In the figure below the two blocks are connected by a string...

In the figure below, the two blocks are connected by a string of negligible mass passing over a frictionless pulley. m1 = 10.0 kg and m2 = 6.70 kg, and the angle of the incline is θ = 39.0°. Assume that the incline is smooth. (Assume the +x direction is down the incline of the plane.) (a) With what acceleration (in m/s²) does the mass m2 move on the incline surface? Indicate the direction with the sign of your answer. m/s² (b) What is the tension in the string in newtons? N (c) For what value of m1 (in kg) will the system be in equilibrium? kg

Transcript

00:01 This problem we have been given that there is an inclined surface and there is no such friction mentioned here.

00:05 So the surface is having no friction and the masses are connected with a light string, m1 and m2.

00:13 So m1 is 10 kg and m2 is 6 .7 kg.

00:17 And the angle of the incline that we have been given is 39 degree.

00:21 And here we need to determine the acceleration that mass m2 has over the inclined surface.

00:28 So here we draw the free body diagram of both these blocks.

00:37 So on mass m1, the force of gravity will be acting.

00:42 So we multiply 10 width acceleration due to gravity, that is 9 .8 meter per second square.

00:50 And on m1, the weight will be 98 neutrons.

00:53 There will be tension here.

00:56 And on m2, there will be weight, which is equal to 6 .7 times 9 .8.

01:03 And that comes off to be approximately 65 .66 newtons.

01:10 So that's the weight of block 2.

01:15 But here we can see that there will be component of this weight along the incline as well as perpendicular to the incline.

01:23 And the perpendicular component will balance the normal reaction that will be applied by the surface.

01:29 So here we take, we apply just simple trigonometry to get the components and the components component along the incline that comes out to be 65 .66 sine 39 degree.

01:42 So when we find out the value of sine 39 degree and multiply that with 65 .66, we're going to get the component as 41 .3 neutrons.

01:57 So this comes out to be 43, so 41 .3 neutrons approximately...

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