Calculating Work Done by a Constant Force on a Moving Body

[swarm17]

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 separated 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?

 

[paisiello2]

Do you know what a dot product is?

 

[swarm17]

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

 

[TheAustrian]

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

 

[dauto]

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 = F_xd_x+F_yd_y+F_zd_z.

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

EDIT: TheAustrian beat me to the punch

 

[swarm17]

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?

 

[dauto]

Yeah, that looks right.

 

[SammyS]

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 separated 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]

Is this problem from a practice test or is it from a current AP test ?

It is from a set of free sample test questions posted on the College Board website.

swarm17, hope everything went well for you yesterday!