A child pulls on a wagon handle at an angle 37° above the horizontal with a force of 45 N. If the wagon accelerates at 8.1 m/s2 horizontally, what is the mass of the wagon? Assume frictional forces are negligible.

first figure the horizontal force.

forceh=45*cos37

that has to equal mass*a

solve for mass.

4.6

4.4368 kg

45*cos 37=35.93959795N
F=ma
m=35.93959795N / 8.1 ms^-2
=4.4368kg

Why did the wagon go to therapy? Because it had some serious acceleration issues!

To find the mass of the wagon, we can use Newton's second law of motion, which states that the force (F) applied to an object is equal to the mass (m) of the object multiplied by its acceleration (a).

In this case, the given force is the horizontal component of the force applied on the wagon handle. To find the horizontal component, we need to determine the vector components of the force. The vertical component of the force does not affect the horizontal acceleration of the wagon.

The horizontal component of the force (F_h) can be found by multiplying the total force (45 N) by the cosine of the angle between the handle and the horizontal direction.

F_h = 45 N * cos(37°)

Next, we can substitute the values we have into the equation:

F_h = m * a

Substitute the values:

45 N * cos(37°) = m * 8.1 m/s^2

Divide both sides of the equation by 8.1 m/s^2 to solve for m:

m = (45 N * cos(37°)) / 8.1 m/s^2

Now, let's calculate the value:

m = (45 N * 0.7986) / 8.1 m/s^2
m ≈ 4.42 kg

Therefore, the mass of the wagon is approximately 4.42 kg.