Photo AI

Sphere A of mass 400 g is travelling horizontally with a speed of 6 m s⁻¹ when it collides with sphere B of mass 150 g travelling in the opposite direction with a speed of 9 m s⁻¹ - Leaving Cert Physics - Question b - 2017

Question b

Sphere A of mass 400 g is travelling horizontally with a speed of 6 m s⁻¹ when it collides with sphere B of mass 150 g travelling in the opposite direction with a sp... show full transcript

Worked Solution & Example Answer:Sphere A of mass 400 g is travelling horizontally with a speed of 6 m s⁻¹ when it collides with sphere B of mass 150 g travelling in the opposite direction with a speed of 9 m s⁻¹ - Leaving Cert Physics - Question b - 2017

Step 1

Apply the Law of Conservation of Momentum

96%

114 rated

Answer

Using the conservation of momentum, we have the equation:

$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$

where:

$m_1$ = mass of sphere A = 0.4 kg (400 g)
$u_1$ = initial velocity of sphere A = 6 m s⁻¹
$m_2$ = mass of sphere B = 0.15 kg (150 g)
$u_2$ = initial velocity of sphere B = -9 m s⁻¹ (negative due to opposite direction)
$v_1$ = final velocity of sphere A = 0 m s⁻¹ (comes to rest)
$v_2$ = final velocity of sphere B (to be calculated)

Substituting the known values:

$(0.4)(6) + (0.15)(-9) = (0.4)(0) + (0.15)v_2$

Step 2

Solve for the New Velocity of Sphere B

99%

104 rated

Answer

Rearranging the equation gives us:

$2.4 - 1.35 = 0.15 v_2$

Thus,

$1.05 = 0.15 v_2$

Now, divide both sides by 0.15:

$v_2 = \frac{1.05}{0.15} = 7 m s^{-1}$

So, the new velocity of sphere B is 7 m s⁻¹.

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

Sphere A of mass 400 g is travelling horizontally with a speed of 6 m s⁻¹ when it collides with sphere B of mass 150 g travelling in the opposite direction with a speed of 9 m s⁻¹ - Leaving Cert Physics - Question b - 2017

Worked Solution & Example Answer:Sphere A of mass 400 g is travelling horizontally with a speed of 6 m s⁻¹ when it collides with sphere B of mass 150 g travelling in the opposite direction with a speed of 9 m s⁻¹ - Leaving Cert Physics - Question b - 2017

Apply the Law of Conservation of Momentum

Solve for the New Velocity of Sphere B

Join the Leaving Cert students using SimpleStudy...

Other Leaving Cert Physics topics to explore