An object with mass M1 of 2.85 kg is held in place on an inclined plane that mak
ID: 1658609 • Letter: A
Question
An object with mass M1 of 2.85 kg is held in place on an inclined plane that makes an angle of 40.0° with the horizontal (see figure below). The coefficient of static friction between the plane and the object is 0.570. A second object that has a mass M2 of 4.75 kg is connected to the first object with a massless string over a massless, frictionless pulley.
1) Calculate the initial acceleration of the system once the objects are released. (Express your answer to three significant figures.)
2) Calculate the tension in the string once the objects are released. (Express your answer to three significant figures.)
Explanation / Answer
M1 has a downslope component of weight
F1 = mgsin = 2.85kg * 9.8m/s² * sin40º = 18 N
M2 weighs F2 = mg = 4.75kg * 9.8m/s² = 46.6 N
The friction force points downslope with magnitude
Ff = µmgcos = 0.570 * 2.85kg * 9.8m/s² * cos40º = 12.2 N
Net motive force Fnet = 46.6N - 12.2N - 18N = 16.4 N
acceleration a = Fnet / mtotal = 16.4N / (2.85+4.75)
= 16.4N / 7.60kg = 2.16 m/s²
tension T = m(g - a) = 4.75kg * (9.8 - 2.16)m/s² = 36.3 N