A toy train engine (3.8_kg) is moving 0.2_m/s to the right when it collides with

Question

A toy train engine (3.8_kg) is moving 0.2_m/s to the right when it collides with a car (4.1_kg) moving 0.14 m/s in the opposite direction, and they stick together. Find the velocity of the engine-car combination as they move off together. Assume "to the right" is the positive direction. 0.03278_m/s 0.02011_m/s 0.01299_m/s 0.02354_m/s 0.04271_m/s 0.02649_m/s On ice skates, a 65_kg man was skating at a leisurely 2.2_m/s. His 31_kg child skated toward his father from the opposite direction, and they grabbed hold of each other and came to rest. What was the speed of the child prior to the collision 5.838_m/s 8.322_m/s 4.763_m/s 4.123_m/s 4.613_m/s 4.704_m/s The force acting on a particle is F_x = 4x^3 + 6x. Assume SI units are being used. Find the work done by this force from x = 3_m to x = 9_m. 10300.J 6696.J 7518.J 5689_J 8409_J 12620 _J A potential energy function for a two-dimensional problem is of the form U = 2x^3y^2 - 5x^2y^3 + 3x. Find the force that acts at the point (8.0, 9.0). Assume SI units are used. F_x -19210 N 27210 N -2444 N 9399 N -30110 N -16720 N F_y 73600 N 52650 N 59330 N 60650 N 68220 N 56000 N

Explanation / Answer

1)

momentum conservation

3.8*0.2 - 4.1*0.14 = (3.8+4.1)*v

v = 0.02354 m/s

2)

65*2.2 - 31*v = 0

v = 4.6129 m/s

3)

W = integration(3 to 9) F.dx

W = [4x4/4 + 6x2/2](3 to 9) = [x4 + 3x2](3 to 9) = [94 + 3*92 - 34 - 3*32] = 6696 J

4)

U = 2x3y2 - 5x2y3 + 3x

Fx = dU/dx = 6x2y2 - 10xy3 + 3

put x= 8 , y = 9

Fx = 6*8*8*9*9 -10*8*9*9*9 + 3 = -27213 J

Fy = dU/dy = 4x3y - 15x2y2 + 3x

Fy = 4*8*8*8*9 - 15*8*8*9*9 + 3*8 = -59304 J

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.