sph3u1 - unit 2 forces
name:
date:
8. as you climb higher and higher on a mountain, the gravitational force due to earth would...
a. increase
b. decrease
c. remain unchanged
d. not enough information is given to decide
9. from the image to the right, which planet would you have a larger mass on?
a. jupiter
b. mars
c. your mass is the same on both
d. not enough information is given to decide
10. which situation below would your weight feel the smallest?
a. an elevator accelerating upwards
b. sitting at rest in a classroom
c. a roller coaster accelerating downwards
d. your weight is the same in all scenarios
short answer problems: show your work where appropriate. 0.5 communication mark will be deducted for each missing/incorrect unit, direction or significant figure, up to 3 marks. 3 marks - c
11. you are dragging a 72 kg tree trunk across the floor at a constant velocity with a force of 380 n right.
a. draw a fbd of the tree trunk. 1 mark - c
b. calculate the coefficient of kinetic friction. 3 marks - t
c. a friend pranks you by pushing on the trunk with a force of 150 n down. calculate the magnitude of horizontal force required now to move the trunk at a constant velocity. 3 marks - t

Question

Accepted Answer

### 8.
# Explanation:
## Step1: Recall gravitational force formula
The gravitational force $F = \frac{GMm}{r^{2}}$, where $G$ is the gravitational constant, $M$ is the mass of the Earth, $m$ is the mass of the object (you), and $r$ is the distance from the center of the Earth.
## Step2: Analyze the change in $r$
As you climb higher on a mountain, $r$ (distance from the Earth's center) increases. Since $F\propto\frac{1}{r^{2}}$, when $r$ increases, $F$ decreases.

# Answer:
b. Decrease

### 9.
# Brief Explanations:
Mass is an intrinsic property of an object. It does not depend on the location (e.g., which planet you are on). It is a measure of the amount of matter in an object.

# Answer:
c. Your mass is the same on both

### 10.
# Explanation:
## Step1: Use the formula for apparent weight
The apparent weight $W_{app}=m(g - a)$ when accelerating downwards ($a$ is the acceleration) and $W_{app}=m(g + a)$ when accelerating upwards. When sitting at rest $W_{app}=mg$.
## Step2: Compare the values
For an elevator accelerating upwards $W_{app}>mg$,  for sitting at rest $W_{app} = mg$, for a roller - coaster accelerating downwards $W_{app}=m(g - a)<mg$

# Answer:
c. A roller coaster accelerating downwards

### 11.
#### a. Free - Body Diagram (FBD)
# Brief Explanations:
- There is a gravitational force $F_g=mg$ acting downwards, where $m = 72\space kg$ and $g = 9.8\space m/s^{2}$.
- A normal force $F_N$ acting upwards.
- An applied force $F_{app}=380\space N$ (right) and a frictional force $F_f$ (left) since the trunk is moving at a constant velocity (so $F_{app}=F_f$ in magnitude for horizontal direction and $F_N = F_g$ in vertical direction)

# Answer:
Draw four vectors: $F_g$ (down), $F_N$ (up), $F_{app}$ (right), $F_f$ (left) with $F_{app}=F_f$ and $F_N = F_g$

#### b.
# Explanation:
## Step1: Find the normal force
Since $F_N=mg$ (vertical equilibrium, $a_y = 0$), $m = 72\space kg$ and $g=9.8\space m/s^{2}$, so $F_N=72\times9.8 = 705.6\space N$
## Step2: Use the frictional force formula
The frictional force $F_f=\mu_kF_N$. Given $F_f = 380\space N$ (because $F_{app}=F_f$ as $a_x=0$), then $\mu_k=\frac{F_f}{F_N}$
Substitute $F_f = 380\space N$ and $F_N=705.6\space N$
$\mu_k=\frac{380}{705.6}\approx0.54$

# Answer:
$\mu_k\approx0.54$

#### c.
# Explanation:
## Step1: Find the new normal force
The new normal force $F_N'=mg + F_{push}$, where $mg = 72\times9.8=705.6\space N$ and $F_{push}=150\space N$
$F_N'=705.6+ 150=855.6\space N$
## Step2: Find the new frictional force
The frictional force $F_f'=\mu_kF_N'$. Since $\mu_k\approx0.54$ (from part b)
$F_f'=0.54\times855.6 = 462.024\space N$

# Answer:
$F\approx462\space N$

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QUESTION IMAGE

Question

Explanation:

8.

Step1: Recall gravitational force formula

Step2: Analyze the change in \(r\)

Step1: Use the formula for apparent weight

Step2: Compare the values

Answer:

9.