# Newton's Laws of motion problem

• sepah50
In summary, the problem involves a block on an inclined plane with a force F pushing it upward at an angle of 35.0° to the horizontal. The coefficients of static and kinetic friction are given as 0.333 and 0.156 respectively. The minimum value of F that will prevent the block from slipping down the plane can be found by summing up the forces in the y-direction (perpendicular to the plane) and setting it equal to the force of gravity. Then, using the equation for static friction, the maximum value of friction can be calculated and used to determine the minimum value of F.
sepah50

## Homework Statement

A block weighing 70.0 N rests on a plane inclined at 25.0° to the horizontal. A force F is applied to the object at 35.0° to the horizontal, pushing it upward on the plane. The coefficients of static and kinetic friction between the block and the plane are, respectively, 0.333 and 0.156.

What is the minimum value of F that will prevent the block from slipping down the plane?

## Homework Equations

$$\sum$$Fy= Sum of all Forces = Newton's Second Law

## The Attempt at a Solution

So in the beginning I draw the Angles and make a Free Body Diagram. I sum up all the forces which is
$$\sum$$Fy = $$\eta$$ + Fsin(10) - 70cos(25) = may

may is 0 since block is not moving away from the plane

what I get then is $$\eta$$= .173648F - 63.4415

After this point I know I have to find Fsmax which equals $$\mu$$s$$\eta$$. After this part I get lost but I can't find $$\eta$$$$\mu$$s
From what I remember $$\mu$$$$\eta$$s = mg*sin$$\theta$$. Hope somebody can help!

Hi sepah50,

sepah50 said:

## Homework Statement

A block weighing 70.0 N rests on a plane inclined at 25.0° to the horizontal. A force F is applied to the object at 35.0° to the horizontal, pushing it upward on the plane. The coefficients of static and kinetic friction between the block and the plane are, respectively, 0.333 and 0.156.

What is the minimum value of F that will prevent the block from slipping down the plane?

## Homework Equations

$$\sum$$Fy= Sum of all Forces = Newton's Second Law

## The Attempt at a Solution

So in the beginning I draw the Angles and make a Free Body Diagram. I sum up all the forces which is
$$\sum$$Fy = $$\eta$$ + Fsin(10) - 70cos(25) = may

may is 0 since block is not moving away from the plane

what I get then is $$\eta$$= .173648F - 63.4415

I think you have a couple of sign errors here.

After this point I know I have to find Fsmax which equals $$\mu$$s$$\eta$$. After this part I get lost but I can't find $$\eta$$$$\mu$$s

When you summed up all the forces, you did it only in the y-direction (perpendicular to the plane). What is the sum of the forces in the x-direction (parallel to the plane)?

From what I remember $$\mu$$$$\eta$$s = mg*sin$$\theta$$. Hope somebody can help!

Thanks! :)

thanks

First, we need to determine the normal force (F_N) acting on the block, which is equal to the component of the weight of the block perpendicular to the plane. We can find this using trigonometry: F_N = 70.0 N * cos(25.0°) = 63.4415 N.

Next, we need to find the maximum possible frictional force (F_smax) that can act on the block without causing it to slip down the plane. This is given by F_smax = \mu_s * F_N, where \mu_s is the coefficient of static friction. Plugging in the values, we get F_smax = 0.333 * 63.4415 N = 21.1465 N.

Now, we can set up an inequality to find the minimum value of F that will prevent the block from slipping down the plane: F * sin(35.0°) ≥ F_smax. Solving for F, we get F ≥ F_smax / sin(35.0°) = 21.1465 N / sin(35.0°) = 38.8591 N.

Therefore, the minimum value of F that will prevent the block from slipping down the plane is 38.8591 N.

## What are Newton's Laws of Motion?

Newton's Laws of Motion are a set of three physical laws that describe the relationship between the forces acting on an object and its motion. They were formulated by Sir Isaac Newton in his book "Philosophiæ Naturalis Principia Mathematica" in 1687.

## What is the first law of motion?

The first law, also known as the Law of Inertia, states that an object at rest will stay at rest and an object in motion will stay in motion at a constant velocity unless acted upon by an external force.

## What is the second law of motion?

The second law states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. This can be mathematically represented as F=ma, where F is the net force, m is the mass of the object, and a is the acceleration.

## What is the third law of motion?

The third law states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert an equal and opposite force back on the first object.

## How can I apply Newton's Laws of Motion to solve problems?

To solve problems involving Newton's Laws of Motion, you must first identify the forces acting on the object and determine their direction and magnitude. Then, you can use the equations derived from the laws to calculate the resulting motion of the object. It is important to draw free-body diagrams and use proper units in your calculations.

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