Change in Linear Momentum with mass and velocity

[vurk]

Homework Statement

A 2700 kg truck traveling north at 37 km/h turns east and accelerates to 47 km/h.

(a) What is the change in the truck's kinetic energy?

(b) What is the magnitude of the change in the linear momentum of the truck?

(c) What is the direction of the change in the linear momentum of the truck?
__° (measured clockwise from east)

Homework Equations

p = m * v

The Attempt at a Solution

Part A is easy enough, i found it to be around 88450 J.

Part B, finding the change in momentum, I tried (m * v) - (M * V), with the latter part being the final speed (after converting to m/s), and got an answer of 7400 kg*m/s, which was wrong. I don't see why this doesn't work, so any explination would be much appreciated.

Part C, I have no clue.. I don't remember seeing any formulas with angles in them.. after searching google i found some confusing looking formulas that have to do with angular momentum, but the problem specifically says linear.. so any insights on that would be appreciated as well, thanks.

 

[physics girl phd]

You're messing this up because momentum is a vector! Find the magnitudes of the initial and final momentum -- but then don't just subtract! Make a diagram and do the vector math (it will involve trig functions).

 

[baba89]

Hello,

First, let's clarify that the change in linear momentum is given by the formula Δp = mΔv, where Δv is the change in velocity. So for part B, the correct calculation would be (2700 kg * 47 km/h) - (2700 kg * 37 km/h), which gives a change in momentum of 27000 kg*m/s. This is because the change in velocity is 10 km/h, which is equivalent to 10,000 m/h, and we need to convert to m/s in order to use the formula.

For part C, you are correct that there are no specific formulas for finding the direction of change in linear momentum. However, we can use the concept of vectors to determine the direction. In this case, the truck is initially traveling north and then turns east, so the change in momentum will be in the direction between north and east. To find this direction, we can use the trigonometric function tangent, which is opposite over adjacent (tanθ = opposite/adjacent). In this case, the opposite side would be the change in velocity in the north-south direction (10,000 m/h) and the adjacent side would be the change in velocity in the east-west direction (0 m/h). Therefore, the angle θ would be tan^-1(10,000/0), which is undefined. This means that the change in momentum is in the east-west direction, or in other words, it is perpendicular to the initial momentum.

I hope this helps! Let me know if you have any other questions.