Kinetic energy & speed in a pursuit - Ek possible to find?

[Tyrannosaurus_]

Homework Statement

A cat is chasing a mouse in a straight line. The cat's mass, m_c, = 5.0kg. The mouse's mass, m_m, is 0.035kg.

Problem 1. If the kinetic energy of the cat is 100 times the kinetic energy of the mouse can the cat catch the mouse?

Problem 2. If the cat and the mouse have the same speed, what is the kinetic energy of the cat?

Homework Equations

Conservation of energy. Kinetic energy = (1/2)mv²

The Attempt at a Solution

Solution for Problem 1.

E_kc = (100)E_km
(1/2)m_cv_c² = (100)(1/2)m_mv_m²
m_cv_c² = (100)m_mv_m²
v_c² = [(100)m_mv_m²] / m_c
v_c² = [ (100)(0.035kg)v_m² ] / 5.0kg
v_c² = (7/10) v_m²
v_c = (7/10)^(1/2) v_m
v_c ≅ 0.83 v_m

Therefore, the cat cannot catch the mouse. The cat's speed is 83% of the mouse's speed

{Is the result correct? Is my therefore statement correct? Is this the proper interpretation of the result?}

Solution for Problem 2. - If the speed of the cat is the speed of the mouse what is the cat's kinetic energy?

v_c = v_m
[(2E_kc)/m_c]^(1/2) = [(2E_km)/m_m]^(1/2)
E_kc/m_c = E_km/m_m
E_kc = m_c E_km / m_m
E_kc = {m_c (1/2m_mv_m²)} / m_m
E_kc = (1/2) m_cv_m²
E_kc = 2.5kg v_m²
E_kc = How can I find this value? All of the known problem info. is stated.

The correct answer according the answer page of the text is "140 times."

What approach should I take to solving this problem.

Many thanks!

 

[rpthomps]

For the second problem why don't you express the velocities as the same variable and then solve for Ec

 

[Tyrannosaurus_]

For the second problem why don't you express the velocities as the same variable and then solve for Ec

Is your suggestion different from how I started the solution? v_c = v_m I do not understand your suggestion.

 

[rpthomps]

v_c = v_m
[(2E_kc)/m_c]^(1/2) = [(2E_km)/m_m]^(1/2)
E_kc/m_c = E_km/m_m

You have the answer here! Just plug in the values for m and solve for E cat!

 

[Tyrannosaurus_]

E_kc is 2.5 * "speed of mouse" squared. What do i use for the speed of the mouse?

 

[rpthomps]

v_c = v_m
[(2E_kc)/m_c]^(1/2) = [(2E_km)/m_m]^(1/2)
E_kc/m_c = E_km/m_m
E_kc = m_c E_km / m_m

Look at the last line of the expression I just quoted, that you generated. Do you see velocity there?

 

[Tyrannosaurus_]

The kinetic energy of the mouse, E_km, is unknown! The velocity of the mouse is unknown! Only the mass of each body is known!

Clearly you're far too brilliant for me! What is the value of E_kc?

 

[rpthomps]

Ek_cat=(m_cat/m_mouse)xEk_mouse
Ek_cat=(5/0.035)xEk_mouse
Ek_cat = 140xEk_mouse

 

[Tyrannosaurus_]

Ek_cat=(m_cat/m_mouse)xEk_mouse
Ek_cat=(5/0.035)xEk_mouse
Ek_cat = 140xEk_mouse

So, like I said, "how do I find the value?"

Thanks for your effort. In the future, save both of our time by confirming my solution. Ek cat is unknown! It might be expressed in terms of Ek mouse, but Ek cat's value is, like I asked, not possible to be found.

 

[rpthomps]

Wow. I wasn't expecting that response. I wasn't trying to save you time. I was trying to help you get to the answer yourself, which is infinitely more valuable than having me just solve the question myself or just confirming your answer. The solution that you yourself indicated is not in itself a value but rather a multiplication of another one. You said the answer was 140 times! 140 times what? Well, 140 times the kinetic energy of the mouse. It is impossible to find the value of the cat's KE given the information of the question.

In the future, don't lambast people who are trying to help you.