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# Three persons wants to push a wheel cart in the direction marked x ?

Three persons wants to push a wheel cart in the direction marked x in Fig. The two person push with horizontal forces F1 and F2 as shown in the figure.

(a) Find the magnitude and direction of the force that third person should exert to stop this cart. You can ignore the effects of friction.

(b) If the third person exerts the force found in part (a), the cart accelerates at 200 m/S2 in the (+) x-direction. What is the weight of the cart?

### 2 Answers

- NCSLv 72 months agoFavorite Answer
The resultant has components

Rx = (45cos70º + 75*cos-20º) N = 86 N

Ry = (45*sin70º + 75*sin-20º) N = 17 N

and so had magnitude

R = √(Rx² + Ry²) = 87 N

and direction Θ = arctan(Ry/Rx) = 11º

and so the EQUILIBRANT has magnitude E = 87 N ◄ (a)

and direction φ = Θ + 180º = 191º ccw from "east" ◄ (a)

or 11º below the -x axis

Note that this force won't stop the cart if it is already moving. Instead, it will keep if from accelerating.

(b) Meaning that the third person has now swung around so that they are helping to push? They must do so from 11º above the -x axis, and so the net force is

F = Fx = (45cos70º + 75*cos20º + 87*cos11º) = 171 N

mass m = F / a = 171N / 200m/s² = 0.86 kg

weight = m*g = 0.86kg * 9.8m/s² = 8.4 kg

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- Anonymous2 months ago
(a) Find the magnitude and direction of the force that third person should exert to stop this cart. You can ignore the effects of friction.

You sum the vector forces and a vector exactly opposite to that sum cancels them. Let's do it:

Horizontal sum

45cos70 + 75cos340 = 85.87 ≈ 86

Vertical sum

45sin70 + 75sin340 = 17

I used 340° instead of -20° to keep signs straight.

86²+17² = 87² at arctan(17/86) = 11°

The opposite or canceling force = 87N at 11+180 = 191° <<<<< (a)

Check:

87cos191 = -86

87sin191 = -17

(b) If the third person exerts the force found in part (a), the cart accelerates at 200 m/s² in the (+) x-direction. What is the weight of the cart?

The x component of F1+F2 = 85.8679 ≈ 86N

F = m*a so Fx/ax = m = 86/200 = 0.43kg

weight = m*g = 0.43*9.8 = 4.2N <<<<< (b)