Mindblown: a blog about philosophy.
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Two Cars on a Curving Road
A) A small car of mass m and a large car of mass 4m drive along a highway. They approach a curve of radius R. To not slip, both cars need to maintain a net force of F as they travel around the curve. How does the speed of the small car (vs) compare to the speed of the large…
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Normal Force and Centripetal Force Ranking Task
A roller-coaster track has six semicircular “dips” with different radii of curvature. The same roller-coaster cart rides through each dip at a different speed For the different values given for the radius of curvature R and speed v, rank the magnitude of the force of the roller-coaster track on the cart at the bottom of each…
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Math Box: Inverse-Square Relationships
Learning Goal: To understand and use inverse-square relationships. Two quantities have an inverse-square relationship if y is inversely proportional to the square of x. We write the mathematical relationship as y = A/x2. Here, A is a constant. This relationship is sometimes written as . SCALING Inverse-square scaling means, for example: If you double x , you decrease y by a factor of 4. If you…
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Accelerating along a Racetrack
A road race is taking place along the track shown in the figure . All of the cars are moving at constant speeds. The car at point F is traveling along a straight section of the track, whereas all the other cars are moving along curved segments of the track. A) Let be the velocity of the…
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Work and Kinetic Energy
Two blocks of ice, one four times as heavy as the other, are at rest on a frozen lake. A person pushes each block the same distance d. Ignore friction and assume that an equal force is exerted on each block. A) Which of the following statements is true about the kinetic energy of the heavier…
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Projectile Motion and Conservation of Energy Ranking Task
Six baseball throws are shown below. In each case the baseball is thrown at the same initial speed and from the same height H above the ground. Assume that the effects of air resistance are negligible. Rank these throws according to the speed of the baseball the instant before it hits the ground. Rank from largest…
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Kinetic Energy and Momentum Conceptual Question
The two toy cars shown in the figure, with masses as given in the figure, are ready to race. Both cars begin from rest. For each question, state whether the correct answer is car A, car B, or whether the two cars have equal values for the parameter in question. For the next three parts…
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Torques on a Seesaw: A Tutorial
Learning Goal: To make the connection between intuitive understanding of a seesaw and the standard formalism for torque. This problem deals with the concept of torque, the “twist” that an off-center force applies to a body that tends to make it rotate. Use your intuition to try to answer the following question. If your intuition fails,…
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PhET Tutorial: Masses & Springs
Learning Goal: To understand how the motion and energetics of a weight attached to a vertical spring depend on the mass, the spring constant, and initial conditions. For this tutorial, use the PhET simulation Masses & Springs. You can put a weight on the end of a hanging spring, stretch the spring, and watch the resulting motion.…
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