Two children pull a sled of mass 15 kg along a frictionless surface as shown in

Question

Two children pull a sled of mass 15 kg along a frictionless surface as shown in Figure P4.43. Find the magnitude and direction of the sled's acceleration. How long does it take the sled to reach a speed of 10 m/s? Figure P4.43

Explanation / Answer

i have done this problem with 13kg mass and 12 m/s in second part. please replace the numbers accordingly... First, you need to find the forces in each direction of the two people pulling the sled. Lets say Larry is pulling at 15N and Moe is pulling at 10N. Larry pulls the sled in the x-direction: cos(30) = Lx/15N --> 15 * cos(30) = Lx; where Lx stands for Larry in the x direction. and in the y direction: sin(30) = Ly/15N --> 15 * sin(30) = Ly; Ly is Larry in the y-direction. ** you should get values of Lx = 13N, Ly = 7.5N, but these are slightly rounded ** Now for Moe in the x-direction: cos(50) = Mx/10N --> 10 * cos(50) = Mx; and in the y-direction: sin(50) = My/10N --> 10 * sin(50) = My; ** you should get values of Mx = 6.43N, My = 7.66N ** As you see, the y components should just about cancel out, which leaves you with a nice simple problem. All you need to do is add the forces in the x direction: Lx + Mx = F = ma; where m=13kg. Solve for acceleration, a. ** your value should be about 1.5 m/s^2 ** Now use the velocity equation v = v0 + at; v0 is initial velocity, v is final velocity. v0 = zero here, a = 1.5, v = 12. Solve for t. Units work out fine, no worries. Hope this helped.

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