Two cars have a collision at an icy intersection, m_1 is headed North before it

Question

Two cars have a collision at an icy intersection, m_1 is headed North before it goes into the collision with speed 18 m/s. m_2 was heading East at 14 m/s. m_1 is 1000 kg. It is known that m_1 is at rest after the collision process and m_2 slid off at 45 degree North of East. (a) What is m_2? (1286 kg) (b) What is the speed of m_2 after the collision? (19.8 m/s) (c) Was this collision perfectly inelastic, perfectly elastic, or something else? (d) Draw an energy bar graph to tell the story of this process. A 3 kg mass is attached to the end of a rigid massless rod of length 0.75 m. The other end of the rod rotates about a stationary frictionless pivot. (a) What speed must the mass have at the bottom of a swing so that when the mass goes over the top the rod pushes out on the mass by 3N? (5.98 m/s) (b) What speed must the mass have at the bottom of a swing so that when the mass goes over the top the rod pulls in on the mass by 3N? (c) What speed must the mass have at the bottom of a swing so that when the mass goes over the top the rod neither pushes out nor pulls in on the mass? (d) In each of the cases above, what was the work done by the rod?

Explanation / Answer

1) By momentum conservation of momentum in North direction,

m1u1 = m2v2 cos 45 degree

now in East direction,

m2u2 = m2v2 sin 45 degree

from both equation,

m2u2 = m1u1

m2= 1000*18/14 = 1286 kg

b) v2 = u2/sin 45 degree

= 14 / sin 45 degree = 19.8 m/s

d) initial energy= 0.5 m2u2^2 +0.5m1u1^2

   = 0.5*1286*14^2 + 0.5*1000*18^2

   = 288028 J

Final energy= 0.5 *1286*19.8^2

   = 252082 J

c) inelastic because energy decreases but not perfectly inelastic because objects don't stick together

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