# Normal forces, Work, and Energy help

• katye
In summary, the cart has a total mass of 17.2 kg and is pulled at constant speed by a rope with a coeffiecient of kinetic friction of .8. The cart moves 19.2 m on a horizontal floor and the acceleration of gravity is 9.8 m/s^2.
katye
a cart loaded with bricks has a total mass of 17.2 kg and is pulled at constant speed by a rope. the rope is inclined at 20.2 degrees above the horizontal and the cart moves 19.2 m on a horizontal floor. the coeffiecient of kinetic friction between the ground and the cart is .8. The acceleration of gravity is 9.8 m/s^2.

what is the normal force exerted on the cart by the floor?
how much work is done on the cart by the rope?
(note the energy change due to friction is a loss of energy) what is the energy change due to friction?

=basically i don;t even know where to start :(

any help is appreciated!
Thanks

Start by drawing a free body diagram with all of the forces on it. Resolve the applied force into its components. Sum up the forces in each direction.

i've done that but i can't figure out how to solve for the applied force's x and y components because i can't set the sum of the forces in the x direction to zero because the box is moving right?

Yes you can because it's not accelerating. It's moving at a constant speed so the net force must be zero.

alright that make since.
but my homework service keeps telling me i';m wrong. do you see any mistakes

F(x)=0=Xcos(20.2) - (.8*17.2*9.8)
and i get X=143.68567
then i use that for
F(y)=0=N+(17.2)(-9.8)+ (143.68567sin(20.2))
and i get N=118.9456

F(x)=0=Xcos(20.2) - (.8*17.2*9.8)
This isn't quite right. The frictional force is $$f = \mu_kN$$, but you don't know what N is yet! That's what you are trying to solve for. In this case N is NOT simply equal to mg. There is a vertical component to the applied force so that affects the normal force. You must leave N as a variable in the first equation.

Your second equation is more or less right except for the 143.68567 part. You don't know what the force is yet so you must leave it as F (or X or whatever you are calling it).

So you have two equations and two unknowns (the applied force, and N), so you can solve for N with what you have.

oh my gosh. thank you so much. i know it seems really simple, but that problem has been killing me. i really appreciate it!

sorry, I'm trying to solve for how much work the rope is doing now and i thought the equation would just be
frictional force=applied force so (frictional coeff)*(Normal force)*(distance) but i was wrong, wrong, wrong. so .8(130.229)(19.2)
because 130.229 was what i found for my first answer for normal force

nevermind i got it! thanks!

and just for anyone who tries to use this in the future, the answer is the normal force you found in the first question*cos(angle)*distance :) best of luck!

## 1. What is a normal force?

A normal force is a type of contact force that acts perpendicular to the surface of an object in contact with another object or surface. It is often referred to as the support force as it prevents objects from passing through each other.

## 2. How is work defined in physics?

In physics, work is defined as the product of the force applied to an object and the displacement of the object in the direction of the force. It is measured in joules (J) and is a scalar quantity.

## 3. Can you explain the relationship between work and energy?

Work and energy are closely related concepts in physics. Work is the transfer of energy from one object to another, or from one form to another. Energy, on the other hand, is the ability to do work. The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy.

## 4. How is kinetic energy related to the normal force?

The normal force does not directly affect an object's kinetic energy. However, the normal force is often involved in situations where work is being done on an object, which can change its kinetic energy. For example, when an object is lifted against the force of gravity, the normal force is what allows the object to move and therefore, work is being done on the object.

## 5. Can you provide an example of how the normal force, work, and energy are related in real life?

Sure, let's take the example of a person pushing a shopping cart. As the person pushes the cart forward, they are applying a force to the cart, and the normal force from the ground supports the weight of the cart. This work being done on the cart increases its kinetic energy, allowing it to move. As the cart moves, its kinetic energy decreases due to friction and air resistance, but the normal force continues to support its weight and keep it from falling through the ground.

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