2) A small object of mass 1 mg is confined to move between two rigid walls separated by 1 cm. a) Calculate the minimum speed of the object? b) If the speed of the object is 3 cm/s find the corresponding value of n?
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- A crate of mass m1 slides down a well-lubricated hill of height h, with negligible friction. At the bottom, where it is moving horizontally, it collides with another crate, of mass m2, that initially was sitting at rest and that is attached to a wall by a spring of spring constant k that initially is at its equilibrium length. Assume that the spring itself has negligible mass. a)Given that the distance d that the crates compress the spring is d=0.35 m, calculate the speed v2 of the crates immediately after the collision, in units of meters per second. Use the following values:k=950 N/mm1=2.4 kgm2=2.6 kgμ=0.49g=9.8 m/s2 b)What was the speed of the crate of mass m1 just before the collision with the second block, in meters per second? c) What is the height h of the hill, in meters?A crate of mass m1 slides down a well-lubricated hill of height h, with negligible friction. At the bottom, where it is moving horizontally, it collides with another crate, of mass m2, that initially was sitting at rest and that is attached to a wall by a spring of spring constant k that initially is at its equilibrium length. Assume that the spring itself has negligible mass. a)Given that the distance d that the crates compress the spring is d=0.35 m, calculate the speed v2 of the crates immediately after the collision, in units of meters per second. Use the following values:k=950 N/mm1=2.4 kgm2=2.6 kgμ=0.49g=9.8 m/s2 b) What was the speed of the crate of mass m1 just before the collision with the second block, in meters per second? c)What is the height h of the hill, in meters?where k is a positive constant characterizing the stiffness of the spring. Compute the work required to expand the spring from its equilibrium position to length l.
- Determine the magnitude and direction of the force F=(690 lb)i +(300 lb)j – (580 lb)k.An 210kg drone hits the ground at 311km/h and penetrates to a depth of 81.0cm.What was the force the ground exerted on the drone?Which of the following assumptions is incorrect according to the Kinetic Molecular Theory of gases? All collisions are perfectly inelastic. The particles move rapidly in constant random motion. A gas is composed of particles usually molecules or atoms. The intermolecular forces of attraction/repulsion among gas particles are negligible.
- The potential energy function for either one of the two atoms in a diatomic molecule is often approximated by U(x) = −a/x¹² — b/x6 where x is the distance between the atoms. (a) At what distance of separation does the potential energy have a local minimum (x = ∞) ?Calculate the average kinetic energy for 1. V(x) = x(5-xz) where x € [0,5]What does the percent difference between GPE and KE tell you about the Efficiency of energy transformations in this experiment ?
- 27.The potential energy function for either one of the two atoms in a diatomic molecule is often approximated by U (x)=-a/x¹² -b/x6 where x is the distance between the atoms. (a) At what distance of seperation does the potential energy have a local minimum (not at x = ¥)?(b) What is the force on an atom at this separation? (c) How does the force vary with the separation distance? Solution a. -2a b 1/6 ; b. 0; c. ~x65. A cart with m= 3.40kg rides on the track shown. The track is frictionless except for a level section 0.40m long where μk = 0.54. The cart is initially at rest against spring 1 (k₁ = 1400N/m) which is compressed by 8.00cm. When released it travels along the track until it reaches spring 2 (k2= 800N/m) which it compresses until the cart stops. If h₁ = 0.38m and h₂ = 0.14m, determine the speed of the cart at points A, B, C and D. Also how much will spring 2 be compressed at the end. framm] =3.40kg kží = 800 N/m Remb A k₁=1 2₁-1400/m h₁-0,38 D B d=0.40m = 0,54 мк of ....... oservation Im h₂= = 0,14