If the slide is inclined at 55 �, what is thecoefficient of friction between the girl and the slide?
To calculate the coefficient of friction between the girl and the slide, we need to know the angle of inclination of the slide and the acceleration of the girl down the slide.
The coefficient of friction can be determined using the equation:
friction force = coefficient of friction × normal force
The normal force is equal to the weight of the girl, which can be calculated as:
normal force = mass × gravitational acceleration
The gravitational acceleration is approximately 9.8 m/s².
Now, we need to find the acceleration of the girl down the slide. To do this, we can use the following equation:
acceleration = gravitational acceleration × sin(angle of inclination)
In this case, the angle of inclination is 55 degrees. Convert it to radians using the formula:
angle in radians = angle in degrees × π/180
Substituting the values we have:
angle in radians = 55 × π/180 ≈ 0.9599 radians
Now, solve for the acceleration:
acceleration = 9.8 m/s² × sin(0.9599 radians)
Once you have the acceleration, you can calculate the normal force and then determine the coefficient of friction by rearranging the equation:
friction force = coefficient of friction × normal force
Rearranging further, we find:
coefficient of friction = friction force / normal force
Remember to measure the friction force parallel to the slide.
So, to calculate the coefficient of friction between the girl and the slide, you need to follow these steps:
1. Convert the angle of inclination from degrees to radians.
2. Use the equation acceleration = gravitational acceleration × sin(angle of inclination) to calculate the acceleration of the girl.
3. Calculate the normal force using the equation normal force = mass × gravitational acceleration.
4. Determine the friction force by multiplying the coefficient of friction by the normal force.
5. Finally, calculate the coefficient of friction by dividing the friction force by the normal force.