two strings are tied to a 3.5 kg ball. One string is tied to the top of the ball

Question

two strings are tied to a 3.5 kg ball. One string is tied to the top of the ball and makes an angle of 20 degrees left of the vertical and is attached to the ceiling above the ball. The other string is fixed at the right side of the ball and is attached to the vertical wall that is to the right side of the ball. a) calculate the tension force Fc in the string that is attached to the ceiling. b) calculate the tension force Fw that is attached to the wall.(Note there is no motion for this case) c) show that the x componet of the tension force Fc in terms of its magnitude is given by -0.3420Fc. d)show that the y componet of the tension force Fc in terms of its magnitude is given by 0.9397Fc

Explanation / Answer

Part A)

By the sum of forces, the vertical component of the Fc = the weight of the ball

Fc(cos20) = (3.5)(9.8)

Fc = 36.5 N

Part B)
By the sum of forces, the horizontal component of Fc = The tensin in the horizontal string (Fw)

Fw = Fc(sin 20)

Fw = (36.5)(sin 20) = 12.5 N

Part C)

Fc's horizontal component is to the left, the negative side of x

Fx = -Fcsin20

Fx = -.3420Fc

Part D)

The vertical component is Fccos 20

Fy = .9397Fc

Parts C and D are just the sin and cos of 20 degrees to get the decimal values.

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