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

AI Thread Summary
To solve the problem of a swinging pendulum hitting a block, the final velocity of the pendulum can be determined by equating potential energy (PE) to kinetic energy (KE). The distance traveled by the block can be calculated using the acceleration derived from the pendulum's motion, factoring in friction. The acceleration of the block, considering friction, can be found by applying Newton's second law. The discussion raises questions about whether to use the curved path distance or the straight-line displacement for calculations. Overall, the approach involves understanding energy conservation and the effects of friction on motion.
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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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