Children sled down a 44m -long hill inclined at 27∘ . At the bottom, the slope levels out.
If the coefficient of friction is 0.11, how far do the children slide on the level ground?
Express your answer using two significant figures.
To find out how far the children slide on the level ground, we need to consider the forces acting on them.
First, let's calculate the gravitational force acting on the children as they slide down the hill. We can use the formula F = mg, where F is the force, m is the mass, and g is the acceleration due to gravity. Assuming the mass of the children is negligible, we can ignore it in this calculation.
Next, let's determine the force of friction acting on the children as they slide on the incline. The formula for the force of friction is given by F_friction = μN, where μ is the coefficient of friction and N is the normal force. The normal force can be calculated using the formula N = mg⋅cos(θ), where θ is the angle of the incline and g is the acceleration due to gravity.
Since the slope levels out at the bottom, the normal force will be equal to the weight of the children, N = mg.
Now, let's substitute the values into the formulas and calculate the forces:
Gravitational force:
F_gravity = mg = 0 (since the mass is assumed to be negligible)
Force of friction:
F_friction = μN = μmg
To determine how far the children slide on the level ground, we need to find the work done against the force of friction. The work done is equal to the force of friction multiplied by the distance traveled. Therefore, we need to find the distance traveled.
The total distance traveled is equal to the length of the inclined hill, 44m, minus the distance traveled against the force of friction.
The work done against the force of friction is equal to the force of friction multiplied by the distance traveled, which we'll denote as d.
Since work done = force × distance, we have:
μmgd = μmg × d
Setting up the equation, we can solve for d:
d = (μmgd) / (μmg)
Simplifying the equation, we find:
d = d
Therefore, the distance traveled on the level ground is the same as the length of the inclined hill, which is 44m.
So, the children slide 44m on the level ground.