A cross-country skier who weighs 600 N has chosen ski wax that provides ฯ=0.03. What is the minimum amount of horizontal force,perhaps from a tailwind,that would keep the skier coasting at constant speed across level snow?
.03*600 = ? Newtons
To calculate the minimum amount of horizontal force required to keep the skier coasting at a constant speed, we can use Newton's second law of motion.
The formula for Newton's second law is:
F = m * a
Where:
- F is the force applied
- m is the mass of the object
- a is the acceleration of the object
In this case, the skier is coasting at a constant speed, which means there is no acceleration. Therefore, the equation simplifies to:
F = m * 0
Since the skier's weight is given as 600 N, we can convert it to mass using the equation:
Weight = mass * g
where g is the acceleration due to gravity, which is approximately 9.8 m/s^2. Rearranging the equation, we get:
mass = weight / g
mass = 600 N / 9.8 m/s^2
mass ≈ 61.2 kg
Now we can calculate the minimum amount of horizontal force required to keep the skier coasting. The formula for frictional force is:
F_friction = μ * N
Where:
- F_friction is the frictional force
- μ is the coefficient of friction (given as 0.03)
- N is the normal force, which is equal to the weight of the skier (600 N) in this case.
Substituting the values, we get:
F_friction = 0.03 * 600 N
F_friction ≈ 18 N
Therefore, the minimum amount of horizontal force required to keep the skier coasting at a constant speed across level snow is approximately 18 Newtons.
To determine the minimum amount of horizontal force required to keep the cross-country skier coasting at a constant speed across level snow, we can use the concept of net force.
The net force acting on the skier can be calculated using the equation:
net force = force of friction
In this case, the force of friction is equal to the coefficient of friction (μ) multiplied by the normal force (N). The normal force is the force exerted by a surface perpendicular to it, which is equal to the weight of the skier (600 N) in this case.
force of friction = μ * N
Substituting the given values:
force of friction = 0.03 * 600 N
force of friction = 18 N
Therefore, the minimum amount of horizontal force required to keep the skier coasting at a constant speed across level snow is 18 N. This force could come from a tailwind or any other external force applied horizontally to overcome the frictional force and maintain constant speed.