A 16-kg sled is being pulled along the horizontal snow-covered ground by a horizontal force of 35 N. Starting from rest, the sled attains a speed of 2.1 m/s in 9.5 m. Find the coefficient of kinetic friction between the runners of the sled and the snow.
35 - ckf * 16 = m*a
where ckf is coefficient of kinetic friction. In your textbook ckf is probably represented as the greek letter mu, but it's really hard to write greek letters here. . .
m is the mass of the sled, and a is its acceleration.
x = 1/2 * a * t^2
v = a * t
where x is the distance traveled by the sled, t is time, and v is the speed
so
9.5 = 1/2 * a * t^2
2.1 = a * t
Using algebra:
t = 2.1/a
plugging into the equation for x:
9.5 = (1/2 * 2.1^2)/a
Use algebra to solve for the acceleration, then plug into
35 - ckf * 16 = 16*a
and solve for ckf
To find the coefficient of kinetic friction between the runners of the sled and the snow, we can use the following formula:
frictional force = coefficient of friction * normal force
In this case, the normal force is equal to the weight of the sled, which can be calculated as:
normal force = mass * gravity
Given that the mass of the sled is 16 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, the normal force can be calculated as:
normal force = 16 kg * 9.8 m/s^2 = 156.8 N
The frictional force can be calculated using Newton's second law of motion:
frictional force = mass * acceleration
Since the sled is being pulled horizontally without any vertical acceleration, the frictional force is equal to the product of the mass and horizontal acceleration. In this case, the sled attains a speed of 2.1 m/s in 9.5 m:
acceleration = (final velocity - initial velocity) / distance
acceleration = (2.1 m/s - 0 m/s) / 9.5 m = 0.221 m/s^2
frictional force = 16 kg * 0.221 m/s^2 = 3.536 N
Now we can substitute the values into the equation to find the coefficient of kinetic friction:
3.536 N = coefficient of friction * 156.8 N
coefficient of friction = 3.536 N / 156.8 N ≈ 0.0225
Therefore, the coefficient of kinetic friction between the runners of the sled and the snow is approximately 0.0225.
To find the coefficient of kinetic friction between the sled and the snow, we can use the concept of Newton's second law and the equation for friction.
1. Determine the force acting on the sled:
- The net force acting on the sled is the horizontal force pulling the sled minus the force of kinetic friction.
- The force pulling the sled is given as 35 N.
- We need to find the force of kinetic friction, which can be represented by the equation: frictional force = coefficient of kinetic friction × normal force.
2. Calculate the normal force:
- The normal force is the force exerted by the ground on the sled perpendicular to the surface.
- Since the sled is on a horizontal surface, the normal force is equal to the weight of the sled, which can be calculated as: weight = mass × acceleration due to gravity.
3. Apply Newton's second law to find acceleration:
- Newton's second law states that the net force acting on an object is equal to the product of its mass and acceleration.
- In this case, the net force is the force pulling the sled minus the force of kinetic friction.
- Set up the equation: net force = mass × acceleration.
4. Use the given distance and final velocity to find acceleration:
- The sled starts from rest, so the initial velocity is 0 m/s.
- Use the formula: final velocity^2 = initial velocity^2 + 2 × acceleration × distance.
- Rearrange the formula and solve for acceleration.
5. Substitute the calculated acceleration into the equation for Newton's second law:
- We now know the mass of the sled and the acceleration, so we can calculate the net force.
6. Substitute the net force and mass into the equation for friction:
- Using the equation for frictional force = coefficient of kinetic friction × normal force, replace the frictional force with the net force calculated in the previous step and the normal force with the weight of the sled.
7. Solve for the coefficient of kinetic friction:
- Now that we have the equation, rearrange it to solve for the coefficient of kinetic friction.
8. Substitute the calculated values into the equation and solve:
- Plug in the known values for the force pulling the sled, the mass of the sled, and the acceleration due to gravity into the equation and solve for the coefficient of kinetic friction.
By following these steps, you can calculate the coefficient of kinetic friction between the runners of the sled and the snow.