Please solve the physics problem below.
A 2.0 kg mass starts from rest at the top of an inclined plane 85 cm long and slides down to the bottom in 0.5 s. What is the net external force acts on the mass along the incline?
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Problem A) The net external force will be found by using Newton's 2nd Law. Net force is equal to mass times acceleration. We know the mass is 2.0 kg, the acceleration must be found using kinematics equations. You know the intial velocity is zero, the distance is 0.85 m and the time is 0.5 s. Use the equation x = v_i * t + (1/2) a t^2
0.85 = (1/2) a (0.5)^2
a = 1.7/0.25 = 6.8 m/s^2
B) find the net force by adding the two vectors. The vectors are perpendicular so you can add them using the pythagorean theorem.
(390)^2 + 180^2 = 429.5 N (net force)
acceleration = net force/mass = 429.5/270 = 1.59 m/s^2
the direction is found using trigonometry
The inverse tangent of (390/180) gives the angle above east that the acceleration vector has, which is 65.2 degrees north of east
At the end of the 0.5 second and the final velocity v of the object is given by v = u+at, where, where u = 0 the initial velocity and a is the acceleration. V = at = 0.5a.
The total distance travelled in 0.5 seconds with an average velocity of (v+v)/2 = 85 cm.
=> (at+0)/2 = 85cm
=> acceleration a => 2*85/0.5^2 = 170/0.25 = 0.68m/sec^2.
Therefore the external force F on the mass of 2kg object = mass*acceleration = mass*acceleration = 2*0.68m/s^2 = 1.36 Newton.
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