# What Is the Maximum Force to Apply on a Sled Before a Penguin Slips Off?

• sonic91
In summary, a sled weighing 52 N is pulled horizontally across snow with a penguin weighing 67.3 N riding on it. The coefficient of static friction between the penguin and the sled is 0.791 and the coefficient of kinetic friction between the sled and snow is 0.097. Using a force diagram and the equation Fnet=ma, it is determined that the maximum horizontal force that can be exerted on the sled before the penguin begins to slide off is 64.8064 N. However, this answer was incorrect and it is determined that there must be a net horizontal force on the penguin that exceeds the maximum available static friction force for the penguin to start slipping.
sonic91

## Homework Statement

A sled weighing 52 N is pulled horizontally
across snow. A penguin weighing 67.3N rides
on the sled,as in the figure. (sorry i can't provide the picture)

If the coefficient of static friction between
penguin and sled is 0.791, find the maximum
horizontal force that can be exerted on the
sled before the penguin begins to slide off.
The coefficient of kinetic friction between sled
and snow is 0.097.

Fnet=ma

## The Attempt at a Solution

i drew a force diagram for the sled and i figured out that:

Fnet(horizontal)= -friction of sled on penguin -friction of the snow on the sled + applied force= 0 Newtons

i solved for the friction forces:

friction of sled on penguin= 67.3N * .791

friction of snow on sled= (52N + 67.3N) * .097

then i pluged those into my Fnet(horizontal) equation and solved for the applied force. i got 64.8064N as my final answer. when i entered this answer into the computer program that i use it said it was wrong. so i guess i am missing a step??

i got the same as you.

did i use the correct method though?

The sled and penguin are accelerating under the applied force. You can't sum forces equal to 0. Think of it this way: if the penquin was not accelerating (with respect to the ground), there would be no friction force acting on it. You'll need two separate force diagrams (free body diagrams).

ok, so if the sled and penguin are pulled with a force equal to the frictional force of the sled and penguin on the ice, the whole sled moves at a constant velocity, as forces are balanced, there is no net force, and so the penguin has no frictional force acting on it.

but then if the pulling force is increased there would be a net force. and so an acceleration of the sled, as hence a frictional force on the penguin. and when this net force was equal to the frictional force of the penguin, it would move?

Lachlan1 said:
ok, so if the sled and penguin are pulled with a force equal to the frictional force of the sled and penguin on the ice, the whole sled moves at a constant velocity, as forces are balanced, there is no net force, and so the penguin has no frictional force acting on it.
yes
but then if the pulling force is increased there would be a net force. and so an acceleration of the sled, as hence a frictional force on the penguin. and when this net force was equal to the frictional force of the penguin, it would move?
I don't think you said that quite corrrectly. When the net horizontal force on the penguin just exceeds the maximum available static friction force on the penquin, it will move (slip) relative to the sled (it is moving and accelerating with respect to the ground before that, but not moving or accelerating with respect to the sled before that). Now you must determine what the maximum horizontal applied force on the sled can be before the penguin starts to slip.

## What is friction and how does it affect a sled?

Friction is the resistance force that occurs when two surfaces rub against each other. It affects a sled by slowing it down and making it harder to move.

## How can friction be reduced to make a sled move faster?

Friction can be reduced by using materials with low coefficients of friction, such as wax or plastic, on the bottom of the sled. Additionally, keeping the sled's surface smooth and free of debris can also minimize friction.

## How does the weight of the sled impact friction?

The weight of the sled can impact friction by increasing the force of the sled pushing against the ground, resulting in more friction. However, if the weight is distributed evenly, it can also help to reduce friction and improve movement.

## What role does the surface of the ground play in friction for a sled?

The surface of the ground can greatly impact friction for a sled. Rougher surfaces, such as snow or gravel, will create more friction and slow the sled down. Smoother surfaces, like ice, will have less friction and allow the sled to move faster.

## Are there any other factors that can affect friction for a sled?

Other factors that can affect friction for a sled include temperature, as colder temperatures can increase friction, and the speed at which the sled is moving. Faster speeds can generate more friction, making it harder for the sled to move.

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