# Physics

Hi, I have two homework problems I am having issues with.

1. Two carts of equal mass, m = 0.250 kg, are placed on a frictionless track that has a light spring of force constant k = 53.0 N/m attached to one end of it. The red cart is given an initial velocity of V = 2.55 m/s to the right, and the blue cart is initially at rest.

(a) If the carts collide elastically, find the velocity of the carts just after collision.
(b) If the carts collide, find the maximum compression in the spring.

I know to use conservation of momentum for part a, but I get stuck when I get to this point:

2.55 = v1 + v2 (I cancelled the masses and plugged in the initial velocity for the red cart). How do I determine the value for each velocity?

2.A race car starts from rest on a circular track of radius 370 m. The car's speed increases at the constant rate of 0.730 m/s2. At the point where the magnitudes of the centripetal and tangential accelerations are equal, find the following.

(a)the speed of the race car
(b) the distance traveled
(c) the elapsed time

I set the equations for centripetal and tangential acceleration equal to one another. I converted the linear quantities to angular so all would be equal. To clarify, I used an quation for tangential acceleration (a= rw , where r is radius and w is ang. speed) that is time independent. I found velocity, did a bunch of convertions between tangential and angular, found speed, found the other values, and got the wrong answer. :(

On the first, you also have the conservation of energy: energy is conserved. So use that for a second equation.

2. v^2/r = angular acceleration
.732m/s^2= tangential acceleration

set them equal. solve for v, then for the distance traveled

vfinal=givenabove=acceleration*time
solve for time
distance= vavg*time= vfinal/2 * time

1. 👍 0
2. 👎 0
3. 👁 115
1. a. 20 m/s
b. 30 m

1. 👍 0
2. 👎 0

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