please show work and answer. 1) A 3 kg mass hangs at the end of a rpe which isat

Question

please show work and answer. 1) A 3 kg mass hangs at the end of a rpe which isattached to a support on a cart. When the cart accelerates, thecord makes an angle of 4 degree with the vertical as shown. Findthe acceleration of the cart.

a) Draw a free body diagram for the hanging mass and draw inall the forces.

b) Determine the tension in the rope

c) Find the horizontal component of the tension.

d) The cart and the mass accelerate togather, so find theacceleration of the mass

              (Hint: use Newton's Second Law in the X direction.) a) Draw a free body diagram for the hanging mass and draw inall the forces. b) Determine the tension in the rope c) Find the horizontal component of the tension. d) The cart and the mass accelerate togather, so find theacceleration of the mass               (Hint: use Newton's Second Law in the X direction.)

Explanation / Answer

A) In the free body diagram the only forces shown will be gravityand the tension of the rope on the ball. on the cart therewill be a pushing force that is causing it to constantlyaccelerate. We know that the y component of tension in the rope will be equalto mg of the hanging mass. 3kg(9.8m/s/s)=29.4N Knowing this and the angle of the rope we can find the tension inthe rope. Cos(4)=29.4N/T B)T=29.47N C)Horizontal component is equal to 2.0558N Found by pythagoreanstheorem. D) F=ma 2.0558N=3kga acceleration=0.6853m/s/s

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