# Homework Help: Find speed given mass, starting speed and time

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1. Dec 16, 2017

### doublev231

• Member advised to use the formatting template for all homework help requests
A cart which weighs 500g is moving on a horizontal table with the starting speed of 7 m/s. At the end of the cart there's a non-elastic wire attached, which is thrown over a pulley, and on the other end of the wire there's a 200g load. I need to find the speed of the cart and the distance it traveled after 5 seconds of movement

Given variables:
m1 = 500g
v (starting speed) = 7 m/s
m2 = 200g
t = 5s

I'm not sure what formula to use there. Any guidance would be appreciated.

2. Dec 16, 2017

### PeroK

You need to use the homework template and to do as much as you can yourself.

The first step is to draw a diagram. This should help you identify what is important in analysing the problem.

3. Dec 16, 2017

### doublev231

I tried drawing a diagram, but am still unsure what formula to use here. I need to calculate the speed of a cart moving in a horizontal line but I also need to account for the weight that's attached to the cart.

4. Dec 16, 2017

### PeroK

That's true, but you still need to use the template.

By the way, my favourite formula is $F = ma$.

5. Dec 16, 2017

### doublev231

Okay, so I think I found one formula because you've mentioned the F=ma. Using it, we can get the velocity like this: v = Ft/m , and to get F we need m and a. We got m ( presumably I'll have to use the m1, which equals 500g ), and now we need a ( acceleration ). However, the problem is that the formula for acceleration is: a = v(final) - v(starting) / t and I don't have v final. How can I find the final v ( speed ) ?

6. Dec 16, 2017

### PeroK

1) Find the final speed; 2) Use this to find acceleration; 3) Use acceleration to find the force.

Can you see anything wrong with that?

What do you have in your diagram?

7. Dec 16, 2017

### doublev231

In my diagram I have drawn a cart that weighs 500 grams, and also marked that the starting speed of it is 7 meters per second. Then I have a wire that's over a pulley and at the end of the wire there's a weight that weighs in at 200 grams. Looks like I can't find the final speed without knowing the acceleration, is that what's wrong?

8. Dec 16, 2017

### PeroK

Yes, so what's missing from your diagram?

9. Dec 16, 2017

### doublev231

Looks like the acceleration of the cart is missing, however, I'm unsure how to calculate it, I need the final speed to do so. Currently I only have the time and the starting speed, and I'm unsure how to get the final one so I can calculate acceleration.

10. Dec 16, 2017

### PeroK

It's more fundamental than that. What's the 200g mass doing in all this?

11. Dec 16, 2017

### doublev231

I think the 200 grams is slowing the cart down, thus reducing it's speed?

12. Dec 16, 2017

### PeroK

I think you are misinterpreting the problem. As I see it, the 200g mass is hanging over a pulley, in mid air.

13. Dec 16, 2017

### doublev231

Yes, the 200g mass is hanging mid air over the pulley. So the 200g mass should add to the mass of the cart then, right?

14. Dec 16, 2017

### PeroK

What about gravity, then? Have you heard of that?!

15. Dec 16, 2017

### doublev231

Oh, of course! So g = 9.81 m/s2, is that what we need?

16. Dec 16, 2017

### doublev231

Ooh, I get it now. We can now caculate F of the 200 g mass object like this: F = 200 * 9.81 = 1962 N, is that correct?

17. Dec 16, 2017

### PeroK

Yes and no. Yes, gravity is exactly what you need. But, be careful, gravity is a force.

Let me point out something general about problems when you have two things joined together. If you have a trolley, say, and it's attached to a car and you try to pull the trolley. You could move the trolley on its own quite easily. But, if it's attached to the car, then in order to move the trolley, you have to move the car as well. Let's assume the trolley has a mass of $10kg$ and the car has a mass of $990kg$. And you apply a force of $10N$.

If you were pulling the trolley on its own, the acceleration would be $a_1 = 10N/10kg = 1ms^{-2}$

But, if the trolley is attached to the car, then the accleleration is $a_2 = 10N/1000kg = 0.01 ms^{-2}$

This is because the force must accelerate the whole system.

You always need to be careful, therefore, to identify everything that must move when a force is applied. It's a common mistake to calculate the acceleration based only on the mass of part of the system.

18. Dec 16, 2017

### PeroK

Yes, except the mass is only 200g, not 200kg!

Another general piece of advice is always to be careful with the units you are given.

19. Dec 16, 2017

### doublev231

Oh, good catch! It's actually 1.962 N. So now I know that the F of the object over pulley is 1.962 N. so now I can get the acceleration by adding the two weighs and then dividing the force by the sum of these objects? Like this: 1.962 N / 0.7 kg. If that's the case, would this mean that acceleration of the whole system is 2.8 m/s2 ?

20. Dec 16, 2017

### PeroK

Yes, that looks good.