# Force required to change direction

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1. Feb 11, 2015

### rasen58

1. The problem statement, all variables and given/known data
The speed of a 2 kg object changes from 30 m/s to 40 m/s during a 5 s time interval. During this same time interval, the velocity of the object changes in direction by 90 degrees. What average force was applied during the time interval?

2. Relevant equations
impulse = F.t

3. The attempt at a solution
I know how to find the force if the object hadn't turned.
2 kg (40 - 30) = 20 = F . t
F = 4 N
But I don't know how to find the force required to move it.

2. Feb 12, 2015

### ehild

Velocity is vector quantity. Draw the initial and final velocities and their difference: They make a right triangle. You need the magnitude of v2-v1.

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3. Feb 12, 2015

### rasen58

So v2-v1 is 50 m/s. But then what do I do. Finding the impulse by using (2 kg)(50m/s - 30m/s) doesn't give me the right answer.

4. Feb 12, 2015

### Staff: Mentor

Take a look at the change in momentum that has to occur in the x and y directions separately. Suppose the object is initially traveling in the +x direction. What's its momentum? After the maneuver, what's the new momentum in the x direction? So the change is? Then do the same for the y-direction.

You'll then have two components of the total change in momentum: $ΔP_x$ and $ΔP_y$. $ΔP$ is a vector quantity. Can you determine the average force required from there?

5. Feb 12, 2015

### ehild

50 m/s is the magnitude of the difference between the initial and final velocities. Why do you subtract the initial speed again?
Multiplied by the mass, you get the change of momentum. Divided by time, it yields the average force.

6. Feb 12, 2015

### haruspex

Right, but it's not going to give 50N. rasen58, are you sure it's 5 sec, not 2 sec?