A loaded dogsled has a mass of 400kg and is being pulled across a horizontal, paced snow surface at a velocity of 4.0m/s (N). Suddenly, the harness separates from the sled. If the coefficient of kinetic friction for the sled on the snow is 0.0500, how far will the sled coast before stopping?
This needs the kinematic equation - vf^2 = vi^2 + 2 x a x d
vf = 0 ( since he'll stop)
vi = 4.0
a = ( must be found)
d = ???? ( for now)
to find a
a is decelleration, because their is no applied force.
fnet = -uk x Ffk
m x a = -0.0500 x m x g
since there are m's cross them out.
a = -0.0500 x g
a = -0.49 m/s^2
fill in to the kinematic equation
vf^2 = vi ^2 + 2 x a x d
0 = 16 + 2 x -0.49 x d
d = -16.32
rounded (16m)
To find the distance the sled will coast before stopping, we need to use Newton's second law of motion and the concept of work and kinetic energy.
Here are the steps to solve the problem:
Step 1: Determine the forces acting on the sled.
In this case, there are two forces acting on the sled: the pulling force and the frictional force. The pulling force is zero because the harness separates from the sled. The only force acting on the sled is the kinetic friction force.
Step 2: Calculate the frictional force.
The frictional force can be calculated using the formula:
Force of friction = coefficient of kinetic friction * normal force
The normal force can be calculated as:
Normal force = mass * gravitational acceleration
In this case, the gravitational acceleration is approximately 9.8 m/s^2.
Normal force = 400 kg * 9.8 m/s^2
Step 3: Calculate the frictional force.
Force of friction = 0.0500 * (400 kg * 9.8 m/s^2)
Step 4: Calculate the deceleration of the sled.
The deceleration of the sled can be calculated using Newton's second law of motion:
Force = mass * acceleration
In this case, the force is the frictional force and the mass is the mass of the sled.
Force of friction = mass * acceleration
Step 5: Calculate the deceleration.
Acceleration = Force of friction / mass
Step 6: Calculate the distance the sled will travel before stopping.
To find the distance the sled will travel, we can use the equation of motion:
vf^2 = vi^2 + 2 * acceleration * distance
In this case, the final velocity (vf) is zero, the initial velocity (vi) is 4.0 m/s, and the acceleration (a) is the deceleration we calculated in Step 5.
0^2 = (4.0 m/s)^2 + 2 * acceleration * distance
Step 7: Solve for the distance.
distance = (0^2 - (4.0 m/s)^2) / (2 * acceleration)
Now, plug in the values into the equation and solve for the distance.
4 m
Solve this equation for X:
Initial kinetic energy = work done aqainst friction
(1/2) M*Vo^2 = M*g *Uk * X
M cancels out. Uk = 0.050