Physics, 05.06.2020 21:08 krlx

You are pushing a cart across the room, and the cart has wheels at the front and the back. Your hands are placed on top of the cart at the center (left to right) of the top edge, pushing horizontally. There is friction between the wheels and the floor. Is the normal force between the floor and the front wheels greater than, smaller than, or equal to the normal force between the floor and the rear wheels? a) The force on the front wheels must be smaller than the force on the rear wheels. b) The force on the front wheels must be equal to the force on the rear wheels. c) The force on the front wheels must be greater than the force on the rear wheels.

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Answer from: madiballet125

The force on the front and rear wheels can be determined by finding the

force acting under equilibrium conditions.

The normal reaction between the floor and the front wheel is larger. The

correct option is c) The force on the front wheels must be greater than the

force on the rear wheels.

Reasons:

The forces acting on the wheels are;

Vertical forces acting on the cart:

The weight of the cart acting on the floor

The normal reaction of the floor on the wheels

The horizontal acting on the cart:

Pushing force acting horizontally

Friction force acting in the reverse direction

At equilibrium, the cart does not tip over

Sum of moment about the rear wheel = $\mathbf{W \times \dfrac{d}{2} + F \times h - N_{front} \times d} = 0$

Where;

h = The height of the cart

d = depth of the cart

$N_{front}$ = The normal reaction at the front wheels

Therefore;

$\displaystyle N_{front} = \frac{W \times \dfrac{d}{2} + F \times h}{d} = \mathbf{ \frac{W}{2} + \frac{F \times h}{d}}$

Sum of moment about the front wheel = $\mathbf{ F \times h + N_{rear} \times d - W \times \dfrac{d}{2} } = 0$

Therefore;

$\displaystyle N_{rear} = \frac{W \times \dfrac{d}{2} - F \times h}{d} = \mathbf{ \frac{W}{2} - \frac{F \times h}{d}}$

Which gives;

$\displaystyle N_{front} = \mathbf{ \displaystyle N_{rear} + 2 \times \frac{F \times h}{d}}$

$\displaystyle 2 \times \frac{F \times h}{d} 0$

Therefore;

$\displaystyle N_{front} \displaystyle N_{rear}$

The correct option is c) The force on the front wheels must be greater than

the force on the rear wheels.

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Answer from: NotYourStudent

The normal force is the force that the floor does as a reaction of the gravitational force that an object does against the floor (is the resistance that objects have when other objects want to move trhough them, and the force comes by the 3rd Newton's law, and this is specially used in cases where the first object is fixed, like walls or the floor). With this in mind, the point in where the normal force will be greater is the point that is closer to the center of mass of the object (the point with more mass)

If the wheels are in the extremes of the object, and the center of mass is in the middle of the object, the normal force will be equal. Now if for example, you put a little mass in one end of the object, now the center of weight displaces a little bit and is not centered, and the side is where you put the weight on will receive a bigger normal force from the floor than the other side.

Answer from: Quest

i wanna say it’s between b and d, leaning more towards b.

Answer from: Quest

graph question answered .. you think better when you are relaxed and happy

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You are pushing a cart across the room, and the cart has wheels at the front and the back. Your hand...

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