Along the remote Racetrack Playa in Death valley, California, stones sometimes gouge out prominent trails in the desert floor, as if they had been migrating. For years curiosity mounted about why the stones moved. One explanation was that strong winds during the occasional rainstorms would drag the rough stones over ground softened by rain. When the desert dried out, the trails behind the stones were hard-baked in place. According to measurements, the coefficient of kinetic friction between the stones and the wet playa ground is about 0.80. What horizontal force is needed on a 19 kg stone (a typical mass) to maintain the stone's motion once a gust has started it moving?

Question

Along the remote Racetrack Playa in Death valley, California, stones sometimes gouge out prominent trails in the desert floor, as if they had been migrating. For years curiosity mounted about why the stones moved. One explanation was that strong winds during the occasional rainstorms would drag the rough stones over ground softened by rain. When the desert dried out, the trails behind the stones were hard-baked in place. According to measurements, the coefficient of kinetic friction between the stones and the wet playa ground is about 0.80. What horizontal force is needed on a 19 kg stone (a typical mass) to maintain the stone's motion once a gust has started it moving?

Answer 1

The horizontal (wind) force must equal the friction force, which you can compute using the weight and the coeficient of kinetic friction

Answer 2

To find the horizontal force needed to maintain the stone's motion, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.

First, we need to calculate the acceleration of the stone. The force responsible for the stone's motion is the horizontal component of the force of friction. We can determine this force using the equation:

Force of friction = coefficient of kinetic friction * normal force

The normal force is the force exerted by the ground on the stone, which is equal to the weight of the stone (mass * acceleration due to gravity, g).

So, the force of friction on the stone can be calculated as:

Force of friction = coefficient of kinetic friction * mass * acceleration due to gravity

Now, we can rearrange Newton's second law of motion:

Net force = mass * acceleration

Since we want to find the force required to maintain the stone's motion, the net force is equal to the force of friction. Therefore:

Force of friction = mass * acceleration

Substituting the value of force of friction we obtained earlier:

coefficient of kinetic friction * mass * acceleration due to gravity = mass * acceleration

Canceling out the mass from both sides of the equation, we get:

coefficient of kinetic friction * acceleration due to gravity = acceleration

Now, we can substitute the values given in the problem:

coefficient of kinetic friction = 0.80
acceleration due to gravity = 9.8 m/s^2

Plugging these values into the equation, we find:

0.80 * 9.8 m/s^2 = acceleration

Simplifying, we get:

acceleration = 7.84 m/s^2

So, the stone will experience an acceleration of 7.84 m/s^2 to maintain its motion once a gust has started it moving.

To find the horizontal force needed to maintain this acceleration, we can use the equation:

Force = mass * acceleration

Plugging in the values:

Force = 19 kg * 7.84 m/s^2

Calculating the result:

Force = 149.36 N

Therefore, a horizontal force of approximately 149.36 Newtons is needed to maintain the 19 kg stone's motion once a gust has started it moving.