Question

1. you are riding in an elevator holding a spring scale with a 1 - kg mass suspended from it. you see that it reads 9.3 n. what does this tell you about the elevators motion?
2. compare the force holding a 10.0 - kg rock on earth and on the moon. the gravitational field on the moon is 1.6 n/kg.
3. you take a ride in a fast elevator to the top of a tall building and ride back down. compare your apparent and real weights at each part of the journey. sketch free - body diagrams to support your answers.
4. you are standing on an ice - skating rink. your friend applies a force of 90 n to you. with a mass of 65.0 kg, what is your resulting acceleration?
5. you have a job loading inventory onto trucks at a meat warehouse. each truck has a weight limit of 10000 n of cargo. you push each crate of meat along a low - resistance roller belt to a scale and weigh it before moving it onto the truck. one night, right after you weigh a 1000 - n crate, the power goes out. describe a way in which you could apply newtons laws to approximate the mass of the crate.

Explanation:

2.

Step1: Recall weight - mass relationship

On Earth, the weight $W = mg$, where $m$ is mass and $g$ is gravitational acceleration ($g_E=9.8\ m/s^2$ on Earth and $g_M=\frac{1}{6}g_E$ on the Moon).
For a $10 - kg$ rock on Earth, $W_E=mg_E$. Substituting $m = 10\ kg$ and $g_E = 9.8\ m/s^2$, we get $W_E=10\times9.8=98\ N$.
On the Moon, $W_M=mg_M$, and since $g_M=\frac{1}{6}g_E$, $W_M = 10\times\frac{9.8}{6}\approx16.3\ N$. The force holding the rock on Earth is its weight on Earth ($98\ N$) and on the Moon is its weight on the Moon ($16.3\ N$).

3.

Step1: Analyze forces on the mass in the elevator

The normal force $N$ measured by the scale is related to the acceleration of the elevator. The force acting on the $1 - kg$ mass is given by Newton's second - law $F = ma$. The gravitational force on the $1 - kg$ mass is $F_g=mg$ where $m = 1\ kg$ and $g = 9.8\ m/s^2$, so $F_g=9.8\ N$. The normal force $N = 9.3\ N$.

Step2: Apply Newton's second - law

$F_{net}=ma$, and $F_{net}=N - mg$. So $a=\frac{N - mg}{m}$. Substituting $N = 9.3\ N$, $m = 1\ kg$ and $g = 9.8\ m/s^2$, we have $a=\frac{9.3-9.8}{1}=- 0.5\ m/s^2$. The negative sign indicates that the elevator is accelerating downwards. This tells us that the elevator is moving with a downward acceleration of $0.5\ m/s^2$.

4.

Step1: Draw free - body diagrams

For the upward part of the journey: The forces acting on the person are the gravitational force $F_g = mg$ (downward) and the normal force $N$ (upward). For the downward part of the journey: The forces are still the gravitational force $F_g=mg$ (downward) and the normal force $N$ (upward).

Step2: Compare

During the upward journey, if the elevator is accelerating upward, $N>mg$; if it is moving at a constant speed, $N = mg$; if it is decelerating upward, $Nmg$.

5.

Answer:

1. On Earth, the force holding the 10 - kg rock is 98 N. On the Moon, it is approximately 16.3 N.
2. The elevator is accelerating downward at $0.5\ m/s^2$.
3. Free - body diagrams show different normal and gravitational force relationships depending on the motion (acceleration, constant speed, deceleration) of the elevator during upward and downward journeys.
4. The resulting acceleration is approximately $1.38\ m/s^2$.
5. We can use an inclined plane to move the crate onto the truck. When pushing, we apply a force to change its state of motion, and Newton's laws govern the interaction between the crate and us, as well as the measurement of its weight before moving.