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A toy rocket engine is securely fastened to a large puck that can glide with negligible friction over a horizontal surface, taken as the xy plane. The 4.00-kg puck has a velocity of
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Principles of Physics: A Calculus-Based Text
- A particle of mass 5.70 kg moves in the horizontal xy plane. The only force acting on the particle with component in the xy plane has expression (in newtons) F =4.70x2ı^, where x is in meters. Assume that the particle's trajectory is a straight line from the position (in meters) r0=2.10ı^ +2.10ȷ^ to the position (in meters) rf=6.50ı^ +2.10ȷ^. Also consider that its speed at position r0 has a magnitude of 3.80 m/s. Calculate the magnitude (in m/s) of the particle's velocity at position rf. Give your answer to three significant figures. (only numbers)arrow_forwardA toy rocket engine is securely fastened to a large puck that can glide with negligible friction over a horizontal surface, taken as the xy plane. The 4.80-kg puck has a velocity of 1.201 m/s at one instant. Eight seconds later, its velocity is (6.001 + 8.0ĵ) m/s. (a) Assuming the rocket engine exerts a constant horizontal force, find the components of the force. We know the change in velocity during an 8 second time interval. How do you calculate the acceleration?Î + Work with x and y components separately.ĵ) N (b) Find its magnitude. X You appear to have correctly calculated the magnitude using your incorrect values from part (a). N Xarrow_forwardForce, Force, Baby! Two constant forces of magnitudes F and F, act on a particle of mass 5.00 [kg] which is at rest at the origin. The force F1 points at 14.5° west of north, while the force F, points at 58.3° west of south. Due to the two forces, the particle accelerates and is later located at 32.4 [m], 17.0° north of west with speed 12.2 [m/s]. What is F1? O 0.524 [N] O 9.03 [N] O 9.28 [N] O 10.7 [N]arrow_forward
- Two constant forces act on an object of mass m = 4.30 kg object moving in the xy plane as shown in the figure below. Force F, is 26.5 N at 35.0°, and force F, is 48.0 N at 150°. At time t = 0, the object is at the origin and has velocity (3.50î + 2.15j) m/s. 150° 35.0° (a) Express the two forces in unit-vector notation. F, - N (b) Find the total force exerted on the object. N (c) Find the object's acceleration. m/s2 Now, consider the instant t = 3.00 s. (d) Find the object's velocity. m/s (e) Find its position. (f) Find its kinetic energy from V½mv2. kJ (g) Find its kinetic energy from 2mv,2 + EF · AF. kJarrow_forwardA drone is being directed across a frictionless ice covered lake. The mass of the drone is 1.50 kg, and its velocity is 3.00i ^ m/s . After 10.0 s, the velocity is 9.00i ^ + 4.00j ^ m/s . If a constant force in the horizontal direction is causing this change in motion, find (a) the components of the force and (b) the magnitude of the force.arrow_forwardAn applied force of 42.3 N directed at an angle of -17.7 degrees with respect to the +x direction acts on a 2.95 kg mass that is initially at rest while on a horizontal surface. In moving a distance of 2.67 m in the +x direction, the object changes its kinetic energy by 31.5 J. What is the coefficient of kinetic frictionarrow_forward
- A block of mass m = 3.65 kg is pushed a distance d = 7.95 m along a frictionless horizontal table by a constant applied force of magnitude F = 16.0 N directed at an angle 0 = 39.0° below the horizontal as shown in the figure below. A block labeled m is on a horizontal surface. An arrow labeled vector F points downward and to the right at an angle e above the horizontal, and acts upon the upper left corner of the block. A faded image of the block is a distance d to the right of the block. (a) Determine the work done on the block by the applied force. (b) Determine the work done on the block by the normal force exerted by the table. (c) Determine the work done on the block by the force of gravity. (d) Determine the work done by the net force on the block.arrow_forwardThe figure shows an overhead view of a 0.0270 kg lemon half and two of the three horizontal forces that act on it as it is on a frictionless table. Force ₁ has a magnitude of 5.00 N and is at 0₁ = 33.0°. Force ₂ has a magnitude of 8.00 N and is at 0₂ = 28.0%. In unit-vector notation, what is the third force if the lemon half (a) is stationary, (b) has the constant velocity v = (12.0î – 15.0)) m/s, and (c) has the varying velocity = (10.0tî - 15.0t)) m/s, where t is time? y (a) Number (b) Number (c) Number î+ î+ î+ i F₁ 又 0₁/ 0₂ x ĴUnits ĴUnits Units <arrow_forwardAt the instant of the figure, a 4.20 kg particle P has a position vector 7 of magnitude 9.40 m and angle 0₁ = 49.0° and a velocity vector of magnitude 3.40 m/s and angle 0₂ = 35.0°. Force F, of magnitude 6.00 N and angle 03 = 35.0° acts on P. All three vectors lie in the xy plane. About the origin, what are the magnitude of (a) the angular momentum of the particle and (b) the torque acting on the particle? (a) Number (b) Number i Units Units 02/01 P xarrow_forward
- At the instant of the figure, a 7.20 kg particle P has a position vector i of magnitude 1.10 m and angle 01 = 40.0° and a velocity vector v of magnitude 1.80 m/s and angle 02 = 31.0°. Force F ,of magnitude 2.70N and angle 03 = 31.0° acts on P. All three vectors lie in the xy plane. About the origin, what are the magnitude of (a) the angular momentum of the particle and (b) the torque acting on the particle? F (a) Number i 91.64 Units kg-m^2 (b) Number 1.52 Units N-marrow_forwardThe figure shows an overhead view of a 0.0270 kg lemon half and two of the three horizontal forces that act on it as it is on a frictionless table. Force Was a magnitude of 5.00 N and is at 9₁ = 33.0°. Force was a magnitude of 8.00 N and is at 92 = 28.0°. In unit- vector notation, what is the third force if the lemon half (a) is stationary, (b) has the constant velocity m/s, and (c) has the varying velocity m/s, where t is time? (a) Number -1.0326 (b) Number i -1.0326 (c) Number i -0.7626 citarrow_forwardA particle with a mass of 10 kg is moving at a velocity of (3t^2 + 4t)j m/s. What would be the expression for the external net force F(t) being applied to the particle? Note: i and j are unit vectorsarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning