A 66.2 kg person sits on the 5.3 kg sled (slope is on an angle, angle not given). It is to be pulled across the snow with a coefficient of friction equal to 0.12. What horizontal force is required to pill the sled at a constant speed?
Fg=m*g = (66.2kg+5.3kg)*9.8N/kg=700.7 N.
= Force of gravity = Combined wt. of
person and sled.
Ff = u*Fg = 0.12 * 700.7 = 84.1 N. =
Force of friction.
Fx-Ff = m*a
Fx-84.1 = m*0 = 0
Fx = 84.1 N.
To find the horizontal force required to pull the sled at a constant speed, we need to consider the forces acting on the system.
The important forces involved in this scenario are the gravitational force, the normal force, and the frictional force.
1. Gravitational force: The downward force due to gravity acting on the person and the sled can be calculated using the mass and the acceleration due to gravity (9.8 m/s^2). The gravitational force (F_gravity) is given by the equation:
F_gravity = (mass of person + mass of sled) * g
F_gravity = (66.2 kg + 5.3 kg) * 9.8 m/s^2
2. Normal force: The normal force (F_normal) is the force exerted by the surface (snow) on the sled, perpendicular to the surface. This force is equal in magnitude but opposite in direction to the gravitational force.
3. Frictional force: The frictional force (F_friction) opposes the motion of the sled and depends on the coefficient of friction (μ) and the magnitude of the normal force.
The frictional force can be calculated using the equation:
F_friction = μ * F_normal
At constant speed, the horizontal force required to pull the sled is equal in magnitude but opposite in direction to the frictional force. So the horizontal force (F_pull) is equal to the frictional force (F_friction).
To find the answer, we need to calculate F_gravity, F_normal, and F_friction. Here's how:
1. Calculate the gravitational force:
F_gravity = (66.2 kg + 5.3 kg) * 9.8 m/s^2
2. Calculate the normal force:
Since the person and sled are on a slope, the normal force (F_normal) is less than the total gravitational force. The formula to find the normal force on an inclined plane is:
F_normal = F_gravity * cos(θ)
where θ is the angle of inclination.
However, the angle of inclination is not given in the question, which means we cannot directly calculate the normal force. But since we want to find the horizontal force required, we don't need the exact value of the normal force. We only need to know that it balances the vertical component of the gravitational force (F_gravity * sin(θ)) to keep the system in equilibrium. Therefore, we can assume that the normal force is equal to the vertical component of the gravitational force.
F_normal = F_gravity * sin(θ)
3. Calculate the frictional force:
F_friction = μ * F_normal
4. Calculate the horizontal force (F_pull):
F_pull = F_friction
Plug in the values into the formulas and solve for the horizontal force.