An 80.0kg skydiver jumps out of a balloon at an altitude of 1 000 m and opens his parachute at an altitude of 200 m. (a) Assuming the total retarding force on the skydiver is constant at 50.0 N with the parachute closed and constant at with the parachute open, find the speed of the skydiver when he lands on the ground. (b) Do you think the skydiver will be injured? Explain. (c) At what height should the parachute be opened so that the final speed of the skydiver when he hits the ground is 5.00 m/s? (d) How realistic is the assumption that the total retarding force is constant? Explain.
(a) The speed of the skydiver when he lands on the ground is 24.5m/s
If the system is isolated, total energy remains constant.
which can be written as:
Ifnon-conservative forces are present, the mechanical energy of the system remains constant.
which can be written as:
Skydiver’s mass: m=80Kg
Altitude at which he jumps: y=1000m
Altitude at which parachute is opened:h=200m
Retarding force when the parachute is closed:f1=50N
Retarding force when the parachute is open:f2=3600N
From step (1), the air drag does work which is equal to a change in mechanical energy; we have
A boy starts at rest and slides down a frictionless slide as in Figure P8.45. The bottom of the track is a height h above the ground. The boy then leaves the track horizontally, striking the ground at a distance d as shown. Using energy methods, determine the initial height H of the boy above the ground in terms of h and d.
In a needle biopsy, a narrow strip of tissue is extracted from a patient using a hollow needle. Rather than being pushed by hand, to ensure a clean cut the needle can be fired into the patient’s body by a spring. Assume that the needle has a mass of 5.60 g, the light spring has a force constant of 375 N/m, and the spring is originally compressed 8.10 cm to project the needle horizontally without friction. After the needle leaves the spring, the tip of the needle moves through 2.40 cm of skin and soft tissue, which exerts on it a resistive force of 7.60 N. Next, the needle cuts 3.50 cm into an organ, which exerts on it a backward force of 9.20 N. Find (a) the maximum speed of the needle and (b) the speed at which the flange on the back end of the needle runs into a stop that is set to limit the penetration to 5.90 cm
A pendulum, comprising a light string of length L and a small sphere, swings in the vertical plane. The string hits a peg located a distance d below the point of suspension (Fig. P8.68). (a) Show that if the sphere is released from a height below that of the peg. It will return to this height after the string strikes the peg. (b) Show that if the pendulum is released from rest at the horizontal position and is to swing in a complete circle centered on the peg, the minimum value of d must be .
A child of mass m starts from rest and slides without friction from a height h along a slide next to a pool (Fig. P8.27). She is launched from a height h/5 into the air over the pool. We wish to find the maximum height she reaches above the water in her projectile motion. (a) Is the child–Earth system isolated or
Non-isolated? Why? (b) Is there a non-conservative force acting within the system? (c) Define the configuration of the system when the child is at the water level as having zero gravitational potential energy. Express the total energy of the system when the child is at the top of the waterslide. (d) Express the total energy of the system when the child is at the launching point. (e) Express the total energy of the system when the child is at the highest point in her projectile motion. (f) From parts (c) and (d), determine her initial speed at the launch point in terms of g and h. (g) From parts (d), (e), and (f), determine her maximum airborne height in terms of h and the launch angle. (h) Would your answers be the same if the waterslide were not frictionless? Explain.
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