Two children, m1 = 50 kg and m2 = 55 kg, and a plastic sled of mass 35 kg start at rest and slide for 5.0 s down a hill. The force of gravity pulling the children and sled down the hill is 470 N but the snow provides a frictional force of 325 N. At the bottom of the hill, the children and sled encounter a frozen pond (frictionless surface). Upon sliding onto the frozen pond, the children and sled continue moving, without any additional force, across the middle to the other side.

If the pond has a circumference of 163 m, to the nearest tenth of a second, how long did it take the children and sled to travel to the other side of the pond?

To find out how long it took the children and sled to travel to the other side of the pond, we need to consider the forces acting on them and the distance they covered.

First, let's calculate the net force acting on the children and sled on the hill. The net force is the difference between the force of gravity pulling them down and the frictional force provided by the snow.

Net force = Force of gravity - Frictional force
Net force = 470 N - 325 N
Net force = 145 N

Next, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F = m * a). In this case, since the sled and children were initially at rest, the net force is equal to the mass of the system multiplied by its acceleration.

Net force = (m1 + m2 + msled) * acceleration
145 N = (50 kg + 55 kg + 35 kg) * acceleration
145 N = 140 kg * acceleration

Now, we can solve for the acceleration of the system:

acceleration = 145 N / 140 kg
acceleration ≈ 1.04 m/s^2

Using the equation of motion d = v0 * t + (1/2) * a * t^2, we can find the distance covered by the children and sled on the hill. However, since they start from rest, the initial velocity (v0) is zero, and the equation simplifies to d = (1/2) * a * t^2.

On the hill: dhill = (1/2) * 1.04 m/s^2 * (5.0 s)^2
dhill ≈ 12.99 m

Since the hill is perpendicular to the circumference of the pond and the pond is frictionless, the distance traveled on the pond will be equal to the circumference of the pond.

On the pond: dpond = 163 m

Finally, to find out the total time it took to travel to the other side of the pond, we can use the equation of motion again, this time solving for time. Rearranging the equation, we get t = (d - (1/2) * a * t^2) / v0. Since the sled and children continue moving on the pond without any additional force, their final velocity (v) will be the same as the velocity at the end of the hill.

On the pond: tpond = (dpond - dhill) / v
tpond = (163 m - 12.99 m) / (1.04 m/s^2 * 5.0 s)

Now, you can solve for tpond to find out how long it took the children and sled to travel to the other side of the pond by substituting the values into the equation.