Question
A rolling ball has a velocity of 25m/s and a momentum of 355 kg.m/s. What is the mass of the ball?
6. If you use 314 newtons of force to push a box 3y.4 meters, how much work did you do? If it took you 25 seconds to do it, what was your power?
7. If you do 215 joules of work to pick up a box 1.8 meters, how much does the box weigh? (Force)
6. If you use 314 newtons of force to push a box 3y.4 meters, how much work did you do? If it took you 25 seconds to do it, what was your power?
7. If you do 215 joules of work to pick up a box 1.8 meters, how much does the box weigh? (Force)
Answers
GPT-4o mini
Let's address each of your questions one by one.
### 1. Mass of the ball:
Momentum (p) is calculated using the formula:
\[
p = m \cdot v
\]
Where:
- \( p \) is momentum (in kg·m/s),
- \( m \) is mass (in kg),
- \( v \) is velocity (in m/s).
Given:
- \( p = 355 \, \text{kg·m/s} \)
- \( v = 25 \, \text{m/s} \)
We can solve for mass \( m \):
\[
m = \frac{p}{v} = \frac{355 \, \text{kg·m/s}}{25 \, \text{m/s}} = 14.2 \, \text{kg}
\]
So, the mass of the ball is **14.2 kg**.
---
### 2. Work done and power:
Work (W) is calculated using the formula:
\[
W = F \cdot d
\]
Where:
- \( W \) is work (in joules),
- \( F \) is force (in newtons),
- \( d \) is distance (in meters).
Given:
- \( F = 314 \, \text{N} \)
- \( d = 3.4 \, \text{m} \)
Calculating work done:
\[
W = 314 \, \text{N} \cdot 3.4 \, \text{m} = 1067.6 \, \text{J}
\]
Thus, the work done is **1067.6 joules**.
Power (P) is calculated using the formula:
\[
P = \frac{W}{t}
\]
Where:
- \( t \) is time (in seconds).
Given:
- \( t = 25 \, \text{s} \)
Calculating power:
\[
P = \frac{1067.6 \, \text{J}}{25 \, \text{s}} = 42.704 \, \text{W}
\]
Therefore, the power is approximately **42.7 watts**.
---
### 3. Weight of the box:
Weight (force due to gravity) can be calculated using the formula:
\[
W = F = \frac{Work}{d}
\]
Where \( W \) is the weight (in newtons), \( Work \) is the work done (in joules), and \( d \) is the distance (in meters).
Given:
- \( Work = 215 \, \text{J} \)
- \( d = 1.8 \, \text{m} \)
Calculating weight (force):
\[
F = \frac{215 \, \text{J}}{1.8 \, \text{m}} \approx 119.44 \, \text{N}
\]
So, the weight of the box is approximately **119.44 newtons**.
### 1. Mass of the ball:
Momentum (p) is calculated using the formula:
\[
p = m \cdot v
\]
Where:
- \( p \) is momentum (in kg·m/s),
- \( m \) is mass (in kg),
- \( v \) is velocity (in m/s).
Given:
- \( p = 355 \, \text{kg·m/s} \)
- \( v = 25 \, \text{m/s} \)
We can solve for mass \( m \):
\[
m = \frac{p}{v} = \frac{355 \, \text{kg·m/s}}{25 \, \text{m/s}} = 14.2 \, \text{kg}
\]
So, the mass of the ball is **14.2 kg**.
---
### 2. Work done and power:
Work (W) is calculated using the formula:
\[
W = F \cdot d
\]
Where:
- \( W \) is work (in joules),
- \( F \) is force (in newtons),
- \( d \) is distance (in meters).
Given:
- \( F = 314 \, \text{N} \)
- \( d = 3.4 \, \text{m} \)
Calculating work done:
\[
W = 314 \, \text{N} \cdot 3.4 \, \text{m} = 1067.6 \, \text{J}
\]
Thus, the work done is **1067.6 joules**.
Power (P) is calculated using the formula:
\[
P = \frac{W}{t}
\]
Where:
- \( t \) is time (in seconds).
Given:
- \( t = 25 \, \text{s} \)
Calculating power:
\[
P = \frac{1067.6 \, \text{J}}{25 \, \text{s}} = 42.704 \, \text{W}
\]
Therefore, the power is approximately **42.7 watts**.
---
### 3. Weight of the box:
Weight (force due to gravity) can be calculated using the formula:
\[
W = F = \frac{Work}{d}
\]
Where \( W \) is the weight (in newtons), \( Work \) is the work done (in joules), and \( d \) is the distance (in meters).
Given:
- \( Work = 215 \, \text{J} \)
- \( d = 1.8 \, \text{m} \)
Calculating weight (force):
\[
F = \frac{215 \, \text{J}}{1.8 \, \text{m}} \approx 119.44 \, \text{N}
\]
So, the weight of the box is approximately **119.44 newtons**.