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A 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 θ as derived in Example 4.3.
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Principles of Physics: A Calculus-Based Text
- A skier with a mass of 63.0 kg starts from rest and skis down an icy slope that has a length of 53.0 m at an angle of 32 degrees with respect to the horizontal. At the bottom of the slope, the path levels out and becomes horizontal, the snow becomes less icy, and the skier begins to slow down, coming to rest in a distance of 122m along the horizontal path. What is the speed of the skier at the bottom of the slope? What is the coefficient of kinetic friction between the skier and the horizontal surface?arrow_forwardFrom a clifftop over the ocean 130 m above sea level, an object was shot straight up into the air with an initial vertical speed of 166.6 ms On its way down it missed the cliff and fell into the ocean. Its height (above sea level) as time passes can be modeled by the quadratic function f, where f(t)=−4.9t^2+166.6t+130 Here t represents the number of seconds since the object’s release, and f(t) represents the object’s height (above sea level) in meters. 1) After this, this object reached its maximum height. 2) This object flew before it landed in the ocean. 3) This object was above sea level 24s after its release. 4) This object was 1526.5 m above sea level twice: once after its release, and again later after its release.arrow_forwardA ski jumper starts from rest 55.0 m above the ground on a frictionless track and flies off the track at an angle of 45.0° above the horizontal and at a height of 15.5 m above the ground. Neglect air resistance. (a) What is her speed when she leaves the track? m/s (b) What is the maximum altitude she attains after leaving the track? m (c) Where does she land relative to the end of the track?arrow_forward
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- Vmax In a laboratory experiment, a sphere of diameter 8.0 mm is released from rest at t = 0 at the surface of honey in a jar, and the sphere's downward speed v when it travels in the honey is found to be given by v = Vmax (1 - e-t/T), where 0.040 m/s and T = 0.50 s. (a) Obtain an expression for a(t). (b) Draw graphs for v(t) and a(t) for the time interval 0 to 2.0 s. (c) Obtain an expression for x(t), choosing the positive x axis as downward, and draw the graph for this func- tion. (d) Use your x(t) graph to determine the time interval needed for the sphere to reach the bottom of the container if the surface of the honey is 0.10 m above the bottom of the jar. ... =arrow_forwardA speedboat increases its speed uniformly from vi = 20.0 m/s to vf = 29.0 m/s in a distance of Δx = 1.60 ✕ 102 m. Find the time it takes the boat to travel the given distance.arrow_forward>V=0 d (m A block of mass m is on an inclined ramp. The ramp makes an angle with respect to the horizontal, as shown. The ramp has friction, with coefficient of kinetic friction and static friction μs. This experiment takes place on earth. The block has an initial speed of v up the ramp. It travels a distance d along the ramp before it stops. There are no numbers in this problem! Answer all questions in terms of the given variables (g, m, µk, µs, 8, v, d) only. Do not use any other variables. a) Draw a free body diagram clearly showing all the forces acting on the block while it is moving up the ramp. b) Calculate the work done by the Normal force as the block travels the distance d. Is it positive, negative, or zero? c) Calculate the work done by the Weight force as the block travels the distance d. Is it positive, negative, or zero? d) Calculate the work done by the Friction force as the block travels the distance d. Is it positive, negative, or zero? e) If the block comes to rest,…arrow_forward
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