Activity 2.5-Newton's Second Law: Inclined Plane Part I: Block sliding down a ramp. A block of mass M slides down a ramp of angle with increasing speed. a. Draw the free body diagram showing the forces acting on the block. Put an arrow to the right of the "=" in the direction of the acceleration labeled "ma" or "0" if the acceleration is zero. To simplify the problem, we use a tilted coordinate system with +x down the ramp and +y perpendicular to the ramp. b. The diagrams to the right, show the component triangle for the weight in this coordinate system. The block is drawn two different ways. Use the component triangle on the left to write the x and y components of the weight in the tilted coordinate system. Write answer in terms of m. g, and e. Pay attention to signs. M Mg b Ng • Which angle, A, B, or C is the same as 8? W₂ = W₂ = Repeat using the component triangle on the right and show you get the same answers as above. W, = W, = • Which angle, D, E, or F is the same as 8? c. To check that you got you chose your trig functions correctly, check that your answers for (b) make sense for 8 = 0. What should the x and y components of the weight be when = 0 (when there is no tilt)? Check that your answers from part b are consistent with what you expect when 6 = 0. In the table below fill in the rand components of the friction force the normal force and the acceleration in
Activity 2.5-Newton's Second Law: Inclined Plane Part I: Block sliding down a ramp. A block of mass M slides down a ramp of angle with increasing speed. a. Draw the free body diagram showing the forces acting on the block. Put an arrow to the right of the "=" in the direction of the acceleration labeled "ma" or "0" if the acceleration is zero. To simplify the problem, we use a tilted coordinate system with +x down the ramp and +y perpendicular to the ramp. b. The diagrams to the right, show the component triangle for the weight in this coordinate system. The block is drawn two different ways. Use the component triangle on the left to write the x and y components of the weight in the tilted coordinate system. Write answer in terms of m. g, and e. Pay attention to signs. M Mg b Ng • Which angle, A, B, or C is the same as 8? W₂ = W₂ = Repeat using the component triangle on the right and show you get the same answers as above. W, = W, = • Which angle, D, E, or F is the same as 8? c. To check that you got you chose your trig functions correctly, check that your answers for (b) make sense for 8 = 0. What should the x and y components of the weight be when = 0 (when there is no tilt)? Check that your answers from part b are consistent with what you expect when 6 = 0. In the table below fill in the rand components of the friction force the normal force and the acceleration in
Chapter2: Newton's Laws
Section: Chapter Questions
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Transcribed Image Text:Activity
2.5-Newton's Second Law: Inclined Plane
Part I: Block sliding down a ramp. A block of mass M slides down a ramp of angle with increasing speed.
+y
a. Draw the free body diagram showing the
forces acting on the block. Put an arrow
to the right of the "=" in the direction of
the acceleration labeled "ma" or "0" if the
acceleration is zero.
To simplify the problem, we use a tilted
coordinate system with +x down the ramp
and +y perpendicular to the ramp.
b. The diagrams to the right, show the
component triangle for the weight in this
coordinate system. The block is drawn
two different ways.
Use the component triangle on the left
to write the x and y components of the
weight in the tilted coordinate system.
Write answer in terms of m, g, and e.
Pay attention to signs.
M
x component
y component
Mg
normal force
• Which angle, A, B, or C is the same as 8?
W₂ =
W₂ =
Repeat using the component triangle on the right and show you get the same answers as above.
Which angle, D, E, or F is the same as 8?
W, =
W, =
c. To check that you got you chose your trig functions correctly, check that your answers for (b) make sense for
8 = 0. What should the x and y components of the weight be when = 0 (when there is no tilt)?
Check that your answers from part b are consistent with what you expect when 6 = 0.
d. In the table below fill in the x and y components of the friction force, the normal force and the acceleration in
the tilted coordinate system. Pay attention to signs. Give answers in terms of the magnitudes f. F, and a
and the angle 6. You may not need all these symbols.
=
D
Mg
friction force
acceleration
Use your free body diagram and the table to write out Newton's 2 law in the tilted coordinate system in the x and
y directions. Set the right-hand side (RHS) of the equation to zero if there is no acceleration in that direction.
EF=ma, →
EF, = ma, →
e. Use your Newton's 2 Law equations above to solve for the normal force in terms of givens M, 9. f. and/or 6.
You do not necessarily need all these symbols.
f. Use your Newton's 2 Law equations above to solve for the acceleration in terms of the givens.
g. Let M = 0.5 kg, f₂ = 1.75 N, and = 25°. Determine numerical values for the normal force and acceleration.
Show numbers you use (including units).
h. The block was initially at rest. How long does it take to slide 0.8 m? Start by writing down the symbolic
relation you use. Solve for the time symbolically first before substituting in numbers. Show the numbers you
used.
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