A 12 kg toboggan is pulled along at a constant velocity on a horizontal surface by a horizontal force of 11 N
How much horizontal force is needed to pull the toboggan at a constant velocity if two 57 kg girls are sitting in it ?
The projections of the equation of motion are
x: F – F(fr) = 0
y: N - m• g = 0
F = F(fr) = K• N= k• m• g.
k = F/m• g = 11/(12•9.8) = 0.093.
The projections of the equation of motion in the second case are
x: F1 – F1(fr) = 0
y: N - M• g = 0
F1 = F1(fr) = k• N1 =k• M• g = 0.093• (2•57+)•9.8 = 114.8 N
To determine the amount of horizontal force needed to pull the toboggan with the added weight of the two girls, we need to consider the total mass of the system.
The mass of the toboggan is given as 12 kg.
The mass of each girl is given as 57 kg.
To find the total mass of the system, we add the mass of the toboggan and the mass of the two girls:
Total mass = Mass of toboggan + 2 * Mass of each girl
Total mass = 12 kg + 2 * 57 kg
Total mass = 12 kg + 114 kg
Total mass = 126 kg
Since the toboggan is pulled at a constant velocity, the net force acting on it is zero. This means that the force of friction is equal to the force applied to pull the toboggan.
Therefore, the horizontal force needed to pull the toboggan at a constant velocity with the weight of the two girls is:
Force = Total mass * Acceleration
Force = 126 kg * 0 m/s² (constant velocity)
Force = 0 N
Hence, no additional horizontal force is needed to pull the toboggan at a constant velocity with the weight of the two girls.
To determine the horizontal force needed to pull the toboggan with the two girls, we first need to consider the additional mass of the girls. The mass of the toboggan is given as 12 kg, and the mass of the two girls sitting in it is 57 kg each, for a total of 114 kg (57 kg + 57 kg).
When the toboggan is pulled at a constant velocity, it means that the net force acting on it is zero. Therefore, the force required to overcome the horizontal frictional force should be equal to the force of friction acting on the toboggan.
To find the force of friction, we can use the equation:
Force of Friction = μ * Normal Force
Where:
μ is the coefficient of friction, and
Normal Force is the perpendicular force exerted by the surface on the toboggan.
Since the toboggan is on a horizontal surface with a constant velocity, the normal force is equal to the weight of the toboggan with the girls:
Normal Force = (mass of toboggan + mass of girls) * acceleration due to gravity
Normal Force = (12 kg + 114 kg) * 9.8 m/s²
Normal Force = 1,134 kg * 9.8 m/s²
Normal Force = 11,123.2 N
Now, to find the force of friction, we need the coefficient of friction between the toboggan and the surface. Without that information, we cannot calculate the exact force required. The coefficient of friction depends on the materials in contact, such as the toboggan's material and the surface it is being pulled on.
Assuming the coefficient of friction is given as μ, we can substitute the values into the equation:
Force of Friction = μ * Normal Force
Therefore, the horizontal force required to pull the toboggan at a constant velocity with the two girls depends on the coefficient of friction between the toboggan and the surface. Without that information, we cannot determine the exact force needed.