University Physics Volume 1
18th Edition
ISBN: 9781938168277
Author: William Moebs, Samuel J. Ling, Jeff Sanny
Publisher: OpenStax - Rice University
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- A student working on a school project modeled a trampoline as a spring obeying Hookes law and measured the spring constant of a certain trampoline as 4617 N/m. If a child of mass 27.0 kg compresses the trampoline vertically by a maximum of 0.25 m, while bouncing up and down, what is the childs acceleration at the moment of maximum compression?arrow_forwardWhen an 80.0-kg man stands on a pogo stick, the spring is compressed 0.120 m. (a) What is the force constant of the spring? (b) Will the spring be compressed more when he hops down the road?arrow_forwardA student is asked to measure the acceleration of a glider on a frictionless, inclined plane, using an air track, a stopwatch, and a meterstick. The top of the track is measured to be 1.774 cm higher than the bottom of the track, and the length of the track is d = 127.1 cm. The cart is released from rest at the top of the incline, taken as x = 0, and its position x along the incline is measured as a function of time. For x values of 10.0 cm, 20.0 cm, 35.0 cm, 50.0 cm, 75.0 cm, and 100 cm, the measured times at which these positions are reached (averaged over five runs) are 1.02 s, 1.53 s, 2.01 s, 2.64 s, 3.30 s, and 3.75 s, respectively. (a) Construct a graph of x versus t2, with a best-fit straight line to describe the data. (b) Determine the acceleration of the cart from the slope of this graph. (c) Explain how your answer to part (b) compares with the theoretical value you calculate using a = g sin as derived in Example 4.3.arrow_forward
- A block of mass 0.250 kg is placed on top of a light, vertical spring of force constant 5 000 N/m and pushed downward so that the spring is compressed by 0.100 m. After the block is released from rest, it travels upward and then leaves the spring. To what maximum height above the point of release does it rise?arrow_forwardCheck Your Understanding Suppose the mass in Equation 8.6 is doubled while keeping the all other conditions the same. Would the maximum expansion of the spring increase, decrease, or remain the same? Would the speed at point B be larger, smaller, or the same compared to the original mass?arrow_forwardIn an iconic movie scene, Forrest Gump (https://openstaxcollege.org/l/21ForrGumpvid) runs around the country. If he is running at a constant speed of 3 m/s, would it take him more or less energy to run uphill or downhill and why?arrow_forward
- When a 3.0-kg block is pushed against a massless spring of force constant constant 4.5103N/m , the spring is compressed 8.0 cm. The block is released, and it slides 2.0 m (from the point at which it is released) across a horizontal surface before friction stops it. What is the coefficient of kinetic friction between the block and the surface?arrow_forwardConsider a block of mass 0.200 kg attached to a spring of spring constant 100 N/m. The block is placed on a frictionless table, and the other end of the spring is attached to the wall so that the spring is level with the table. The block is then pushed in so that the spring is compressed by 10.0 cm. Find the speed of the block as it crosses (a) the point when the spring is not stretched, (b) 5.00 cm to the left of point in (a), and (c) 5.00 cm to the right of point in (a).arrow_forwardWhen a 4.25-kg object is placed on top of a vertical spring, the spring compresses a distance of 2.62 cm. What is the force constant of the spring?arrow_forward
- A bungee cord is essentially a very long rubber bandthat can stretch up to four times its unstretched length.However, its spring constant varies over its stretch [seeMenz, P.G. “The Physics of Bungee Jumping.” The PhysicsTeacher (November 1993) 31: 483-487]. Take the length ofthe cord to be along the x-direction and define the stretchx as the length of the cord l minus its un-stretched lengthl0; that is, x = l − l0 (see below). Suppose a particularbungee cord has a spring constant, for 0 ≤ x ≤ 4.88 m , ofk1 = 204 N/m and for 4.88 m ≤ x , of k2 = 111 N/m.(Recall that the spring constant is the slope of the forceF(x) versus its stretch x.) (a) What is the tension in thecord when the stretch is 16.7 m (the maximum desired for agiven jump)? (b) How much work must be done against theelastic force of the bungee cord to stretch it 16.7 m?arrow_forwardThe tension in a ligament in the human knee is approximately proportional to the extension of the ligament, if the extension is not too large. If a particular ligament has an effective spring constant of 152 N/mm as it is stretched, what is the tension in this ligament when it is stretched by 0.800 cm?arrow_forwardWhen a 3 kg mass is hung on a vertical spring, it extends the spring by 2.00 m. What is the spring constant of the spring in N/m? (Assume g = 10m/s2).arrow_forward
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