# Free Body Diagram of a Truck with a Box

• Cinnamon
In summary, the large box containing your new computer slides toward the back of the truck when you accelerate. The forces on the truck are: normal force from the ground, reaction force from the tires pushing the box back, and friction force between the box and the truck bed. The length of the reaction force (Fk) is shorter than the length of the friction force (Froad).
Cinnamon

## Homework Statement

A large box containing your new computer sits on the bed of your pickup truck. You are stopped at a red light. The light turns green and you stomp on the gas and the truck accelerates. To your horror, the box starts to slide toward the back of the truck. (Assume that the truck is accelerating to the right.)

Draw clearly labeled free-body diagram for the truck. (The bed of the truck is not frictionless.)
Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded.

## Homework Equations

Nground: Normal force
Nb: Reaction to the normal force on the box from the truck
Froad: Reaction force to tires' backward push
Fk: The box's friction force on the truck bed
WT: Weight of the truck

## The Attempt at a Solution

Nground points up.
WT and Nb point down.
Fk points left.

I made the length of Nground = length of WT = length of Nb.

Now I'm thinking that the length of WT and Nb should be equal but together add up to the length of Nground so that the net force in the y direction is 0.

Can you attach a picture of your sketch? That would help a lot.

Yes you'll have to add the weight of box and truck for the force between truck and ground - in the same way you cannot simply remove the mass of the driver or any part of the truck from this force.

My only options are the ones I provided in relevant equations. I assume that WT includes the weight of the box in the truck too so I don't think that's the issue here. Here's the sketch, the two overlapping vectors at the bottom are WT and Nb.

#### Attachments

• 4.34-2.png
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Here's a little diagram I made too if that helps at all.

#### Attachments

• 4.34 sketch.png
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Since you are listing all the forces on the truck, and the normal force between the truck and the box is one of these, you should not include that in WT. So the normal force from the ground should equal their sum.
But why do you think WT and Nb would be equal? And why have you drawn Fk about equal in length to Froad?

## What is a free body diagram?

A free body diagram is a visual representation of all the forces acting on an object, typically drawn as vectors, without considering the object's motion or response to those forces.

## Why is a free body diagram important when studying a truck with a box?

A free body diagram is important because it helps us to understand and analyze the different forces acting on the truck and box, such as weight, friction, and tension, which can affect the stability and movement of the truck.

## How do you draw a free body diagram of a truck with a box?

To draw a free body diagram of a truck with a box, you would first identify all the forces acting on the truck and box, including the weight of the truck and box, the normal force exerted by the ground, and any external forces like friction or tension. Then, you would draw arrows to represent the direction and magnitude of these forces on the diagram.

## What are some common assumptions made when drawing a free body diagram of a truck with a box?

Some common assumptions include treating the truck and box as point masses, neglecting any rotational forces, and assuming that the ground is flat and level.

## How can a free body diagram be used to solve problems related to a truck with a box?

A free body diagram can be used to solve problems by breaking down the forces acting on the truck and box, and using Newton's laws of motion to calculate the net force and acceleration. This can help us understand the stability of the truck, the force required to move it, and the impact of different forces on the truck and box.

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