Problem 35By Brianna Barta

Physics Honors Review

Problem 35

An empty sled of mass 25 kg slides down a muddy hill with a constant speed of 2.4 m/s. The slope of the hill is inclined at an angle of 15º with the horizontal as shown in the figure above.

Part A

Calculate the time it takes the sled to go 21 meters down the slope

The velocity is constant so just divide 21 meters by 2.4 meters per second.

Part A

Meters cancel out and were left with a unit of time. That’s exactly what we want!

Part B

On the dot below that represents the sled, draw and label a free-body diagram for the sled as it slides down the slope.

Part B

First, the weight force. Weight always points straight down, even if the object is on a slope.

Part B

Now the normal force. The normal force is always perpendicular to the surface that the object is on.

Part B

Now friction. Friction is the along the surface the object is traveling on.

Part C

Calculate the frictional force on the sled as it slides down the slope.

Change the axis so that the weight force is off at an angle

Part CNow that the FBD is rotated, the legs of the triangle formed by the weight force are equal to the Normal and friction forces because the sled is in equilibrium.

Part C

How to find the values of the normal and friction forces. (aka the legs of the triangle)

Used 10 for gravity

MAKE SURE YOUR CALCULATOR IS IN DEGREES!!!

Part C

We use sine because friction equals the side opposite to the angle. After multiplying by the weight force (the hypotenuse) we see that the force by friction is 64.705 Newtons

250 N

Part D

Calculate the coefficient of friction between the sled and the muddy surface of the slope.

To find the coefficient of friction we use the FUN equation.

Part D

Part D

Cosine 15 degrees times the weight force equals the normal force (the adjacent leg of the triangle) 250

N

Part DNow we can plug in numbers to the FUN equation.

f = 64.705 NN = 241.481 N

NN

N

N

N

N

And solve for μ

Part E

The sled reaches the bottom of the slope and continues on the horizontal ground. Assume the same coefficient of friction.

Part E

i. In terms of velocity and acceleration, describe the motion of the sled as it travels on the horizontal ground.

• The acceleration of the sled is now negative, meaning the sled’s velocity is decreasing and it is slowing down.

Part Eii. On the axes below, sketch a graph of

speed (v) versus time (t) for the sled. Include both the sled’s travel down the slope and across the horizontal ground. Clearly indicate with the symbol tι the time at which the sled leaves the slope.

Part E

The velocity is constant at 2.4 meters per second until the sled leaves the slope. After that it begins decreasing until velocity equals 0 and it stops moving.