Final answer:
The normal force is the support force exerted by a surface, and the weight force is the mass times acceleration due to gravity. These forces may not be equal when pushing an object with a handle at an angle because of the additional forces introduced by the angle of application, making it indeterminable without more information.
Step-by-step explanation:
When you push a heavy object by using a handle that is attached to the object at an angle, the normal force and the object's weight force are typically not equal. The weight force is simply the mass of the object times the acceleration due to gravity (mg), and it always acts downwards. The normal force, on the other hand, is the support force exerted by a surface that is perpendicular to it. If the surface is horizontal, and there is no additional vertical acceleration, the normal force can be equal to the weight force. However, when pushing with a handle that is at an angle, you introduce additional forces to the system.
In general, if the handle you are pushing on is above the center of mass of the object, the normal force will likely decrease because some of the force you apply will be directed upwards, reducing the normal force needed to balance the object's weight. Conversely, if the handle is below the center of mass, the normal force may increase, as part of the force you apply will have a downward component, which adds to the weight force the surface has to support. This reflects the fact that the inclination of the force can change the effective weight that the surface has to support. Because the exact relationship depends on the specific angle and manner of the force applied, the comparison cannot be determined without additional information about the angle of the handle and the direction and magnitude of the force applied. Therefore, the correct answer is D) Cannot be determined.