Two children are playing on stools at a restaurant counter. Their feet do not reach the footrests, and the tops of the stools are free to rotate without friction on pedestals fixed to the floor. One of the children catches a tossed ball, in a process described by the equation
(a) Solve the equation for the unknown
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- Rank the following quantities of energy from largest to the smallest. State if any are equal. (a) the absolute value of the average potential energy of the SunEarth system (b) the average kinetic energy of the Earth in its orbital motion relative to the Sun (c) the absolute value of the total energy of the SunEarth systemarrow_forwardA space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass ml = 48.0 kg travels in the positive x-direction at 12.0 m/s, and a second piece of mass m2 = 62.0 kg travels in the xy-plane at an angle of 105 at 15.0 m/s. The third piece has mass m3 = 112 kg. (a) Sketch a diagram of the situation, labeling the different masses and their velocities, (b) Write the general expression for conservation of momentum in the x- and y-directions in terms of m1, m2, m3, v1, v2 and v3 and the sines and cosines of the angles, taking to be the unknown angle, (c) Calculate the final x-components of the momenta of m1 and m2. (d) Calculate the final y-components of the momenta of m1 and m2. (e) Substitute the known momentum components into the general equations of momentum for the x- and y-directions, along with the known mass m3. (f) Solve the two momentum equations for v3 cos and v3 sin , respectively, and use the identity cos2 + sin2 = 1 to obtain v3. (g) Divide the equation for v3 sin by that for v3 cos to obtain tan , then obtain the angle by taking the inverse tangent of both sides, (h) In general, would three such pieces necessarily have to move in the same plane? Why?arrow_forwardIf a particle of mass 100 g initially had a speed of 100 cm/s, what would be its approximate kinetic energy at the end of its 10 cm fall? The correct answer is 15 x 10⁵ ergsarrow_forward
- A 0.50 g/cm³ B 0.80 g/cm³ C 1.40 g/cm³ D 2.00 g/cm³ 20g 20g /40cm² = 0.5g/cm 10 A cube of side 2 cm is placed in a graduated measuring cylinder. 145 cm³ of oil is then added and the cube remains at the bottom of the cylinder. What will be the reading on the measuring cylinder? A 147 cm³ B 149 cm³ C 151 cm³ 153 cm³ D Structured Questions (Paper 2 Section A) 1 The diameter of a screw was measured as accurately as possible using the following instruments: a micrometer, vernier calipers and a metre rule. The table below shows the readings obtained. Complete the table to inarrow_forward(a) 15.4 kg m^2/s (a) 18.5 kg m^2/s (a) 6.4 kg m^2/s (a) 10 kg m^2/s (b) 0.30 m (b) 3.34 m (b) 5.14 m (b) 4.11 m (c)-14.9 J (c) 14.9 J (c)-17.4 J (c) 17.4 J entum Ho of the p (b) the distance r₁1 between O and Q,arrow_forwardA particle P of mass m = 0.56 kg is released from rest at a point h = 7 m above the surface of a liquid in a container. P falls through the air into the liquid. Assume there is no air resistance and there is no instantaneous change in speed of P as it enters the liquid. When P is at a distance of d = 0.71 m below the surface of the liquid, P's speed is v = 4.9 m/s. The only force acting on P due to the liquid is a constant resistance to motion of magnitude R N. Find the following: v1: The speed (in m/s) of P the moment just before it strikes the surface of the fluid.a1: The magnitude of the deceleration (in m/s2) of P while it is falling through the liquid.R: The magnitude of the resistance force (in N). The depth of the liquid in the container is dp = 3.9 m. P is taken from the container and attached to one end of a light inextensible string. P is placed at the bottom of the container and then pulled vertical upwards with a constant acceleration, a2. The resistance force to motion R N…arrow_forward
- Consider the double pendulum shown on figure below. A double pendulum is formed by attaching a pendulum directly to another one. Each pendulum consists of a bob connected to a massless rigid rod which is only allowed to move along a vertical plane. The pivot of the first pendulum is fixed to a point OO. All motion is frictionless. X2 m g 02 marrow_forwardA 2.29 µg particle moves at 2.03 × 10° m/s. What is its momentum p? 0.464 p = kg-m/s Incorrectarrow_forwardif A⃗ =2i+3j+6kA→=2i+3j+6k and A⃗ =3i−4j+2kA→=3i−4j+2k, then the angle between the two vectors isarrow_forward
- A snowball is thrown with a speed of 42.0 km/h, giving it momentum with a magnitude of 2.00 Ns. The mass of the snowball, in grams, is what?arrow_forwardA man walks up to you and hands you an energy drink with mass 0.4 kg. You decide energy drinks aren't for you and throw it on the ground. At the moment the energy drink leaves your hand, it is moving downwards with a speed of 7 m/s and is 1 meter above the ground. Calculate the speed of the energy drink in m/s just before it impacts the ground. As before, assume g = 10 m/s^2. You may neglect air friction. Round your answer to one decimal place.arrow_forwardIn the figure, the incoming mass (m₁) is an alpha particle, with mass of 4.00 atomic mass units (4.00 amu). Target particle (m₂) is a carbon nucleus (m₂ = 12.0 amu). The alpha particle is scattered at an angle 0₁ = 56 degrees and the carbon nucleus moves off with a speed of 1.24 x 105 m/s at an angle 0₂ = 46 degrees. What is the final speed of the alpha particle (V₁f)? Your answer should be in m/s. You can use notation such as 9.99e5, where "e5" stands for "x 105" captie Mal m₁ V₁i m₂ y V2f 0₂ 81 Vif Xarrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning