6. Intro to Forces (Dynamics)

A constant force is applied to an object, causing the object to accelerate at 10 m/s². What will the acceleration be if the force is halved?

A single force with x-component Fₓ acts on a 2.0 kg object as it moves along the x-axis. A graph of Fₓ versus t is shown in FIGURE P5.32. Draw an acceleration graph aₓ versus t) for this object.

A single force with x-component Fₓ acts on a 500 g object as it moves along the x-axis. The object's acceleration graph aₓ versus t) is shown in FIGURE P5.30. Draw a graph of Fₓ versus t.

FIGURE EX5.8 shows an acceleration-versus-force graph for three objects pulled by rubber bands. The mass of object B is 0.20 kg. What are the masses of objects A and C? Explain your reasoning.

The 100 kg block in FIGURE EX7.24 takes 6.0 s to reach the floor after being released from rest. What is the mass of the block on the left? The pulley is massless and frictionless.

Two blocks are attached to opposite ends of a massless rope that goes over a massless, frictionless, stationary pulley. One of the blocks, with a mass of 6.0 kg, accelerates downward at (3/4)g. What is the mass of the other block?

A 27-kg chandelier hangs from a ceiling on a vertical 3.4-m-long wire. What horizontal force would be necessary to displace its position 0.15 m to one side?

A 27-kg chandelier hangs from a ceiling on a vertical 3.4-m-long wire. What will be the tension in the wire?

According to a simplified model of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from 0.25 m/s to 0.35 m/s during a period of 0.10 s. What is the magnitude of the force exerted by the heart muscle?

(III) A person jumps from the roof of a house 2.8 m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find the average force exerted on his torso by his legs during deceleration.

An object is hanging by a string from your rearview mirror. While you are accelerating at a constant rate from rest to 28 m/s in 5.0 s, what angle θ does the string make with the vertical? See Fig. 4–46.

A package of mass m is placed onto a horizontal conveyor belt moving at speed v (Fig. 7–32). The coefficient of kinetic friction between package and belt is μ_k. How long does it take the package to stop sliding on the belt? [Hint: Use F = ma.]

(II) A 3.0-kg object has the following two forces acting on it:

${\vec{F}}_1=(16\hat{i}+12\hat{j})\text{N}$

${\vec{F}}_2=(-10\hat{i}+22\hat{j})\text{N}$

If the object is initially at rest, determine its velocity $\overrightarrow{v}$ at t = 4.0s .