6. Intro to Forces (Dynamics)

(II) A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of 27m/s. What was the average force of air resistance?

Why is force considered a vector quantity in physics?

An object moves along a curved path and is at position c, where its velocity vector points to the right and the path curves upward. What is the direction of the net force acting on the object at position c?

An object of mass $m$ is suspended from a scale inside an elevator that is at rest. Which of the following correctly ranks the magnitude of the forces acting on the object: the gravitational force ($F_g$), the tension in the string ($T$), and the net force ($F_{\text{net}}$)? Assume upward is positive.

(II) The drag force on large objects such as cars, planes, and sky divers moving through air is more nearly F_D = -cv². For this quadratic dependence on v, determine a formula for the terminal velocity v_T, of a vertically falling object..

Two rock climbers, Paul and Jeanne, use safety ropes of similar length. Jeanne's rope is more elastic, called a dynamic rope by climbers. Paul has a static rope, not recommended for safety reasons. Jeanne (Fig. 4–72) falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m. Estimate how large a force (assume constant) she will feel from the rope. (Express the result in multiples of her weight.)

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When jumping straight up from a crouched position, an average person can reach a maximum height of about $60$ cm. During the jump, the person's body from the knees up typically rises a distance of around $50$ cm. To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump. With what initial speed does the person leave the ground to reach a height of $60$ cm?

An 800-kg car is traveling along a horizontal road directly towards a cliff. The driver notices and brakes, resulting in a 5,000-N net force slowing the car down. If the car's initial speed was 20 m/s and the car stops just before going over the cliff, how far away was the car from the cliff when the driver hit the brakes?

The forces in FIGURE EX6.9 act on a 2.0 kg object. What are the values of a_x and a_y, the x- and y-components of the object's acceleration?

(II) A child on a sled reaches the bottom of a hill with a velocity of 10.0 m/s and travels 25.0 m along a horizontal straightaway to a stop. If the child and sled together have a mass of 60.0 kg, what is the average retarding force on the sled on the horizontal straightaway?

You are driving home in your 860-kg car at 15 m/s. At a point 45 m from the beginning of an intersection, you see a green traffic light change to yellow, which you expect will last 4.0 s, and the distance to the far side of the intersection is 65 m (Fig. 4–71). If you choose to accelerate, your car's engine will furnish a forward force of 1200 N. Will you make it completely through the intersection before the light turns red?

(III) An object moving vertically has ${\overrightarrow{v}}_{}={\overrightarrow{v}}_0$ at t = 0. Determine a formula for its velocity as a function of time assuming a resistive force F = -bv as well as gravity for two cases: ${\overrightarrow{v}}_0$ is upward.

Your forehead can withstand a force of about 6.0 kN before fracturing, while your cheekbone can withstand only about 1.3 kN. Suppose a 140 g baseball traveling at 30 m/s strikes your head and stops in 1.5 ms. What is the magnitude of the force that stops the baseball?