2. 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.
3. 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.
4. Part A
Meters cancel out and were
left with a unit of time. That’s
exactly what we want!
5. 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.
6. Part B
First, the weight force. Weight always points
straight down, even if the object is on a slope.
7. Part B
Now the normal force. The normal force is
always perpendicular to the surface that
the object is on.
8. Part B
Now friction. Friction is the along the
surface the object is traveling on.
9. 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
10. Part C
Now 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.
11. 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!!!
12. Part C
We use sine because friction equals the
side opposite to the angle. After
250 N multiplying by the weight force (the
hypotenuse) we see that the force by
friction is 64.705 Newtons
13. 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.
15. Part D
Cosine 15 degrees times the weight
force equals the normal force (the
adjacent leg of the triangle)
250 N
16. Part D
Now we can plug in numbers to the
FUN equation.
f = 64.705 N
N = 241.481 N
N N
N
N
N N And solve for μ
17. Part E
The sled reaches the bottom of the slope and
continues on the horizontal ground. Assume the
same coefficient of friction.
18. 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.
19. Part E
ii. 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 tιthe time
at which the sled leaves the slope.
20. 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.
