Category: General Physics
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Ladybugs on a Rotating Disk
Two ladybugs sit on a rotating disk, as shown in the figure (the ladybugs are at rest with respect to the surface of the disk and do not slip). Ladybug 1 is halfway between ladybug 2 and the axis of rotation. A) What is the angular speed of ladybug 1? => the same as the angular…
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Balancing Torques Ranking Task
A sign is to be hung from the end of a thin pole, and the pole supported by a single cable. Your design firm brainstorms the six scenarios shown below. In scenarios A, B, and D, the cable is attached halfway between the midpoint and end of the pole. In C, the cable is attached…
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Axis of Rotation and Moment of Inertia Ranking Task
Two identical uniform solid spheres are attached by a solid uniform thin rod, as shown in the figure. The rod lies on a line connecting the centers of mass of the two spheres. The axes A, B, C, and D are in the plane of the page (which also contains the centers of mass of…
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A Sculpture in Equilibrium
The abstract sculpture shown in the figure can be placed on a horizontal surface without tipping over. Different parts of the sculpture may be hollow or solid, or made of different materials, but the artist isn’t revealing any such information. A) Five locations labeled A through E are indicated on the diagram. Which of these,…
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Velocity of a Roller Coaster Ranking Task
Six roller-coaster carts pass over the same semicircular “bump.” The mass M of each cart (including passenger) and the normal force n of the track on the cart at the top of each bump are given in the figures. Rank the speeds of the different carts as each passes over the top of the bump. =>v2/R =…
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Understanding Newton’s Law of Universal Gravitation
Learning Goal: To understand Newton’s law of universal gravitation and be able to apply it in two-object situations and (collinear) three-object situations; to distinguish between the use of G and g. In the late 1600s, Isaac Newton proposed a rule to quantify the attractive force known as gravity between objects that have mass, such as those shown in…
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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…