 2.0 kgkg wood block is launched up a wooden ramp that is inclined at a 25 ∘∘ angle. The block's initial speed is 11 m/sm/s . The coefficient of kinetic friction of wood on wood is μk=0.200μk=0.200. Part A What vertical height does the block reach above its starting point?

The B part of the question is missing and it says;

What speed does it have when it slides back down to its starting point?

A) vertical height the block reaches above its starting point = 3.568m

B) Speed of block when it slides back down to its starting point = 6.323 m/s

Explanation:

A) Since inclined at an angle of 30°,thus;

For kinetic friction, h = mg cosθ

Thu kinetic friction force(Fk) is ;

Fk = μmg cosθ

Let's choose the x-direction to be parallel to the ramp surface.

Resolving all the forces on the block in the x-direction;

ΣFx; μmg cosθ = -ma - mg sinθ

Divide each term by m to get;

μg cosθ = -a - g sinθ

Making a the subject of the formula,

a = -μg cosθ - g sinθ

a = - g(μ cosθ + sinθ)

So a = - 9.81[0.2(cos25°) + sin 25°]

a = - 9.81[ 0.1813 + 0.4226]

a = -5.924 m/s²

Using equations of motion,

v² = u² + 2as

Now v = 0m/s while u= 10m/s and s=Δx since ramp is chosen to be parallel to x-direction

Thus 0² = 10² + 2(-5.924)(Δx)

So making (Δx) the subject ;

11.85(Δx) = 100

So, Δx = 100/11.85 = 8.44m

Thus; vertical height which is the vertical component displacement = (Δx) x sinθ = 8.44Sin(25) = 8.44 x 0.4226 = 3.568m

B) when the block is sliding down, the sign of the friction changes.

Thus;

ΣFx; - μmg cosθ = -ma - mg sinθ

So, a = μg cosθ - g sinθ

a = g(μ cosθ - sinθ)

So a = 9.81[0.2(cos25°) - sin 25°]

a = 9.81[ 0.1813 - 0.4226] = - 2.37 m/s²

Again, using equations of motion,

v² = u² + 2as

So in thus case u =0 and since it is moving down the plane, the displacement will be negative, thus

(Δx) = - 8.44m

So, v² = 2(-2.37)(-8.44) = 40

Thus, v = √40 = 6.323 m/s

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strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force