# Calculating Work & Final Velocity of a 70kg Mass

• magma_saber
In summary, the total work done is 508.75 J. To find the final velocity, you can use the equation Initial ½mv² + ΔW = Final ½mv². The initial kinetic energy should not be included in the calculation of ΔW.
magma_saber

## Homework Statement

A 70kg mass is in a space and moving at 2.5 m/s. You push it with 200N for 4 m. You then move to the front of the mass and push it backwards with 170N for 3 m.

What was the total work done?
What was the final velocity?

## Homework Equations

W = rest energy + F1*r - F2*r

## The Attempt at a Solution

rest energy = 1/2*70*(2.5)2 = 218.75
F1*r = 200*4 = 800
F2*r = 170*3 = 510
W = 218.75 + 800 - 510 = 508.75 J

How would i get the final velocity?

magma_saber said:
How would i get the final velocity?

Initial KE + Work = Final KE

Initial ½mv² + W = Final ½mv²

so its 218.75 + 800 + 510?

magma_saber said:
so its 218.75 + 800 + 510?

Perhaps I should rephrase that since you want to plug in numbers literally without thinking about the signs:

Initial ½mv² + ΔW = Final ½mv²

Btw your initial calculation incorrectly includes the initial KE in the ΔW they asked you to find.

## 1. How do you calculate the work done on a 70kg mass?

The work done on a 70kg mass can be calculated by multiplying the force applied to the mass by the distance the mass moves in the direction of the force. The formula for work is W = F x d, where W is work, F is force, and d is distance.

## 2. What is the unit of measurement for work?

The unit of measurement for work is joules (J).

## 3. How do you calculate the final velocity of a 70kg mass?

The final velocity of a 70kg mass can be calculated using the formula v = √(2 x W/m), where v is final velocity, W is work, and m is mass. Alternatively, if the initial velocity (u) and acceleration (a) of the mass are known, the formula v = u + at can be used.

## 4. What is the difference between work and power?

Work is the amount of energy transferred to or from an object by a force, while power is the rate at which work is done. In other words, work is a measure of the total energy involved, whereas power is a measure of how quickly that energy is being transferred.

## 5. Can the final velocity of a 70kg mass be negative?

Yes, the final velocity of a 70kg mass can be negative if it is moving in the opposite direction of its initial velocity. A negative final velocity indicates that the mass is decelerating or moving in the opposite direction of the applied force.

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