# Solving Block on Incline Homework Problem

• shikamarufoo
In summary, the problem involves a 725 gm block sliding down an inclined plane at an angle of 30° with the horizontal. The block accelerates at a rate of 1.5 m/s2. The task is to find the magnitude and direction of the total force exerted on the block by the plane, as well as the magnitude and direction of the force exerted on the plane by the block. The force of friction has been calculated to be 2465, but it may not be needed in the solution. To solve the problem, the sum of the forces on the block must be equal to the mass of the block times its acceleration. This can be calculated using either horizontal and vertical directions or along and into the plane
shikamarufoo

## Homework Statement

A 725 gm block slides down an inclined plane that makes an angle of 30° with the horizontal. It accelerates at 1.5 m/s2.

a) Find the magnitude and direction of the total force exerted on the block by the plane. For the direction, give the angle as measured counterclockwise from the vertical (in degrees).

b)What are the magnitude and direction of the force exerted on the plane by the block? For the direction, give the angle as measured counterclockwise from the vertical (in degrees).

I figured out the force of Friction was 2465

## Homework Equations

fnet = ma
Not really sure on what other equations to use

## The Attempt at a Solution

For a) I tried drawing a fbd and making a a triangle to find the hypotenuse to get the magnitude of the normal force, but I'm not getting it right. I also did sqrt(NormalForce^2 + Friction^2). For b), I'm not sure where to start.

Could you please walk me through this because I'm a bit confused now. Thanks~
Can someone please walk me through this because I'm a bit confused.

I figured out the force of friction was 2465
Probably on the right track, but did you remember to convert the grams to kg?
I don't think you need this force because it is part of the plane on box force you are trying to find.

This is an unusual question! Back to basics, I think.
Sum of the forces on the box = ma.
Gravity force + force of plane on box = ma

It is 2D so you need to work with two perpendicular directions. You could do it with horizontal and vertical directions or go with along the plane and into the plane.

Sure, solving this problem involves using Newton's laws of motion and some trigonometry. First, let's draw a free body diagram for the block on the inclined plane.

The forces acting on the block are its weight (mg) acting vertically downwards, the normal force (N) acting perpendicular to the plane, and the force of friction (Ff) acting parallel to the plane in the opposite direction of motion. Since the block is accelerating, there must be a net force acting on it. Using Newton's second law (Fnet = ma), we can set up the following equation:

Fnet = ma

Where Fnet is the sum of all the forces acting on the block. In this case, it is equal to the weight (mg) minus the force of friction (Ff):

Fnet = mg - Ff

Now, let's break down the forces into their components. The weight can be broken down into its x and y components, where the x component is mg sin(30°) and the y component is mg cos(30°). The normal force is equal to the y component of the weight (mg cos(30°)) since it is acting perpendicular to the plane. The force of friction is equal to the x component of the weight (mg sin(30°)).

Now, we can substitute these values into our equation for Fnet:

Fnet = (mg cos(30°)) - (mg sin(30°))

Since we know the mass (725 gm) and the acceleration (1.5 m/s^2), we can solve for the magnitude of the net force:

Fnet = (0.725 kg)(1.5 m/s^2) = 1.088 N

To find the direction of the net force, we can use trigonometry to find the angle between the net force and the vertical. This angle will be the same as the angle of the inclined plane (30°). So, the magnitude and direction of the net force is 1.088 N at an angle of 30° counterclockwise from the vertical.

Next, let's consider the force exerted on the plane by the block. By Newton's third law, we know that for every action, there is an equal and opposite reaction. This means that the force exerted on the plane by the block is equal in magnitude and opposite in direction to the force exerted on the block by the plane. So

## What is the basic setup for solving a block on incline homework problem?

The basic setup for solving a block on incline homework problem involves drawing a free body diagram of the block, labeling all the forces acting on the block, and applying Newton's second law to find the acceleration of the block.

## How do you find the normal force in a block on incline problem?

The normal force in a block on incline problem can be found by taking the component of the weight of the block that is perpendicular to the incline. This can be calculated using trigonometry or by using the formula N = mg cos(theta), where m is the mass of the block, g is the acceleration due to gravity, and theta is the angle of the incline.

## What is the role of friction in a block on incline problem?

Friction plays a crucial role in a block on incline problem as it is responsible for the block's motion or lack thereof. The direction and magnitude of friction depend on the coefficient of friction between the block and the incline, as well as the normal force acting on the block. In some cases, friction may prevent the block from sliding down the incline, while in others it may cause the block to accelerate down the incline.

## How do you determine the acceleration of a block on incline?

The acceleration of a block on incline can be determined by using Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In a block on incline problem, the net force is equal to the component of the weight of the block that is parallel to the incline minus the force of friction.

## What are some common mistakes to avoid when solving a block on incline problem?

Some common mistakes to avoid when solving a block on incline problem include forgetting to include all the forces acting on the block, using the wrong angle for theta, and not considering the direction and magnitude of friction correctly. It is also important to use consistent units throughout the problem and to double-check all calculations to ensure accuracy.

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