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 analyze the forces acting on the wagon.

1. First, let's calculate the force required to overcome the friction between the wagon and the ground. The frictional force is given by the equation:

Frictional force = µ * Normal force,

where µ is the coefficient of kinetic friction and the Normal force is the force exerted by the ground on the wagon perpendicular to the surface. In this case, the Normal force is equal to the weight of the wagon, which is 56 N.

Frictional force = 0.40 * 56 N = 22.4 N.

2. Next, let's break down the force that the child applies into horizontal and vertical components. The horizontal component of the force is responsible for overcoming the friction, while the vertical component is responsible for supporting the weight of the wagon.

The vertical component of the force can be calculated using the equation:

Vertical component = Weight * sin(angle),

where the angle is given as 12 degrees.

Vertical component = 56 N * sin(12°) = 11.72 N.

3. The horizontal component of the force is equal to the force required to overcome friction. Therefore, the child must exert a force of 22.4 N to pull the wagon.

However, since the child is pulling at an angle of 12 degrees, the force that the child pulls on the handle would be the hypotenuse of a right triangle formed by the horizontal and vertical components of the force.

By applying the Pythagorean theorem, we can find the magnitude of the force:

Force (magnitude) = √(Horizontal component^2 + Vertical component^2),

Force (magnitude) = √(22.4^2 + 11.72^2) = √(501.76 + 137.4384) = √639.1984 = 25.30 N.

Therefore, the child pulls on the handle with a force of approximately 25.30 N.

To find out how hard the child pulls on the handle, we need to consider the force required to overcome the friction and the force required to move the wagon.

Step 1: Calculate the force required to overcome friction.
The force of friction can be calculated using the equation: frictional force = coefficient of friction * normal force.
Since the wagon is on a flat surface, the normal force is equal to the weight of the wagon, which is 56 N.
Therefore, the frictional force = 0.40 * 56 N = 22.4 N.

Step 2: Resolve the force of pulling into horizontal and vertical components.
The horizontal component of the force of pulling is given by: force of pulling * cos(angle).
The vertical component of the force of pulling is given by: force of pulling * sin(angle).

Step 3: Equate the horizontal component of the force of pulling to the force required to overcome friction.
Since the wagon is moving horizontally, the horizontal component of the force of pulling must be equal to the force required to overcome friction.
Therefore, force of pulling * cos(angle) = 22.4 N.

Step 4: Solve for the force of pulling.
Divide both sides of the equation by cos(angle) to isolate the force of pulling.
force of pulling = 22.4 N / cos(angle).

Step 5: Substitute the given angle into the equation and calculate.
Substitute the angle of 12 degrees into the equation.
force of pulling = 22.4 N / cos(12 degrees).
Using a calculator or trigonometric table, the value of cos(12 degrees) is approximately 0.978.

Step 6: Calculate the force of pulling.
force of pulling = 22.4 N / 0.978.
force of pulling ≈ 22.9 N.

Therefore, the child pulls on the handle with a force of approximately 22.9 Newtons.