Question

A block is being held in place on a frictionless surface. The block has a mass of 3.9 kg and is held in place on an incline of angle = 32° by a horizontal force F, as shown in the figure below.

(a) Find the magnitude of the normal force
(b) Find the magnitude of F. (Ignore friction)

Answer 1

block is being held in place on a frictionless surface. The block has a mass of 3.9 kg and is held in place on an incline of angle = 32° by a horizontal force F, as shown in the figure below.

Step-by-step explanation:

Answer 2

The magnitude of the normal force can be calculated with N = mgcos(θ), and the magnitude of the horizontal force F needed to hold the block in place on a frictionless incline can be found using F = mgsin(θ), with m being the mass of the block, g the gravitational acceleration, and θ the angle of the incline.

Step-by-step explanation:

To find the magnitude of the normal force acting on a block on an incline, we must consider the components of the gravitational force in relation to the incline. The normal force is the component of the gravitational force that is perpendicular to the surface of the incline.

Since there is no friction and the surface is frictionless, the normal force (N) can be calculated using the equation N = mgcos(θ), where m is the mass of the block, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the incline.

To find the magnitude of the horizontal force (F), we need to counteract the parallel component of the gravitational force, which can be calculated using F = mgsin(θ).

Here's a step-by-step calculation for both parts:

1. Calculate the normal force: N = (3.9 kg)(9.8 m/s²)cos(32°).
2. Calculate the horizontal force needed to hold the block in place: F = (3.9 kg)(9.8 m/s²)sin(32°).