QuestionQuiz 3.2 Energy (Take-Home Quiz) Extra Time 8 of 8 (ㄷ) 09:24 /
A constant force of 900 N pushes a 100 kg mass up the inclined plane shown above at a uniform speed of $4 \mathrm{~m} / \mathrm{s}$ . The power developed by the 900 N force is most nearly 400 W 800 W 900 W $1,000 \mathrm{~W}$ 3,600 W

Studdy Solution

STEP 1

What is this asking? How much power is needed to push a mass up a slope at a constant speed with a given force? Watch out! The inclined plane angle is a distraction!
We don't need it.
Don't overthink it!

STEP 2

1. Define power
2. Calculate power

STEP 3

Alright, so, power is all about how much work gets done over a period of time.
Think of it like this: if you lift a heavy weight really fast, that's high power!
If you lift the same weight slowly, it's low power.
The work done is the same, but the time taken is different.

STEP 4

Mathematically, power $P$ is defined as work $W$ divided by time $t$ . $P = \frac{W}{t}$

STEP 5

Work is force $F$ times distance $d$ .
So we can rewrite the power formula as: $P = \frac{F \cdot d}{t}$

STEP 6

But wait!
Distance divided by time... that's just speed ( $v$ )!
So, we get this super useful formula: $P = F \cdot v$

STEP 7

We're given that the force is $\bf{900 N}$ and the speed is $\bf{4 m/s}$ .
Let's plug those values into our power formula: $P = F \cdot v$ $P = 900 \text{ N} \cdot 4 \text{ m/s}$

STEP 8

Now, let's multiply: $P = 3600 \text{ N} \cdot \text{m/s}$

STEP 9

Remember, a Newton-meter per second ( $N \cdot m/s$ ) is the same as a Watt (W), which is the unit of power.
So, our final answer is: $P = \bf{3600 \text{ W}}$

STEP 10

The power developed by the 900 N force is $\bf{3600 W}$ .

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Studdy Solution

STEP 1

What is this asking? How much power is needed to push a mass up a slope at a constant speed with a given force? Watch out! The inclined plane angle is a distraction!
We don't need it.
Don't overthink it!

STEP 2

1. Define power
2. Calculate power

STEP 3

Alright, so, power is all about how much work gets done over a period of time.
Think of it like this: if you lift a heavy weight really fast, that's high power!
If you lift the same weight slowly, it's low power.
The work done is the same, but the time taken is different.

STEP 4

Mathematically, power $P$ is defined as work $W$ divided by time $t$ . $P = \frac{W}{t}$

STEP 5

Work is force $F$ times distance $d$ .
So we can rewrite the power formula as: $P = \frac{F \cdot d}{t}$

STEP 6

But wait!
Distance divided by time... that's just speed ( $v$ )!
So, we get this super useful formula: $P = F \cdot v$

STEP 7

We're given that the force is $\bf{900 N}$ and the speed is $\bf{4 m/s}$ .
Let's plug those values into our power formula: $P = F \cdot v$ $P = 900 \text{ N} \cdot 4 \text{ m/s}$

STEP 8

Now, let's multiply: $P = 3600 \text{ N} \cdot \text{m/s}$

STEP 9

Remember, a Newton-meter per second ( $N \cdot m/s$ ) is the same as a Watt (W), which is the unit of power.
So, our final answer is: $P = \bf{3600 \text{ W}}$

STEP 10

The power developed by the 900 N force is $\bf{3600 W}$ .

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Studdy Solution

STEP 1

What is this asking? How much power is needed to push a mass up a slope at a constant speed with a given force? Watch out! The inclined plane angle is a distraction!We don't need it.Don't overthink it!

STEP 2

1. Define power2. Calculate power

STEP 3

Alright, so, power is all about how much work gets done over a period of time.Think of it like this: if you lift a heavy weight really fast, that's high power!If you lift the same weight slowly, it's low power.The work done is the same, but the time taken is different.

STEP 4

Mathematically, power PPP is defined as work WWW divided by time ttt. P=WtP = \frac{W}{t}P=tW​

STEP 5

Work is force FFF times distance ddd.So we can rewrite the power formula as: P=F⋅dtP = \frac{F \cdot d}{t}P=tF⋅d​

STEP 6

But wait!Distance divided by time... that's just **speed** (vvv)!So, we get this super useful formula: P=F⋅vP = F \cdot vP=F⋅v

STEP 7

We're given that the force is 900N\bf{900 N}900N and the speed is 4m/s\bf{4 m/s}4m/s.Let's plug those values into our power formula: P=F⋅vP = F \cdot vP=F⋅v P=900 N⋅4 m/sP = 900 \text{ N} \cdot 4 \text{ m/s}P=900 N⋅4 m/s

STEP 8

Now, let's **multiply**: P=3600 N⋅m/sP = 3600 \text{ N} \cdot \text{m/s}P=3600 N⋅m/s

STEP 9

Remember, a Newton-meter per second (N⋅m/sN \cdot m/sN⋅m/s) is the same as a **Watt (W)**, which is the unit of power.So, our final answer is: P=3600 WP = \bf{3600 \text{ W}}P=3600 W

STEP 10

The power developed by the 900 N force is 3600W\bf{3600 W}3600W.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? How much power is needed to push a mass up a slope at a constant speed with a given force? Watch out! The inclined plane angle is a distraction!
We don't need it.
Don't overthink it!

1. Define power
2. Calculate power

Alright, so, power is all about how much work gets done over a period of time.
Think of it like this: if you lift a heavy weight really fast, that's high power!
If you lift the same weight slowly, it's low power.
The work done is the same, but the time taken is different.

Mathematically, power $P$ is defined as work $W$ divided by time $t$ . $P = \frac{W}{t}$

Work is force $F$ times distance $d$ .
So we can rewrite the power formula as: $P = \frac{F \cdot d}{t}$

But wait!
Distance divided by time... that's just speed ( $v$ )!
So, we get this super useful formula: $P = F \cdot v$

We're given that the force is $\bf{900 N}$ and the speed is $\bf{4 m/s}$ .
Let's plug those values into our power formula: $P = F \cdot v$ $P = 900 \text{ N} \cdot 4 \text{ m/s}$

Now, let's multiply: $P = 3600 \text{ N} \cdot \text{m/s}$

Remember, a Newton-meter per second ( $N \cdot m/s$ ) is the same as a Watt (W), which is the unit of power.
So, our final answer is: $P = \bf{3600 \text{ W}}$

The power developed by the 900 N force is $\bf{3600 W}$ .