What were the original speeds of the cars?

  • Thread starter Libohove90
  • Start date
  • #1
41
0

Homework Statement


One car has twice the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 7.0 m/s, then they have the same kinetic energy. What were the original speeds of the two cars?


Homework Equations


Initial, K1 = 1/2 K2

Final, K1 = K2

m1 = 2m2

K=1/2 mv^2

v1 = 1/2 v2

The Attempt at a Solution



Since K1 = K2 after the cars' velocities were increased by 7.0 m/s, I can write:

1/2 m1 (v1+7.0 m/s)^2 = 1/2 m2 (v2+7.0 m/s)^2

Since I know m1 = 2m2, I plug it in and I get

1/2 * 2m2 (v1+7.0m/s)^2 = 1/2 m2 (v2+7.0 m/s)^2 and then simplified:

m2 (v1 + 7.0 m/s)^2 = 1/2 m2 (v2 + 7.0 m/s)^2, and then simplified again:

2(v1 + 7.0 m/s)^2 = (v2 + 7.0 m/s)^2

I know that by the initial conditions given, 2v1 = v2 and I plug it in and get:

2(v1 + 7.0 m/s)^2 = (2v1 + 7.0 m/s)^2 and then I get rid of the squares and get:

Sqrt 2 (v1 + 7.0 m/s) = (2v1 + 7.0 m/s)

I start having trouble from here on. According to my teacher's notes, the step after the previous equation above given is v1 = 7.0 / sqrt 2, giving the answer of v1 = 4.9 seconds. Where did that come from?
 

Answers and Replies

  • #2
cepheid
Staff Emeritus
Science Advisor
Gold Member
5,192
36
Distribute the sqrt(2) in the left hand side over both terms. Then collect like terms on each side of the equation (so that everything that multiplies v1 is on one side, and everything that multiplies 7 m/s is on the other side). Then, solve for v1. On the other side of the equation, you'll have a fractional expression multiplying 7 m/s. Rationalize the denominator of this expression and simplify.
 

Related Threads on What were the original speeds of the cars?

  • Last Post
Replies
3
Views
2K
Replies
12
Views
10K
Replies
1
Views
2K
Replies
5
Views
2K
Replies
22
Views
3K
Replies
1
Views
6K
Replies
3
Views
1K
Replies
6
Views
36K
  • Last Post
Replies
5
Views
21K
Top