Work, energy and forces in a horizontal plane

[The Liberator]

Thanks in advance guys, and it does not need to be treated as a high priority question.

Homework Statement

This is not so much a homework question, as it is a query about a question that I am getting a wrong answer for (that is to the book's answer).

This is the straight question that the book gives me:

"A student supplies a constant force of 200 N at an angle of 60 degrees to the horizontal to pull a 50 kg object, initially at rest across a flat surface for 10 s. A constant frictional force acts on the mat, and the velocity after the 10 s is 3 ms-¹"The question asks how much work is done on the mat by the student?

Homework Equations

$$W = F * x * cosine (theta)$$

The Attempt at a Solution

I have substituted the values for cosine theta as 0.5, and F is 200 N, I tried to find the value for x, by using v * t = x, and substituted it as 3 * 10 = 30 m.

The answer that I found was 6 * 10³ joules, and the book gave the answer as 1.28 * 10³.

 

[tiny-tim]

Welcome to PF!

Hi The Liberator! Welcome to PF!

A student supplies a constant force of 200 N at an angle of 60 degrees to the horizontal to pull a 50 kg object, initially at rest across a flat surface for 10 s. A constant frictional force acts on the mat, and the velocity after the 10 s is 3 ms-¹
…
I tried to find the value for x, by using v * t = x, and substituted it as 3 * 10 = 30 m.

Nope … v is only the final velocity …

try one of the constant acceleration equations ​

 

[The Liberator]

Ahhh, okay. thanks. I will do, then report back to see answers.

By the way, thanks for welcoming me here. :)

Edit:I looked at the links, and I am sorry, but I don't follow.

 

[tiny-tim]

The object starts at rest, and after t = 10s is moving at v =3 ms-1.

Its acceleration, a, is constant.

You should be able to find an equation connecting v t and a, so you can find the value of a, and then an equation connecting x and a, so you can find the value of x

 

[The Liberator]

Oh, okay thanks. I understand now. :D

I think this one will do… $$v = u + at$$

I substituted the numbers and have it as 3 = 0 + 10a

I found a = 0.3 ms-²

and therefore [v² = u²+ 2ax

Substituted the numbers and have it as 9 = 0 + 2 * 0.3 x

I found x = 15 m.

The only thing is my final answer is different to what the book says.

Thanks.

 

[tiny-tim]

I found x = 15 m.

The only thing is my final answer is different to what the book says.

ah … got it … i wondered why they gave you the mass …

the question asks for the work done on the mat, not on the object

(I assume the mat is fixed to the floor, and the object is moving across it)

so you have to calculate the friction force between the mat and the object (use good ol' Newton's second law, with the acceleration you found), and the work done by that …

alternatively, use the work-energy theorem, and just subtract the energy gained by the object from the work done by the student

 

[The Liberator]

Oh, I am very sorry, I miss-read the answer in the book. I actually do have the right answer now…

My working out:

$$W = F * x * cosine(theta)$$

W = 200 * 15 * 0.5

W = 1500 joules.

Thanks very much Tim.

Also, sorry for confusing you, but I also miss-used the wording, as the object is also the mat.

By the way, this is a solved problem. It can now have the solved icon thing on it.