The figure shows a container of mass m₁ = 4.8 kg connected to a block of mass m₂ by a cord looped around a frictionless pulley. The cord and pulley have negligible mass. When the container is released from rest, it accelerates at 2.5 m/s² across the horizontal frictionless surface. What are (a) the tension in the cord and (b) mass m₂? m₁ mą

Two forces of F₁ = 112 √2 N and F₂ = 388 √2 What is the resultant force in terms of the force vectors F₁ and F2? What is the magnitude of an equal and opposite force, F3, which balances the first two forces? sin() cos() tan() T HOME cotan() acos EM4 asin() atan() acotan() sinh() 7 8 9 5 6 1 2 3 * 0 END cosh() tanh() cotanh() ⒸDegrees O Radians VO BACKSPACE DEL CLEAR Submit Hint Feedback I give up! Given your observations from parts a and b, if working with vectors in 3 dimensions (i, j, k); what will the normalizing term n be for (i- j+ k) (i − j+ k) the two vectors F₁ = C₁ N and F₂ = 0₂ N. √T | Fren | Given the normalizing term n found in the previous part in 3 dimensions (i, j, k); what will the magnitude of the resultant vector be in terms of the constants c₁ and ₂. (i − j+ k) (i- j+k) The vectors in question are F₁: N and F₂ = 0₂ √√T √π F3 = = C1 N act on an object.

A runner of mass 62.0 kg initially moves at a speed of 8.05 m/s.How long must an average external force of 1.60* 10^2 N act to bring the runner to rest?

A 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.

Vector F₁ = 625 N makes an angle of 2700 when rotated counterclockwise from the +x axis. Vector F2 = 875 N makes a 1200 angle from Vector F₁ when rotated counterclockwise. What is the magnitude a vector needed to balance the two forces? O 680.6 N O86.2 N -980.6 N O-670.6 N O980.6 N 78.2 N O 580.6 N 780.6 N

A sailboat with a mass of 2 x 103 kg experiences a tidal force of 3 x 103 N directed to the east and a wind force against its sails with a magnitude of 6 x 103 N directed toward the northwest (45°N of W). What is the magnitude of the resultant acceleration of the boat? O 9.68 m/s^2 O 2.21 m/s^2 O 5.14 m/s^2 8.92 m/s^2

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. kJ

A wedge with mass M rests on a frictionless horizontal tabletop. A block with mass m is placed on the wedge and a horizontal force F~ is applied to the wedge. There is no friction between the block and the wedge. For α = π/7, what must the magnitude of F~ be if the block is to remain at a constant height above the tabletop? (g is the magnitude of the gravitational acceleration. Take m = 1 kg, M = 5 kg and g = 10 m/s 2) (a) 29 N (b) 35 N (c) 44 N (d) 60 N (e) 104 N

A desperate hiker has to think fast to help his friend who has fallen below him. Quickly, he ties m, a rope to a rock of mass m, = 3.90 x 10? kg and makes his way over the ledge (see the figure). If the coefficient of static friction between the rock and the ground is µs = 0.283, and the mass of the hiker is m, = 70.1 kg, what is the maximum mass of the friend m; that the rock can hold so the hikers can then make their way up over the ledge? Assume the rope is parallel to the ground and the point where the rope passes over the ledge is frictionless. kg II