A 20 kg wagon is pulled along the level ground by a rope inclined at 30 deg above horizontal. A frictional force of 30 N opposes the motion, how large is the pulling force if the wagon is moving at constant velocity?
horizontal force=frictional force
force*cos30=30N
solve for force pulling=30/cos30
To determine the pulling force on the wagon, we need to analyze the forces acting on it.
First, let's identify the forces acting on the wagon:
1. Weight force (mg): This force is equal to the mass (m) of the wagon multiplied by the acceleration due to gravity (g). In this case, the weight force is given by 20 kg × 9.8 m/s² = 196 N, directed vertically downward.
2. Normal force (N): This force is perpendicular to the inclined plane (horizontal ground) and counteracts the weight force. Since the wagon is moving at a constant velocity and not accelerating in the vertical direction, the normal force is equal to the weight force, which is 196 N.
3. Frictional force (f): This force opposes the motion and has a magnitude of 30 N acting opposite to the direction of motion.
Now, let's analyze the forces acting along the inclined plane:
1. Pulling force (F): This is the force we are trying to find. It acts parallel to the inclined plane, directed uphill.
2. Component of weight force (mg*sinθ): This force acts downhill, parallel to the inclined plane, and is given by the weight force multiplied by the sine of the angle of inclination (θ = 30°). In this case, mg*sinθ = 20 kg × 9.8 m/s² × sin(30°) = 98 N.
3. Component of weight force perpendicular to the inclined plane (mg*cosθ): This force acts perpendicular to the inclined plane (horizontally) and doesn't affect the motion along the inclined plane. Therefore, it is not relevant for determining the pulling force.
Since the wagon is moving at a constant velocity, it implies that the net force acting along the inclined plane is zero. In other words, the magnitude of the pulling force (F) must be equal to the magnitude of the component of the weight force (mg*sinθ) uphill, plus the magnitude of the frictional force (f) acting downhill.
Thus, the pulling force (F) = mg*sinθ + f = 98 N + 30 N = 128 N.
Therefore, the pulling force required to move the wagon at a constant velocity is 128 Newtons.