a child is pulled on a sled across a snow-covered yard. the combined mass of the child and the sled is 35 kg. the angle that the rope pulling the sled makes with the horizontal is 34 degrees. the person pulling on the rope applies a force of 182 N. given that the coefficient of friction between the sled and the snow is .28, how far must the child and sled be pulled before they reach a speed of 10.0 m/s?
You need to break up the pulling force of 182N into vertical and horizontal forces (given the angle). The horzontal force then equals mass*acceleratin minus friction.
Friction is (mg-vertical force)mu
Solve for acceleration.
Then, vf^2=2*acceleration*distance and you can solve for distance.
so you get the distance to equal .84?
To find the distance the child and sled must be pulled before reaching a speed of 10.0 m/s, we can use the concepts of work, friction, and kinetic energy.
1. Let's start by finding the force of friction acting on the sled. The force of friction can be calculated using the equation:
Force of friction (f) = coefficient of friction (μ) * normal force (N)
The normal force is equal to the weight of the child and sled, which can be calculated using:
Weight (W) = mass (m) * acceleration due to gravity (g)
Given that the combined mass of the child and sled is 35 kg and the acceleration due to gravity is approximately 9.8 m/s², we can substitute these values into the equation to find the weight:
W = (35 kg) * (9.8 m/s²) = 343 N
Now, we can substitute the weight into the equation for the force of friction:
f = (0.28) * (343 N) = 95.84 N
2. Since the sled is being pulled by a force of 182 N at an angle of 34 degrees, we need to find the component of this force parallel to the direction of motion. This can be done using trigonometry:
Force parallel to the motion (F_parallel) = Force applied (F_applied) * cos(angle)
F_parallel = (182 N) * cos(34 degrees) ≈ 151.56 N
3. To find the work done in moving the sled and child over a certain distance (d), we can use the equation:
Work (W) = Force parallel to the motion (F_parallel) * distance (d)
Rearranging the equation to find the distance:
d = W / F_parallel
However, the work done is equal to the change in kinetic energy, so we can write:
W = ΔKE
Since the initial kinetic energy is zero and the final kinetic energy is given as (1/2) * mass * velocity^2, we can substitute the values into the equation:
W = ΔKE = (1/2) * mass * (final velocity)^2
Rearranging the equation to find the distance:
d = (1/2) * mass * (final velocity)^2 / F_parallel
Plugging in the values:
d = (1/2) * 35 kg * (10.0 m/s)^2 / 151.56 N ≈ 11.3 meters
Therefore, the child and sled must be pulled a distance of approximately 11.3 meters before they reach a speed of 10.0 m/s.