a small child is sliding down a 25 degree slide at a uniform velocity of 1.0 m/s. If the child weighs 210 N, find the coefficient of friction between the slide and the child.
Resolve forces along and perpendicular to the inclined plane:
Along the plane,
mg sinθ - μN = 0
N is the normal force equal to mgcosθ
Substituting,
mgsinθ-μmgcosθ=0
Solve for μ to get:
μ=tan(θ)
Note that μ is not dependent on the mass of the moving object, nor the magnitude of the uniform velocity.
To find the coefficient of friction between the slide and the child, we can use the equation:
friction force = coefficient of friction * normal force
In this case, the only force acting along the slide is the force of gravity. The component of the force of gravity acting along the slide is given by:
force along slide = weight * sin(angle of the slide)
where weight is the force of gravity acting on the child (210 N) and the angle of the slide is 25 degrees.
force along slide = 210 N * sin(25°)
Next, we can find the friction force using the equation:
friction force = mass * acceleration
Since the child is sliding down the slide at a uniform velocity, the acceleration is 0 m/s² and the friction force is also 0 N.
Now we can set up the equation:
0 N = coefficient of friction * normal force
Since the normal force is equal to the weight of the child (210 N), the equation becomes:
0 N = coefficient of friction * 210 N
Solving for the coefficient of friction:
coefficient of friction = 0 N / 210 N
Therefore, the coefficient of friction between the slide and the child is 0.
To find the coefficient of friction between the slide and the child, we can use the equation:
frictional force = coefficient of friction * normal force
In this case, the normal force is equal to the weight of the child, which is given as 210 N. The frictional force can be calculated using the formula:
frictional force = mass * acceleration
Since the child is sliding down the slide at a uniform velocity, there is no acceleration. So the frictional force is zero.
Now we can substitute the values into the first equation:
0 = coefficient of friction * 210 N
Since the frictional force is zero, the coefficient of friction must also be zero. Therefore, there is no coefficient of friction between the slide and the child in this scenario.