Final answer:
The magnitude of the smallest force that the child should exert is 242 N. The angle that the force makes with the +x-direction is 0 degrees. The weight of the cart is equal to the force exerted by the child.
Step-by-step explanation:
To find the magnitude of the smallest force that the child should exert, we need to consider the forces acting on the cart. The two adults are pushing with forces of 117 N and 125 N in the horizontal direction. Since the cart is starting from rest, the net force acting on it must be zero. This means that the force exerted by the child should be equal in magnitude but opposite in direction to the sum of the forces exerted by the adults. Therefore, the magnitude of the smallest force that the child should exert is 117 N + 125 N = 242 N.
To find the angle that the force makes with the +x-direction, we can use trigonometry. Let's denote the angle as θ. We can calculate θ using the following formula:
θ = arctan(Fy/Fx)
Here, Fx is the sum of the x-component of the forces exerted by the adults, and Fy is the y-component of the force exerted by the child. Since the forces are acting in the horizontal direction, Fy = 0. Therefore, the angle θ is 0 degrees, meaning that the force exerted by the child is in the same direction as the +x-direction.
To find the weight of the cart, we need to use Newton's second law of motion, which states that force equals mass times acceleration (F = ma). In this case, the force is the net force exerted on the cart, which is the force exerted by the child. The acceleration is given as 1.90 m/s². Rearranging the equation, we can solve for the mass of the cart: m = F/a. Once we have the mass, we can calculate the weight of the cart using the formula weight = mass x gravitational acceleration. The weight of the cart is equal to the force exerted by the child.
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