Question

In: Physics

A mass is moving at 10 m/s in the +x direction and it collides in a...

A mass is moving at 10 m/s in the +x direction and it collides in a perfectly elastic collision with a mass of 2 kg moving in the -x direction. The collision takes places in 0.21 seconds and after the collision the mass that was moving in the +x direction is moving in the -x direction at 9 m/s and the mass that was moving in the -x direction is moving in the +x direction at 13 m/s. What is the magnitude of the average force, in Newtons, on the first mass which was originally moving in the +x direction before the collision?

Solutions

Expert Solution


ELASTIC COLLISION


m1 = ?                                  m2 = 2 kg


speeds before collision


v1i = 10 m/s                                 v2i = 0
?

speeds after collision


v1f = -9 m/s                                        v2f = 13 m/s


initial momentum before collision


Pi = m1*v1i + m2*v2i

after collision final momentum

Pf = m1*v1f + m2*v2f

from momentum conservation


total momentum is conserved

Pf = Pi


m1*v1i + m2*v2i = m1*v1f + m2*v2f .....(1)


from energy conservation


total kinetic energy before collision = total kinetic energy after collision


KEi = 0.5*m1*v1i^2 + 0.5*m2*v2i^2

KEf =   0.5*m1*v1f^2 + 0.5*m2*v2f^2


KEi = KEf


0.5*m1*v1i^2 + 0.5*m2*v2i^2 = 0.5*m1*v1f^2 + 0.5*m2*v2f^2 .....(2)

solving 1&2


we get


v1f = ((m1-m2)*v1i + (2*m2*v2i))/(m1+m2)


-9 = ((m1-2)*10 + 2*2*v2i)/(m1+2)............(3)


v2f = ((m2-m1)*v2i + (2*m1*v1i))/(m1+m2)


13 = ((2 - m1)*v2i + 2*m1*10)/(m1+2)..................(4)


solving above equations 3 and 4

m1 = 2.63 kg


v2i = -12 m/s


F1 = m1*(V1f - v1i)/t

F1 = 2.63*(-9-10)/0.21


F1 = 238 N


Related Solutions

A mass is moving at 10 m/s in the +x direction and it collides in a...
A mass is moving at 10 m/s in the +x direction and it collides in a perfectly elastic collision with a mass of 4 kg moving in the -x direction. The collision takes places in 0.22 seconds and after the collision the mass that was moving in the +x direction is moving in the -x direction at 8 m/s and the mass that was moving in the -x direction is moving in the +x direction at 14 m/s. What is...
Mass 1 is moving at 6 m/s in the +x direction and it collides in a...
Mass 1 is moving at 6 m/s in the +x direction and it collides in a perfectly elastically with mass 2 of 2 kg moving at 15 in the -x direction. They collide for 0.2 seconds, and the average force on mass 1 is 149 N in the -x direction. What is the mass of mass 1 in kg?
4) Mass 1 is initially moving at 3 m/s in the +x direction and it collides...
4) Mass 1 is initially moving at 3 m/s in the +x direction and it collides perfectly elastically with mass 2 moving at 10 m/s in the -x direction. After the collision, mass 1 is moving at 5 m/s in the +x direction. What is the final velocity of mass 2 in m/s? If in the negative x direction, include a negative sign. (Note: the masses are not needed to answer this question.)
An object of mass m is moving in +x direction at u velocity and collides elastically...
An object of mass m is moving in +x direction at u velocity and collides elastically with a stationery object in the x direction having a mass M. after the collision the object with mass m travels in +y direction and the object with mass M travels in a direction with an angle theeta to the x axes. find the value of theeta?
A 15.0 kg object moving in the +x direction at 5.5 m/s collides head-on with a...
A 15.0 kg object moving in the +x direction at 5.5 m/s collides head-on with a 11.5 kg object moving in the −x direction at 4.0 m/s . Part A- Find the final velocity of each mass if the objects stick together. Express your answers using two significant figures. Enter your answers numerically separated by a comma. Part B- Find the final velocity of each mass if the collision is elastic. Express your answers using two significant figures. Enter your...
8) 3 kg mass moving with 10 m/s in the x-direction hits a 5 kg mass...
8) 3 kg mass moving with 10 m/s in the x-direction hits a 5 kg mass at rest. After the collision 3 kg is deflected by 30 degree while the 5 kg is deflected by 45 degrees. a) Draw a diagram for the initial and final motion including the directions of the velocities b) Find the final velocities of each mass c) Determine if the collision is elastic or not. d) Qualitatively, show the direction of the impulse (or the...
A 2 kg mass moving to the right at 10 m/s collides elastically with a 2.4...
A 2 kg mass moving to the right at 10 m/s collides elastically with a 2.4 kg mass moving to the left at 8.33 m/s. After the collision the 2 kg mass moved at a speed vgf in a direction of 30 degrees and the 2.4 kg object at a speed vbf in a direction 30 degrees south of west. (5 pts) a. What is the difference between an elastic and an inelastic collision? (15 pts) b. Find the velocity...
A railroad car of mass 3.10 ✕ 10^4 kg moving at 3.50 m/s collides and couples...
A railroad car of mass 3.10 ✕ 10^4 kg moving at 3.50 m/s collides and couples with two coupled railroad cars, each of the same mass as the single car and moving in the same direction at 1.20 m/s. (a) What is the speed of the three coupled cars after the collision? __m/s (b) How much kinetic energy is lost in the collision? __J
A ball of mass 0.576 kg moving east (+x+x direction) with a speed of 3.78 m/sm/s...
A ball of mass 0.576 kg moving east (+x+x direction) with a speed of 3.78 m/sm/s collides head-on with a 0.288 kg ball at rest. Assume that the collision is perfectly elastic What is be the speed of the 0.576-kg ball after the collision? What is be the direction of the velocity of the 0.576-kg ball after the collision? What is the speed of the 0.288-kg ball after the collision? What is the direction of the velocity of 0.288-kg ball...
A railroad car of mass 18800 kg moving at 3.85 m/s collides and couples with two...
A railroad car of mass 18800 kg moving at 3.85 m/s collides and couples with two coupled railroad cars, each of the same mass as the single car and moving in the same direction at 2.31 m/s. How much kinetic energy is lost in the collision? Answer in units of J.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT