Use UAM equation to calculate the amount of time an object with a mass of 53.7g  to pass through an inclined plane that is 60cm at an angle 9 degrees.

To calculate the amount of time an object takes to pass through an inclined plane using the Uniformly Accelerated Motion (UAM) equation, we need to find the acceleration of the object along the plane. The mass of the object is not directly necessary for time calculation if friction is neglected. Here's how to proceed:

### 1. **Determine the acceleration along the inclined plane:**
The acceleration \(a\) of an object sliding down an inclined plane with no friction is given by the formula:

\[
a = g \sin(\theta)
\]

where:
- \( g \) is the acceleration due to gravity, approximately \( 9.81 \, \text{m/s}^2 \).
- \( \theta \) is the angle of inclination of the plane.

For the given problem:
- \( \theta = 9^\circ \).

So, we have:

\[
a = 9.81 \sin(9^\circ)
\]

### 2. **Calculate the acceleration:**
Let's compute the acceleration using the given values.

\[
a = 9.81 \times \sin(9^\circ)
\]

### 3. **Calculate the time using the UAM equation:**
The UAM equation for distance is:

\[
s = ut + \frac{1}{2} a t^2
\]

Since the object starts from rest, initial velocity \( u = 0 \).

So, the equation simplifies to:

\[
s = \frac{1}{2} a t^2
\]

Solving for time \( t \):

\[
t = \sqrt{\frac{2s}{a}}
\]

where:
- \( s = 0.60 \, \text{m} \) (the length of the inclined plane).

### 4. **Compute the time:**
Now, we can substitute the values of \( s \) and \( a \) to find the time \( t \).

I'll calculate the acceleration and time for you.The acceleration of the object along the inclined plane is approximately \( 1.53 \, \text{m/s}^2 \).

The time it takes for the object to pass through the inclined plane is approximately \( 0.88 \, \text{seconds} \).

Would you like more details or have any other questions?

### Related Questions:
1. How would the time change if the angle of the inclined plane increased?
2. How does friction affect the motion down the inclined plane?
3. What would be the impact of doubling the mass on the time taken?
4. How would you calculate the velocity at the end of the inclined plane?
5. What are the conditions under which this calculation is valid?

**Tip:** For accurate results, always consider the effect of friction and air resistance when dealing with real-world problems involving inclined planes.

Use UAM equation to calculate the amount of time an object with a mass of 53.7g to pass through an inclined plane that is 60cm at an angle of 9 degrees.

Learn how to calculate the time it takes for an object with a mass of 53.7g to pass through a 60cm inclined plane at a 9-degree angle using the Uniformly Accelerated Motion (UAM) equation. This detailed guide covers key concepts in kinematics and includes step-by-step calculations. Suitable for high school students in Grades 9-12.

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