Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Oblique Impact of Smooth Elastic Spheres

Worksheet • 3 Questions

Q1:

A body 𝐴 of mass 5 kg, moving with a velocity ⃑ 𝑣 = 2 ⃑ 𝑖 + ⃑ 𝑗 / 1 m s , collided with another body 𝐡 , of mass 10 kg that was moving with a velocity ⃑ 𝑣 = βˆ’ 6 ⃑ 𝑖 βˆ’ 3 ⃑ 𝑗 / 2 m s . After the impact, if the velocity of body 𝐴 became ⃑ 𝑣 = βˆ’ 6 ⃑ 𝑖 βˆ’ 3 ⃑ 𝑗 / β€² 1 m s , determine the speed of body 𝐡 .

  • A √ 5 m/s
  • B 2 √ 5 m/s
  • C βˆ’ 2 ⃑ 𝑖 + ⃑ 𝑗 m/s
  • D βˆ’ 2 ⃑ 𝑖 βˆ’ ⃑ 𝑗 m/s

Q2:

Two spheres, 𝐴 and 𝐡 , have equal radii and are moving across a smooth horizontal surface. Sphere 𝐴 has a mass of 4 kg and is moving with velocity ( 3 ) j m/s. Sphere 𝐡 has a mass of 5 kg and moves with a velocity ( βˆ’ 3 ) i j m/s. The spheres collide when the line of their centres is parallel to j . Sphere 𝐴 has a velocity of 𝑣 1 immediately after the impact and sphere 𝐡 has a velocity of 𝑣 2 immediately after the impact. Find the velocities 𝑣 1 and 𝑣 2 in vector form, taking the coefficient of restitution between the spheres to be 1 2 .

  • A 𝑣 = ( βˆ’ 2 ) / 1 j m s , 𝑣 = ( + ) / 2 i j m s
  • B 𝑣 = ( 2 ) / 1 j m s , 𝑣 = ( + ) / 2 i j m s
  • C 𝑣 = ( βˆ’ 2 ) / 1 i j m s , 𝑣 = ( βˆ’ 2 ) / 2 j m s
  • D 𝑣 = ( βˆ’ 2 ) / 1 j m s , 𝑣 = ( + 2 ) / 2 i j m s
  • E 𝑣 = ( + 2 ) / 1 i j m s , 𝑣 = ( ) / 2 j m s

Q3:

Two smooth spheres of equal radii and masses π‘š kg and 5 π‘š kg collided while moving on a smooth horizontal surface. Before the collision, the sphere of mass π‘š kg was moving at ( 9 + 5 ) i j m/s and the sphere of mass 5 π‘š kg was moving at ( βˆ’ 5 ) i j m/s. After the collision, the sphere of mass π‘š kg was moving at ( 5 + 7 ) i j m/s. Find the speed of the sphere of mass 5 π‘š kg after the collision.

  • A 9 √ 1 0 5 m/s
  • B 6 √ 5 5 m/s
  • C 9 √ 1 0 m/s
  • D 5 √ 5 8 m/s
  • E 3 √ 7 4 5 m/s
Preview