3. write the equation for the impulse-momentum theorem and define all the variables.
4. what is the si unit for impulse?
5. professional boxers wear 8 oz. or 10 oz. gloves depending on the weight class. with the impulse - momentum theorem in mind, describe why boxers use gloves for the safety of themselves and their opponents. use complete sentences to receive full credit.
6. give an example of a system whose mass is not constant?
a. a spinning top
b. a baseball flying through the air
c. a rocket launched from earth
d. a block sliding on a frictionless inclined plane
7. a soccer ball with a mass of 0.4 kg is kicked with a force on 50 n for 0.1 seconds. what is the cha momentum of the ball?
8. a truck with a mass of 2000 kg is traveling at 15 m/s. the driver applies the brakes, exerting a f 4000 n for 10 seconds. what is the trucks final speed?

Question

Accepted Answer

### Question 3
# Brief Explanations:
The Impulse-Momentum Theorem states that impulse equals change in momentum. Impulse is force times time, and momentum change is mass times velocity change.
# Answer:
Equation: $J = \Delta p$ or $F \Delta t = m(v_f - v_i)$
Definitions: $J$ = impulse, $F$ = net force, $\Delta t$ = time interval, $\Delta p$ = change in momentum, $m$ = mass, $v_f$ = final velocity, $v_i$ = initial velocity

### Question 4
# Brief Explanations:
Impulse is force (SI unit: newton, N) times time (SI unit: second, s), so the unit is newton-second.
# Answer:
Newton-second (N·s)

### Question 5
# Brief Explanations:
Gloves increase collision time. By Impulse-Momentum Theorem ($F \Delta t = \Delta p$), if $\Delta p$ is fixed, longer $\Delta t$ reduces force $F$, lowering injury risk.
# Answer:
Boxers use gloves because gloves increase the time interval of impact. According to the impulse-momentum theorem, the impulse (change in momentum) is constant for a given punch, so increasing the time interval decreases the force exerted on both the boxer and their opponent, reducing the risk of injury.

### Question 6
# Brief Explanations:
A rocket loses mass as it burns fuel and expels exhaust, so its mass is not constant.
# Answer:
c. A rocket launched from Earth

### Question 7
# Explanation:
## Step1: Recall impulse-momentum relation
Change in momentum equals impulse ($\Delta p = F \Delta t$)
## Step2: Substitute values
$F = 50\ 	ext{N}$, $\Delta t = 0.1\ 	ext{s}$
$\Delta p = 50 	imes 0.1$
# Answer:
$5\ 	ext{kg·m/s}$

### Question 8
# Explanation:
## Step1: Note missing force value
The problem mentions a force but the value is cut off. Assuming the force is $F$ (let’s suppose the intended force is 4000 N as partially visible):
## Step2: Calculate impulse
$\Delta p = F \Delta t = 4000 	imes 10 = 40000\ 	ext{kg·m/s}$
## Step3: Relate to momentum change
$\Delta p = m(v_f - v_i) \implies v_f = v_i - \frac{\Delta p}{m}$ (since force is opposite to motion)
$v_f = 15 - \frac{40000}{2000} = 15 - 20 = -5\ 	ext{m/s}$ (unphysical, so likely force magnitude is smaller; if force is 2000 N: $v_f = 15 - 10 = 5\ 	ext{m/s}$)
*Note: Original problem has a missing force value, but assuming the visible "4000 N" is correct, the calculation follows.*
# Answer:
(Depends on full force value; if force is 4000 N: $-5\ 	ext{m/s}$ (unphysical, suggesting a typo); if force is 2000 N: $5\ 	ext{m/s}$)

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