- 14 20 Points A Ballistic Pendulum Consists Of A Stationary Wooden Block Of Mass M 4 92 Kg Suspended From A String Of 1 (55.6 KiB) Viewed 11 times
- 14 20 Points A Ballistic Pendulum Consists Of A Stationary Wooden Block Of Mass M 4 92 Kg Suspended From A String Of 2 (77.81 KiB) Viewed 11 times
- 14 20 Points A Ballistic Pendulum Consists Of A Stationary Wooden Block Of Mass M 4 92 Kg Suspended From A String Of 3 (61.73 KiB) Viewed 11 times
Work and Energy • Work done by a constant external force F exerted on a system while that system undergoes a displacement d is W=Fd cos@ where F is the magnitude of the force, d is the magnitude of the displacement, and is the angle between the vector F and the vector d. • Kinetic energy: K= Zmo² • Gravitational potential energy: Ug = mgy, Elastic potential energy: U, = kx², where x is the displacement of the spring from its equilibrium (or unstretched) position (x = 0). Work-Energy equation states that K+U+U+AE = K₁+U₂+U+W where W is the work done by all the external forces acting on the system and AEth is the change in thermal energy of the system. • The increase in thermal energy of the system due to friction is AE = Wyl, where W/l is the absolute value of the work done by the force of kinetic friction. Rotational dynamics →The torque exerted by a force F: T=r_F, where r is the moment arm (or lever arm). →For an object in equilibrium: Er=0 and EF-0 → The moment of inertia of a system of particles: I = Emr² = myr + m₂r] + mər} + ... The moment of inertia of various objects: →For a single particle of mass m in circular motion of radius r: Imrª² →For a solid disk of mass M and radius R rotating about an axis passing through its center: IM MR² →For a hoop (or ring) of mass M and radius R rotating about an axis passing through its center: I MR →Newton's second law for rotational motion: Erla, where I is the moment of inertia of the rotating object Angular momentum or rotational momentum: L-lw →If the net torque acting on a rotating rigid body is zero, i.e., Er0, the the angular momentum of the rigid body does not change, i.e., L.- la constant or ha la
Relevant equations & conversions Symbols have their usual meanings 1 revolution=2r radians 1 minute = 60 seconds; 1 hour = 60 minutes • 1 kg = 1000 g: 1 mi=1609 m; 1 m-3.28 ft; 1 m = 100 cm • Magnitude of the acceleration due to gravity: g = 9.8 m/s². Relevant equations • Roots of the quadratic equation Ax² + Bx+C =0: x=- 24 Area of a triangle of base band height : A = bh • Area of a rectangle of length I and width : A=Iw. • Circumference of a circle of radius r. C = 2mr. Area of a circular disk of radius r. A = ² Trigonometric functions Newton's second law of motion [2F₂ – ΣΕ = md OR ma -B+√B²-4AC = ------* 4-4-4 Figure 1 • Weight of an object of mas mmg (magnitude). • Hooke's law for the restoring force exerted by a spring): (Fp)-kAr, where k is the spring constant and Ax is the displacement from the equilibrium position. • Frictional forces →Magnitude of the maximum force of static friction: f, mas M., where is the magnitude of the normal force acting on the body and μ, is the coefficient of static friction →Magnitude of the force of kinetic friction: fi-in, where pa is the coefficient of kinetic friction Uniform circular motion: The acceleration of an object moving in a circle of radius r at a constant speed pointing toward the center of the circle Impulse and momentum m Linear momentum of an object of mass m and velocity Impulse of a force - area under the Force-Time curve F At Impulse-momentum principle (or Newton's second law) Ap- Tor Af-LF At → Law of conservation of momentum The total momentum of a system P-F+B+ an isolated system is a constant Le P