A 2000 kg truck traveling north at 38 km/hr turns east and accelerates to 55 km/hr. What is the change in the truck's kinetic energy? What is the magnitude of the change in the linear momentum of the truck? What is the direction of the change in linear momentum of the truck? (give an angle, measured from east)
Convert the speeds to m/s and use (1/2) MV^2 for the kinetic energy. Momentum is MV, but is a vector so you must account for direction changes when calculating momentum change.
You need to learn the basic concepts and try applying them yourself. We will be happy to check your work.
I'm trying to do a similar problem for: 'What is the magnitude of the change in the linear momentum of the truck?'
Can you calculate it by just subtracting the initial momentum from the final momentum? ie
Change in momentum =
M x V(final) - M x V(initial)
Using this approach I can't get the right answer but I don't know any other way to do it.
by 110,000-76000 we get the answer 34000
To calculate the change in linear momentum of the truck, you are correct in using the formula:
Change in momentum = M x V(final) - M x V(initial)
Where:
M represents the mass of the truck
V(final) represents the final velocity of the truck
V(initial) represents the initial velocity of the truck
However, keep in mind that momentum is a vector and has both magnitude and direction. So when calculating the change in momentum, you need to consider both the magnitude and direction changes.
For the given problem, let's first convert the speeds from km/hr to m/s:
Initial velocity: 38 km/hr = (38 * 1000) m/3600 s = 10.55 m/s (approximately)
Final velocity: 55 km/hr = (55 * 1000) m/3600 s = 15.28 m/s (approximately)
Now, let's plug these values into the formula:
Change in momentum = M x V(final) - M x V(initial)
= M x (V(final) - V(initial))
Since the mass of the truck is given as 2000 kg, the formula becomes:
Change in momentum = 2000 kg x (15.28 m/s - 10.55 m/s)
Calculating this, we get:
Change in momentum = 2000 kg x (4.73 m/s)
= 9460 kg * m/s
So the magnitude of the change in linear momentum of the truck is 9460 kg * m/s.
Now, to determine the direction of the change in linear momentum, we need to consider the angle between the initial and final velocities. The truck turns from traveling north to traveling east, which is a change in direction of 90 degrees counterclockwise.
Hence, the direction of the change in linear momentum is 90 degrees counterclockwise from east.