A child is walking along the sidewalk at a speed of 1 m/s while pulling his wagon. The wagon weighs 56 N. If the child pulls at an angle of 12o, and the the coefficient of kinetic friction is 0.40, then how hard does the child pull on the handle?
To find out how hard the child pulls on the handle, we need to consider the forces acting on the wagon.
The force of friction opposing the motion of the wagon can be found using the equation:
Frictional force = coefficient of kinetic friction × normal force
The normal force is the force exerted by the ground on the wagon, which is equal to the weight of the wagon:
Weight = mass × gravity
Given that the weight of the wagon is 56 N, we can calculate the normal force.
The normal force is equal to the weight of the wagon because the wagon is on a flat horizontal surface, and there is no vertical acceleration:
Normal force = 56 N
Now, we can calculate the frictional force using the value of the coefficient of kinetic friction (0.40) and the normal force:
Frictional force = 0.40 × 56 N
Next, we need to resolve the force of pulling into its horizontal and vertical components. The horizontal component of the pulling force is the force that opposes the frictional force:
Force of pulling (horizontal component) = Frictional force
Finally, to find the total force of pulling on the handle, we can use the horizontal component of the pulling force along with the angle of 12°. We can calculate the force using the following formula:
Total force of pulling = Force of pulling (horizontal component) / cos(angle)
Substituting the values:
Total force of pulling = Frictional force / cos(12°)
Therefore, to find out how hard the child pulls on the handle, you can substitute the calculated values into the formula Total force of pulling = Frictional force / cos(12°) and solve it.