help When attaching a mass of 50g on a force table at 90 degree and un unknown m

Question

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When attaching a mass of 50g on a force table at 90 degree and un unknown mass at 0 degree, you get an equilibrant mass to have 230 g positioned at 225 degree How big is the unknown mass in kg? Draw a picture to show this situation in terms of vectors. A car is sliding down an incline plane with an angle of inclination of 10 degree, the velocity of the cart is recorded at 10 cm, 20 cm, 30 cm and 40 cm down the track to be respectively: 0.55 m/s, 0.86 m/s, 1.07 m/s and 1.20 m/s. Make a free body diagram of the cart and find the acceleration of the cart when neglecting friction.

Explanation / Answer

1)the forces in x and y directions are

m1g x cos(A1) + m2g x cos(A2) = m3g x cos(A3) -------------(1)

and m1g x sin(A1) + m2g x sin(A2) = m3g x sin(A3) ----------(2)

where m1 = 50 g,A1 = 90o,m2 is unknown mass,A2 = 0o,m3 = 230 g,A3 = 225o and g = 9.8 m/s^2

solving equations (1) and (2) for m2

2)the acceleration of the cart is

a = (v^2 - u^2/2S)

where v = 0,u = 0.55 m/s and S = 10 cm = 10 x 10^-2 m

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