A sled with a weight of 200N is being pulled from rest by a force of 40 N across ice which has a coefficient of kinetic friction of ,070. If air resistance is negligible, find the acceleration of the sled. How far will the sled slide in 6 Sec?

23m

To find the acceleration of the sled, we need to understand the forces acting on it. In this case, we have two forces: the applied force pulling the sled and the frictional force opposing the motion.

First, let's find the frictional force. The coefficient of kinetic friction (μ) is given as 0.070 and the weight of the sled (W) is 200N.

The frictional force (F_friction) can be calculated using the formula:
F_friction = μ * W

Substituting the given values:
F_friction = 0.070 * 200N
F_friction = 14N

Now, let's find the net force acting on the sled.

The net force (F_net) is the difference between the applied force (40N) and the frictional force (14N):
F_net = F_applied - F_friction
F_net = 40N - 14N
F_net = 26N

Finally, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a):

F_net = m * a

Rearranging the equation, we get:
a = F_net / m

The weight of an object is equal to its mass (m) multiplied by the acceleration due to gravity (g). In this case, the weight is 200N, so:

200N = m * 9.8 m/s^2 (acceleration due to gravity)

Rearranging this equation, we find the mass (m):
m = 200N / 9.8 m/s^2
m = 20.41 kg

Plugging in the values for F_net and m, we can now calculate the sled's acceleration (a):

a = 26N / 20.41 kg
a ≈ 1.27 m/s^2

So, the acceleration of the sled is approximately 1.27 m/s^2.

To find the distance the sled will slide in 6 seconds, we can use the formula for distance (d) traveled by an object with constant acceleration (a):

d = (1/2) * a * t^2

Plugging in the values for a (1.27 m/s^2) and t (6 s), we can calculate the distance (d):

d = (1/2) * 1.27 m/s^2 * (6 s)^2
d = (1/2) * 1.27 m/s^2 * 36 s^2
d = 22.86 m

Therefore, the sled will slide approximately 22.86 meters in 6 seconds.

net force= mass*acceleration

where net force= pulling force -mg*mu

net force (F) = 40 - (0.07*200) = 26 N

acceleration (a) = F/m = 26/(200/g)
= 1.27 m/s^2

Sliding distance in time t = (1/2) a t^2