45. Here the same stone is being accelerated vertically upward.
a. Draw force vectors to some suitable scale showing relative forces acting on the stone.
b. Which is the longer vector, and why?
To draw force vectors and determine which vector is longer, we should consider the forces acting on the stone. In this case, the stone is being accelerated vertically upward. Let's break down the forces:
1. Gravitational force (Weight): The stone will experience a force due to gravity pulling it downward. The weight is equal to the mass of the stone multiplied by the acceleration due to gravity (9.8 m/s²).
2. Normal force: As the stone is being accelerated vertically upward, there will be a reaction force exerted by the surface on the stone. This force is known as the normal force and acts in the opposite direction to the weight.
Now, let's answer the questions:
a. Drawing force vectors: To represent the forces acting on the stone, we'll draw them as arrows. The weight vector will point downward since it acts in the opposite direction of the stone's motion, and the normal force vector will point upward to counteract the weight. The scale will depend on the specific problem and the forces involved.
b. Longer vector: In this case, the weight vector will be longer than the normal force vector. This is because the gravitational force (weight) acting on the stone is stronger than the normal force. The weight vector is longer due to the force of gravity pulling the stone downward, while the normal force vector only needs to counteract the weight and keep the stone from sinking into the surface.
Note: The length of the vectors can be determined by considering the magnitudes of the forces involved. Gravitational force is generally stronger than normal force in most cases involving objects at or near the Earth's surface.