Question

1. a force of 500 n is used to pull an object up an inclined plane. in order to move the object, the total amount of work done was 1500 joules. calculate the distance the object was moved. show your work. include proper units in your answer

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1. calculate the amount of work done when a 70 kg person is lifted a vertical distance of 1.2 meters. (don’t forget to convert mass to force of gravity first). show your work. include proper units in your answer.

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1. consider the following diagram of a ramp.

a. calculate the force of gravity on the 70 kg object.
b. calculate the work which would be done to raise the 70 kg mass straight up a vertical distance of 2 meters. (that is, without using the ramp.)
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c. calculate the work done when the object is moved 14 meters up the ramp using a force of 100 n.
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d. what is the advantage of using a ramp like this to move an object up instead of lifting it straight up?

Explanation:

Problem 6

Step1: Recall work formula

Work is defined as $W = F \times d$, where $W$ is work, $F$ is force, $d$ is distance. Rearrange to solve for $d$: $d = \frac{W}{F}$

Step2: Substitute given values

$W = 1500\ \text{J}$, $F = 500\ \text{N}$
$d = \frac{1500}{500}$

Step3: Calculate distance

$d = 3\ \text{m}$

Problem 7

Step1: Calculate gravitational force

Force of gravity $F = m \times g$, where $m=70\ \text{kg}$, $g=9.8\ \text{m/s}^2$
$F = 70 \times 9.8 = 686\ \text{N}$

Step2: Calculate work done

Use $W = F \times d$, $d=1.2\ \text{m}$
$W = 686 \times 1.2$

Step3: Compute final work value

$W = 823.2\ \text{J}$

Problem 8a

Step1: Calculate gravitational force

Use $F = m \times g$, $m=70\ \text{kg}$, $g=9.8\ \text{m/s}^2$
$F = 70 \times 9.8$

Step2: Compute force value

$F = 686\ \text{N}$

Problem 8b

Step1: Use work formula with gravity force

$W = F \times d$, $F=686\ \text{N}$, $d=2\ \text{m}$
$W = 686 \times 2$

Step2: Compute work value

$W = 1372\ \text{J}$

Problem 8c

Step1: Use work formula with applied force

$W = F \times d$, $F=100\ \text{N}$, $d=14\ \text{m}$
$W = 100 \times 14$

Step2: Compute work value

$W = 1400\ \text{J}$

Problem 8d

Step1: Explain ramp mechanical advantage

A ramp acts as an inclined plane, a simple machine that reduces the amount of force needed to move an object to a higher elevation, even though the total work done is approximately the same (accounting for small frictional losses).

Answer:

1. Problem 6: $\boldsymbol{3\ \text{meters}}$
2. Problem 7: $\boldsymbol{823.2\ \text{Joules}}$
3. Problem 8a: $\boldsymbol{686\ \text{N}}$
4. Problem 8b: $\boldsymbol{1372\ \text{J}}$
5. Problem 8c: $\boldsymbol{1400\ \text{J}}$
6. Problem 8d: A ramp reduces the amount of force required to lift an object to a given height, making the task easier, even though the total work done is nearly equal to lifting the object straight up.