Two packages at UPS start sliding down the 20 degree ramp shown in the figure. Package A has a mass of 6.00kg and a coefficient of kinetic friction of 0.220. Package B has a mass of 8.00kg and a coefficient of kinetic friction of 0.170.
How long does it take package A to reach the bottom?
http://session.masteringphysics.com/problemAsset/1073551/3/knight_Figure_08_25.jpg
^ there is picture of the diagram
I keep getting 2.34 seconds, but it says I'm wrong. Can anyone tell me what they got and explain why?
thanks!
How long does it take package A to reach the bottom?
http://session.masteringphysics.com/problemAsset/1073551/3/knight_Figure_08_25.jpg
^ there is picture of the diagram
I keep getting 2.34 seconds, but it says I'm wrong. Can anyone tell me what they got and explain why?
thanks!
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Before doing any math, let's look at the problem from this perspective: We need to find how fast it takes package A to reach the bottom. Package A will accelerate down the ramp along with Package B. BOTH Package A AND Package B MUST have the same acceleration down the ramp. Since Pacakge B is bigger and has less kinetric friction (0.170 compared to 0.220), it's going to push Package A down the ramp. Both packages are thus going down the ramp at the same speed. By knowing the acceleration of both packages, we can find how long it'll take Package A to reach the bottom (if we were told to find the time it took Package B to travel down, it would take longer than the given 2 m since Package B is behind Package A).
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PACKAGE A:
First, draw a free body diagram of Package A. If drawn correctly, our equations are :
ΣFx = max (the sum of the forces in the direction of motion equals the product of mass and acceleration)
(1) m1gsin(20°) + Fb - Ff_A = m1a
where:
m1 = mass of Package A (6 kg)
Fb = the force of Package B on Package A (remember, Package B is pushing Package A so a pushing force is present)
Ff_A = the frictional force on Package A
a = acceleration
ΣFy = 0
(2) N - m1gcos(20°) = 0
However, Ff_A = μk1*N = μk1*m1gcos(20°)
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PACKAGE A:
First, draw a free body diagram of Package A. If drawn correctly, our equations are :
ΣFx = max (the sum of the forces in the direction of motion equals the product of mass and acceleration)
(1) m1gsin(20°) + Fb - Ff_A = m1a
where:
m1 = mass of Package A (6 kg)
Fb = the force of Package B on Package A (remember, Package B is pushing Package A so a pushing force is present)
Ff_A = the frictional force on Package A
a = acceleration
ΣFy = 0
(2) N - m1gcos(20°) = 0
However, Ff_A = μk1*N = μk1*m1gcos(20°)
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