Suppose a 46-N sled is resting on packed snow. The coefficient of kinetic friction is 0.11. If a person weighing 625 N sits on the sled, what force is needed to pull the sled across the snow at constant speed?
To find the force needed to pull the sled at a constant speed, we need to consider the forces acting on the sled.
1. Weight force: This is the force exerted by the sled due to gravity. The weight force is equal to the mass of the sled multiplied by the acceleration due to gravity (9.8 m/s^2).
Weight force = mass of sled * acceleration due to gravity
Given that the weight of the sled is 46 N, we can convert this into mass:
Weight force = mass of sled * 9.8 m/s^2
46 N = mass of sled * 9.8 m/s^2
mass of sled = 46 N / 9.8 m/s^2
2. Normal force: This is the force exerted by the packed snow on the sled perpendicular to the surface of contact. It is equal to the weight of the sled plus the weight of the person sitting on it.
Normal force = weight of sled + weight of person
Given that the weight of the person is 625 N, we can calculate the total normal force:
Normal force = 46 N + 625 N
3. Friction force: This is the force exerted in the opposite direction of motion due to the coefficient of kinetic friction. It is given by:
Friction force = coefficient of kinetic friction * normal force
4. Force needed to pull the sled: Since the sled is moving at constant speed, the force needed to pull the sled must be equal to the friction force.
Force needed = friction force
Putting all these values together, we can solve for the force needed to pull the sled.
To find the force needed to pull the sled across the snow at a constant speed, we can use the concept of friction.
First, let's calculate the total weight acting on the sled. The weight of the sled is given as 46 N, and the weight of the person sitting on the sled is given as 625 N. Therefore, the total weight acting on the sled is:
Total weight = weight of sled + weight of person
Total weight = 46 N + 625 N
Total weight = 671 N
Next, we need to calculate the force of kinetic friction acting on the sled. The force of kinetic friction is given by the equation:
Force of kinetic friction = coefficient of kinetic friction × normal force
The coefficient of kinetic friction is given as 0.11, and the normal force is the force acting perpendicular to the surface, which is equal to the total weight acting on the sled.
Force of kinetic friction = 0.11 × total weight
Force of kinetic friction = 0.11 × 671 N
Force of kinetic friction ≈ 73.81 N
Finally, to keep the sled moving at a constant speed, we need to apply a force equal in magnitude and opposite in direction to the force of kinetic friction. So, the force needed to pull the sled across the snow at a constant speed is approximately 73.81 N.
Ws = 46N. = Weight of sled.
Fs = 46N @ 0deg. = Force of sled.
Fp = 46sin(0) = 0=Force parallel to the snow.
Fv = 46cos(0) = 46N. = Force perpendicular to the snow.
Ff = u(Fv+625),
Ff = 0.11(46 + 625) = 671N. = Force of
friction.
Fn = Fap - Fp - Ff = 0,
Fap - 0 - 671 = 0,
Fap = 671N. = Force applied to pull sled.