A loaded 150-kg mine cart is rolling at 4 m/s down an inclineat 30 degrees to th

Question

A loaded 150-kg mine cart is rolling at 4 m/s down an inclineat 30 degrees to the horizontal, when a force P is applied to thecable at time t=0. The force P is increased uniformly with timeuntil it reaches 600 N at t=4 seconds, after which the forceremains constant at 600N. Calculate a) the time t1 at which thecart reverses its direction and b) the velocity of the cart at t =8 seconds. You may treat the cart as a particle.
I'm very lost here.. help!!! :( A loaded 150-kg mine cart is rolling at 4 m/s down an inclineat 30 degrees to the horizontal, when a force P is applied to thecable at time t=0. The force P is increased uniformly with timeuntil it reaches 600 N at t=4 seconds, after which the forceremains constant at 600N. Calculate a) the time t1 at which thecart reverses its direction and b) the velocity of the cart at t =8 seconds. You may treat the cart as a particle.
I'm very lost here.. help!!! :(

Explanation / Answer

A) t=4+t [Fx.dt = mVx] 1/2(4)(600)+2(600)t-150(9.81).sin30(4+t)=15(0-[-4]) 464t=1143    t=2.46s    t=4+2.46=6.46s B) [Fx=mVx] 1/2(4)(600)+4(2)(600)-150(9.81)sin30(8)=150(V-[-4]) 150V=714   V=4.76m/s        the same result will be obtained by analyzing the initialfrom T1 to 8s.

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