How to solve these Newtons Law equations.

Question

Question 4.1a:

The block shown in the figure is sliding along a frictionless horizontal surface The block's mass is m = 4.85 kg,

the magnitude of the applied force is F = 20.5 N,

and the angle of the applied force F

from the horizontal is 𝜃 = 28.0°.

Three forces act on a block labeled m that is on a horizontal surface. The three forces acting on the block are as follows.

1. An arrow labeled vector F starts on the right side of the block and points up to the right at an angle 𝜃above the horizontal.
2. An arrow labeled vector n starts at the top of the block and points up.
3. An arrow labeled vector F_g extends from the bottom of the block and points down.

Determine the magnitude n of the normal force acting on the block.

_______N

Question 4.1b:

The block shown in the figure is sliding along a frictionless horizontal surface. The block's mass is m = 4.90 kg,

the magnitude of the applied force is F = 24.0 N,

and the angle of the applied force F

below the horizontal is 𝜃 = 32.5°.

Three forces act on a block labeled m that is on a horizontal surface. The three forces acting on the block are as follows.

1. An arrow labeled vector F starts on the right side of the block and points down to the right at an angle 𝜃 below the horizontal.
2. An arrow labeled vector n starts at the top of the block and points up.
3. An arrow labeled vector F_g extends from the bottom of the block and points down.

Determine the magnitude n of the normal force acting on the block.

 ________N

Question 4.1c:

The block shown in the figure is sliding down a frictionless surface inclined at an angle 𝜃 = 27.1°

above the horizontal. The block's mass is m = 4.55 kg.

A block labeled m is positioned upon the incline of a right-triangular wedge that makes an acute angle 𝜃 with a horizontal surface. Two arrows extend from the block.

1. A diagonal arrow labeled vector n starts on the block and points in a direction perpendicular to the incline and upward.
2. A vertical arrow labeled vector F_g starts on the block and points downward.

Determine the magnitude of the normal force n acting on the block.

 ________N

Answer 1

4.1 a) n = F_g - Fsinθ = 4.85 * 9.8 - 20.5 *sin28 = 37.9 N

4.1 b) n = F_g + Fsinθ = 4.90 * 9.8 + 24 *sin32.5 = 60.9 N

4.1 c) n = F_gcosθ = 4.55 * 9.8 *cos27.1 = 39.7 N