Swinging Pendulum hits Block on Table- Find Distance and Acceleration?

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SUMMARY

The discussion centers on calculating the distance traveled by a block after being struck by a pendulum and determining the block's acceleration under specific conditions. The pendulum has a mass of 1.00 kg and a length of 1.50 m, while the block has a mass of 4.00 kg with a coefficient of friction of 0.30. The user proposes using the potential energy (PE) and kinetic energy (KE) equations to find the final velocity of the pendulum and subsequently the acceleration of the block. The user seeks clarification on the correct approach to determine the distance traveled by the block and whether to consider the path of the pendulum or just the displacement.

PREREQUISITES
  • Understanding of potential energy (PE) and kinetic energy (KE) equations
  • Familiarity with Newton's second law (F=ma)
  • Knowledge of friction and its impact on motion
  • Basic principles of circular motion and displacement
NEXT STEPS
  • Calculate the final velocity of the pendulum using PE=KE
  • Determine the acceleration of the block considering friction using F=ma
  • Explore the difference between distance traveled along a curve and straight-line displacement
  • Investigate the effects of varying the coefficient of friction on the block's motion
USEFUL FOR

Physics students, educators, and anyone interested in mechanics, particularly in analyzing pendulum motion and frictional effects on moving objects.

Merlinnair
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Homework Statement


A 1.00 kg pendulum hanging from a length 1.50 m starts horizontal to the ceiling and swings (until it's perpendicular to the ceiling) to hit a 4.00 kg block. The coefficient of friction is .30.
a) What distance does the block travel?
b) Assuming there is no friction, what would be the acceleration of the block?
So given:
m_p=1.00 kg
l=1.50 m
m_b=4.00 kg
μ = .30


Homework Equations


PE = mgh
KE = 1/2 mv^2
v_f - v_i = 2ad
F=ma

The Attempt at a Solution



A) So I can find the final velocity of the pendulum by setting PE=KE and solving for v, and then solving for a using the third equation listed. But first, what would I use for d in that 3rd equation, since the pendulum's path is circular?
Next, once I have a, I was simply going to give the block that value of a to start with, and use F= ma_1 = ma_2 - f and solve for a_1 which would be the actual acceleration of the block taking into account frictoin, and then just use that to find the distance.
Is this process correct, and how do I find the distance traveled by the pendulum?

B) Wouldn't this just be the acceleration of the pendulum, since no friction is slowing it down?
 
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Wait a second, to find the change in distance, would I find the distance of the curve or just the displacement?
 

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