Question

Un bloque de 750 kg es empujado hacia arriba por una pista inclinada 15º respecto de la horizontal. El coeficiente de rozamiento es 0.4. Determinar la fuerza necesaria para iniciar la subida del bloque por la pista.

Answer 1

To determine the force required to initiate the ascent of the block up the inclined track, we need to calculate the force of friction and the force of gravity parallel to the incline and sum them up.

Step-by-step explanation:

To calculate the force required to initiate the ascent of the block up the inclined track, we need to consider the forces acting on the block. Assuming there is no external force, the force applied would need to overcome the force of friction. The force of friction can be calculated by multiplying the coefficient of friction (μ) by the normal force (Fn). The normal force can be calculated by multiplying the mass of the block (m) by the acceleration due to gravity (g). Therefore, the force of friction (Ff) is given by Ff = μ * m * g.

Next, we need to calculate the component of the weight acting in the direction of the incline. This component, known as the force of gravity parallel to the incline (Fg parallel), is given by Fg parallel = m * g * sin(θ), where θ is the angle of the incline.

The force required to initiate the ascent is equal to the sum of the force of friction and the force of gravity parallel to the incline. Therefore, the force required is F = Ff + Fg parallel.

Answer 2

4776.98 N is the minimum force to start the rise.

Step-by-step explanation:

We can use the first Newton's law to find the minimum force to move the block.

So we will have:

`F-W_(x)-F_(f)=0`

Where:

• F is the force
• W(x) is the weight of the block in the x direction, W = mg*sin(15)
• F(f) is the static friction force (F(f) = μN), μ is the static friction coefficient 0.4.

`F=W_(x)+F_(f)=mgsin(15)+\mu N`

`F=mgsin(15)+\mu mgcos(15)`

`F=mg(sin(15)+\mu cos(15))`

`F=750*9.81(sin(15)+0.4*cos(15))`

`F=4776.98 N`

Therefore 4776.98 N is the minimum force to move the block.

I hope it helps you!