Physics, horizontal force

Question

A horizontal force of 171 N pushes a 18 kg block up a frictionless incline that makes an angle of 55° with the horizontal.

(a) What is the normal force that the incline exerts on the block?

? N 

(b) What is the acceleration of the block? (Hint: assume up the block as the positive direction.)

? m/s²

^{Please show steps! thank you}

Answer 1

I would recommend drawing a force diagram for the block on the incline. You can choose the direction of your coordinates; the y direction can be aligned with either gravity or the block's normal force (perpendicular to the inclined surface). I am assuming the latter, that the blocks normal force is in the y direction, and the block acceleration is only in the x direction.

a) There are three forces on the block: gravity, the applied force, and the block's normal force. To find the magnitude of the normal force, we should do a force balance in the y direction. Using your force diagram, you should see that the portion of gravity in the negative y direction is F_gcos(Θ). Since the applied force is in the horizontal direction (aligned with the ground), only a portion of the applied force is in the negative y direction: F • sin(Θ). Let's complete the force balance:

F_y = N - F_gcos(Θ) - F • sin(Θ)= 0

0 = N - mg•cos(Θ) - F • sin(Θ)

N = 18 kg * 9.8 m/s² * cos(55°) + 171 N * sin(55°)

= 18 kg * 9.8 m/s² * 0.5736 + 171 N * 0.8191

= 241.255 N

b) To find the acceleration of the block, we need to do a force balance in the x direction, which is aligned with the surface of the incline. The only forces acting on the block in this direction are gravity and the applied force. The magnitude of the gravitational force in this direction is F_gsin(Θ). The magnitude of the applied force in this direction is F cos(Θ). Let's complete the force balance:

F_x = F_gsin(Θ) - F • cos(Θ)= 0

F_x = mg•sin(Θ) - F • cos(Θ)

F_x = 18 kg * 9.8 m/s² * sin(55°) - 171 N * cos(55°)

= 18 kg * 9.8 m/s² * 0.8191 - 171 N * 0.5736

= 46.404 N (positive)

Now to find the acceleration, we apply this to Newton's second law:

F = m * a

a = F / m

= 46.404 N / 18 kg

= 2.578 m/s²

Since this is a positive number, the acceleration is up the incline.