Here are the solutions to the problems on your worksheet, broken down step-by-step.
1. Explain why free-fall acceleration can be regarded as a constant...
Reasoning:
Gravity gets weaker the farther away you are from Earth. However, Earth is very large (about 4,000 miles in radius). If you are falling within "a few hundred miles" of the surface, that distance is tiny compared to the size of the whole planet. Because the change in distance from the center of the Earth is so small relative to the total distance, the pull of gravity hardly changes at all. Therefore, we treat it as a constant number ($9.8 \text{ m/s}^2$).
2. Identify which pair of objects would have greater gravitational force...
Reasoning:
The Law of Universal Gravitation states two main things:
1.
Mass matters: The heavier the objects, the stronger the pull.
2.
Distance matters: The closer the objects, the stronger the pull.
Looking at the diagram:
* In both Pair A and Pair B, the circles appear to be the same distance apart.
* However, the circles in
Pair A are much larger than the circles in Pair B. Larger circles usually represent more mass.
* Since Pair A has more mass and the distance is the same, the gravitational force will be stronger.
3. Predict the path of the cannonball...
Reasoning:
Projectile motion works in two directions at once:
*
Horizontal: The ball moves forward at a steady speed (ignoring air resistance). You draw an arrow pointing straight out from the cannon's mouth.
*
Vertical: Gravity pulls the ball down. It starts moving up but slows down, stops, and falls faster and faster toward the ground. You draw an arrow pointing straight down from the ball.
*
Path: When you combine moving forward and falling down, the result is a curved line shaped like an upside-down "U" (a parabola).
4. Calculate the mass in kg of an object that weighs 1,225 N on Earth.
Step-by-Step Calculation:
1.
Identify the formula: Weight is the force of gravity on an object. The formula is:
$$Weight = Mass \times Gravity$$
$$W = m \times g$$
2.
Identify the known values:
* Weight ($W$) = $1,225 \text{ N}$
* Gravity on Earth ($g$) $\approx 9.8 \text{ m/s}^2$
3.
Rearrange the formula to solve for Mass ($m$):
$$m = \frac{W}{g}$$
4.
Plug in the numbers:
$$m = \frac{1225}{9.8}$$
5.
Calculate:
$$1225 \div 9.8 = 125$$
***
Final Answer:
1. Free-fall acceleration is considered constant because the distance fallen (a few hundred miles) is very small compared to the radius of the Earth. Therefore, the change in gravitational pull is negligible.
2. Pair A has the greater gravitational force. According to the law of universal gravitation, force increases with mass. Since the objects in Pair A are larger (more massive) than those in Pair B, and the distance appears to be the same, Pair A exerts a stronger pull.
3. *(Description for drawing)*:
*
Path: Draw a curved line starting from the cannon, arching upward, and then curving down to hit the ground (a parabola).
*
Horizontal Component: Draw an arrow pointing horizontally to the right (forward) from the cannonball. Label it "$v_x$" or "Horizontal Velocity".
*
Vertical Component: Draw an arrow pointing straight down from the cannonball. Label it "$v_y$" or "Vertical Velocity" (or simply "Gravity").
4. 125 kg
Parent Tip: Review the logic above to help your child master the concept of holt science spectrum worksheet.
