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In this lesson, we will learn how to calculate the sum of multiple forces with arbitrary directions and how to calculate the acceleration produced by such forces.

Q1:

Find the acceleration of the object of mass 5.0 kg shown in the accompanying diagram.

Q2:

An object with a mass of 5.0 kg accelerates at a rate of 2.0 m/s^{2} in the positive 𝑥 -direction when two forces are applied to it. One of the forces acts in the positive 𝑦 -direction with magnitude 12.0 N. Find the magnitude of the other force.

Q3:

The body shown being acted on by three forces has a mass of 10.0 kg. Find the acceleration of the body.

Q4:

A particle is accelerated when acted on by two forces, as shown in the accompanying diagram. The force has twice the magnitude of force . Find the direction in which the particle’s net acceleration occurs, in terms of the angle below the negative -direction from the position of the particle.

Q5:

A body of mass 2.00 kg is pushed straight upward by a 25.0 N vertical force. What is the magnitude of its acceleration?

Q6:

Two forces of 25 and 45 N act on an object. Their directions differ by 7 0 ∘ . The resulting acceleration has magnitude of 10.0 m/s^{2}. What is the mass of the body?

Q7:

Two muscles in the back of the leg pull upward on the Achilles tendon, as shown in the figure.

Find the magnitude of the total force on the Achilles tendon.