Ind the Distance D Traveled by the Sled From the End of the Slope Until It Comes to a Stop.

You can use physics to summate how far an object will slide down an inclined surface, such equally a ramp. For instance, say you and your friends are pushing a refrigerator upward a ramp onto a moving van, when suddenly your combined strength gives out and the refrigerator begins to plummet dorsum down the three.0-meter ramp. As you watch with dismay, it picks up speed. A car is parked behind the ramp, just 7.2 meters away. Will the errant refrigerator smash information technology?

Assuming that the ramp and the footing both have the same kinetic coefficient of friction and that the refrigerator starts to slide from the tiptop of the ramp, you lot demand to calculate how far the fridge will slide. You quickly pull out a pencil and newspaper and describe a effigy showing the fridge as it slides down the 3.0-meter ramp.

All the forces interim on an object sliding down a ramp.

When an object slides downward, the forces acting on information technology are dissimilar from the forces used to push it up the ramp (see the effigy). With the fridge, there'south no F _{pu sh} forcefulness to push information technology upward the ramp. Instead, the component of the refrigerator's weight acting forth the ramp pulls the refrigerator downward. And while the refrigerator slides down, friction opposes that forcefulness. You also need to know the coefficient of kinetic friction,

For this example, the coefficient of kinetic friction is 0.15.

So what force accelerates the fridge downward? The weight acting along the ramp is

and the normal force is

which ways that the strength of kinetic friction is

The cyberspace force accelerating the refrigerator down the ramp, F _{acc due east leration} , is the difference betwixt the component of the refrigerator'south weight forth the ramp and the frictional strength opposing it:

Annotation that you subtract F_F, the strength due to friction, because that force ever acts to oppose the force causing the object to move. Plugging in the numbers gives you

The cyberspace force pulling the refrigerator downwards the ramp is 360 newtons. Because the refrigerator is 100 kilograms, you lot accept an dispatch of 360 Northward/100 kg = 3.6 m/southward^two, which acts along the unabridged 3.0-meter ramp. Y'all tin can calculate the final speed of the fridge at the bottom of the ramp this mode:

Plugging in the numbers, y'all get

The final speed of the refrigerator when it starts traveling along the street toward the parked car is about 4.half-dozen meters per second.

Now you demand to calculate how far the refrigerator is going to become. Considering information technology'southward traveling along the pavement now, yous demand to factor in the force due to friction. Gravity volition no longer accelerate the object considering the street is apartment. Sooner or later, the refrigerator will come up to a stop. Just how close volition it come to a car that's parked in the street 7.two meters away? As usual, your first adding is the strength acting on the object. In this case, y'all figure the magnitude of the strength due to friction:

Because the refrigerator is moving along a horizontal surface, the normal forcefulness, F _Northward , is but the weight of the refrigerator, mg, which ways the strength of friction is

Plugging in the information gives you

A force of 150 newtons acts to stop the sliding fridge that'south now terrorizing the neighborhood. So how far volition it travel before it comes to remainder? If you take the refrigerator to be moving horizontally in the positive direction, and then because the strength is acting in the opposite direction, its horizontal component is negative. Because of Newton's second police, the acceleration is also negative and is given by

Yous can find the distance through the equation

The altitude the refrigerator slides is

In this case, you lot want the final velocity, v _f , to be nil, because you need to know where the refrigerator will end. Therefore, this equation breaks down to

Whew! The refrigerator slides just 7.1 meters, and the motorcar is 7.2 meters away. With the force per unit area off, you watch the show as your panic-stricken friends hurtle afterwards the fridge, only to run into it come up to a stop right before hitting the car — just as you lot expected.

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