In the physics laboratory, a glider is released from rest on a frictionless air track inclined at an angle. If the glider has gained a speed of 24.1 cm/s in traveling 68.5 cm from the starting point, what was the angle of inclination of the track?

To solve this problem, we can use the principle of conservation of energy. The potential energy at the start is converted into kinetic energy at the end.

Step 1: Convert the given values to SI units. Speed = 24.1 cm/s = 0.241 m/s and distance = 68.5 cm = 0.685 m.

Step 2: Calculate the initial potential energy (PE) using the formula PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s²), and h is the height. We don't know the mass or the height, but we know that the height is related to the distance traveled and the angle of inclination (h = d*sin(θ)).

Step 3: Calculate the final kinetic energy (KE) using the formula KE = 0.5mv², where m is the mass and v is the speed. The mass will cancel out in our calculations.

Step 4: Set the initial potential energy equal to the final kinetic energy (since energy is conserved) and solve for the angle θ.

Let's do the calculations:

0.5v² = gdsin(θ) 0.5(0.241 m/s)² = 9.8 m/s² * 0.685 m * sin(θ) 0.029 m²/s² = 6.713 m²/s² * sin(θ)

Solving for sin(θ) gives us:

sin(θ) = 0.029 m²/s² / 6.713 m²/s² = 0.00432

Finally, to find the angle θ, we take the inverse sine (sin⁻¹) of 0.00432:

θ = sin⁻¹(0.00432) = 0.248 degrees.

To solve this problem, we can use the principle of conservation of energy. The potential energy at the start is converted into kinetic energy at the end.

1. First, convert the given values to SI units. Speed = 24.1 cm/s = 0.241 m/s and distance = 68.5 cm = 0.685 m.

2. Calculate the initial potential energy (PE) using the formula PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s²), and h is the height. We don't know the mass or the height, but we know that the height is related to the distance traveled and the angle of inclination (h = d*sin(θ)).

3. Calculate the final kinetic energy (KE) using the formula KE = 0.5mv², where m is the mass and v is the speed. The mass will cancel out in the next step, so we don't need to know its value.

4. Set the initial potential energy equal to the final kinetic energy (since energy is conserved) and solve for the angle. This gives us:

   mgdsin(θ) = 0.5m*v²

   gdsin(θ) = 0.5*v²

   sin(θ) = 0.5v² / (gd)

5. Use the inverse sine function to find the angle:

   θ = arcsin[0.5v² / (gd)]

6. Substitute the known values into the equation:

   θ = arcsin[0.5*(0.241 m/s)² / (9.8 m/s² * 0.685 m)]

7. Solve for θ to find the angle of inclination.