Phys 270 Newton’s Laws

Two Blocks and Tension

Solving the Equations

Recipe for Multiple Objects Consider each object independently Draw the force diagram for each object Apply Newton’s Second Law to each object Solve the equations obtained from step 3 You must be careful to write down all the forces, even those that may not be obvious. Number of unknowns must equal to the number of equations.

Example: Mass m1 sits on a horizontal frictionless table, and mass m2 hangs over a pulley. If the system is let go, compute the acceleration and the tension in the string. M1 M2

Solution M1 M2

Two blocks connected by a string Two blocks, with masses m1=1kg and m2 =2kg, are connected by a string on a frictionless horizontal surface. A force F =3N is applied to m2 at an angle θ=60o above the horizontal. Find the acceleration of the two blocks and the tension in the string, in terms of the masses, the angle and the force F.

Decomposing the force

Force Diagram Horizontally:

Solution

Normal Forces Vertically:

Using Newton’s Laws What is the acceleration of a mass m sliding off an incline making angle θ with the horizontal. Fg Fn m frictionless surface

Solution Fg Fn Consider directions parallel and perpendicular to the planes.

If you are confused, remember this… Fg Fn = Fn and Fg combines to give a net force of magnitude mgsinθ.

An inclined plane problem Two blocks with mass m and 2m are connected by a string of negligible mass over a pulley as shown. The plane is a frictionless surface inclined at an angle θ from the horizontal. After the block 2m is released, find the acceleration of the system and the tension in the string, in terms of m and θ. m 2m θ

Solution

What does the scale read? The elevator is accelerating upward at a = 4m/s2. The mass of the fish is 2kg, what is the weight of the fish according the scale on the elevator?

How about now? The elevator is accelerating downward at a = 4m/s2. The mass of the fish is 2kg.