# AP physics exam question

## Homework Statement

I have this packet and one of the questions state:
The constant force F with components Fx=3N and Fy=4N act on a body while that body moves from the point P (x=2 m, y=6 m) to the point Q (x=14 m, y=1 m). How much does the force do on the body during this process?

the options are as follows:
a. 16 J
b. 30 J
c. 46 J
d. 56 J
e. 65 J

## Homework Equations

I have the equations to find energy:
kinetic: K=(1/2)mv^2
gravitational: mgh

## The Attempt at a Solution

but I'm not sure if I'm missing something. So far I have figured out you need to keep the x and y components seperated and calculate each but I think I'm doing something wrong. I've gotten to Work = Force * cos(t) * change in distance but I'm just confusing myself. Help?

Also, I am taking the Physics: C Mechanics exam, what are some topics and questions that would help me prepare for it?

Last edited:

Do you know what a dot product is?

I don't know what a dot product is other than its used in calculus

I don't know what a dot product is other than its used in calculus

It is quite a simple operation, I am sure you must have come across it in high school maths, but for a refresher...

Dot product is defined as:
$a_{i} b_{j}\delta_{ij}=a_{i} b_{i}$

Example:
$\vec{a} = (2\hat{e}_{1} +2\hat{e}_{2} + 2\hat{e}_{3} )$
$\vec{b} = (0\hat{e}_{1} +2\hat{e}_{2} + 4\hat{e}_{3} )$

then
$a_{i} b_{j}\delta_{ij}= ( 2 \bullet 0) + (2 \bullet 2) + (2 \bullet 4)$
$a_{i} b_{j}\delta_{ij}= 12$

You have the right formula. But it easier to use the dot product formula (which may be used by people that don't know calculus)

W = Fxdx+Fydy+Fzdz.

Those are the components of the forceF and the displacement d.

EDIT: TheAustrian beat me to the punch

1 person
Would the answer be a. 16 J?
I used:
F=(3i+4j) N
s=(14-2i + 1-6j)
m = 12i+-5j) m
W=f•s=36-20=16J
16 J?

Yeah, that looks right.

1 person
SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

I have this packet and one of the questions state:
The constant force F with components Fx=3N and Fy=4N act on a body while that body moves from the point P (x=2 m, y=6 m) to the point Q (x=14 m, y=1 m). How much does the force do on the body during this process?

the options are as follows:
a. 16 J
b. 30 J
c. 46 J
d. 56 J
e. 65 J

## Homework Equations

I have the equations to find energy:
kinetic: K=(1/2)mv^2
gravitational: mgh

## The Attempt at a Solution

but I'm not sure if I'm missing something. So far I have figured out you need to keep the x and y components seperated and calculate each but I think I'm doing something wrong. I've gotten to Work = Force * cos(t) * change in distance but I'm just confusing myself. Help?

Also, I am taking the Physics: C Mechanics exam, what are some topics and questions that would help me prepare for it?
Is this problem from a practice test or is it from a current AP test ?

Redbelly98
Staff Emeritus