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

In summary, the problem involves a 1.00 kg pendulum hanging from a length of 1.50 m that swings and hits a 4.00 kg block with a coefficient of friction of 0.30. The goal is to determine the distance traveled by the block and the acceleration of the block assuming no friction. To find the distance traveled, the final velocity of the pendulum can be calculated by setting potential energy equal to kinetic energy and solving for velocity. The acceleration of the block can then be found by using the equation v_f - v_i = 2ad and substituting the calculated velocity for v_f. The actual acceleration of the block can be found by using F=ma_1 = ma_2 -
  • #1
Merlinnair
9
0

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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  • #2
Wait a second, to find the change in distance, would I find the distance of the curve or just the displacement?
 

1. How does the distance of the pendulum affect its acceleration?

The distance of the pendulum affects its acceleration because the longer the pendulum, the longer the distance it has to travel and therefore the longer it takes to complete one full swing. This means that the acceleration is slower for longer pendulums compared to shorter ones.

2. What factors can affect the accuracy of the distance and acceleration measurements?

Factors that can affect the accuracy of these measurements include friction between the pendulum and the air, as well as the angle at which the pendulum is released. Other factors such as the mass of the pendulum and the position of the block on the table may also have an impact.

3. How can you determine the distance and acceleration of the pendulum experimentally?

The distance and acceleration of the pendulum can be determined experimentally by measuring the time it takes for the pendulum to complete one full swing, as well as the length of the pendulum. Using these values, the distance and acceleration can be calculated using the formula d = 0.5 * g * t^2 and a = 4 * pi^2 * d / (t^2 * L), where d is the distance, g is the acceleration due to gravity, t is the time, and L is the length of the pendulum.

4. How does the mass of the block on the table affect the distance and acceleration of the pendulum?

The mass of the block on the table does not have a direct effect on the distance and acceleration of the pendulum. However, it may affect the amount of friction between the block and the table, which can indirectly impact the accuracy of the measurements.

5. Are there any other factors that may influence the results of this experiment?

Yes, there are several other factors that may influence the results of this experiment, such as air resistance, the precision of the timing device, and the accuracy of the measurements. It is important to control these factors as much as possible to ensure accurate and reliable results.

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