1. Two horizontal forces act on a 2.0 kg chopping block that can slide over a frictionless kitchen counter, which lies in an ry plane. One force is F = (3.0 N)i + (-4.0 N)j. Find the acceleration of the chopping block in unit-vector notation when the other force is (a) F2 = (-3.0 N)ê + (-4.0 N), (b) F2 = (-3.0 N)î + (4.0 N)j, and (c) F = (3.0 N)ê + (-4.0 N)ĝ.
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- 5. A 40 kg girl and an 8.4 kg sled are on the frictionless ice of a frozen lake, 15 m apart but connected by a rope of negligible mass. The girl exerts a horizontal 5.2 N force on the rope.What are the acceleration magnitudes of (a) the sled and (b) the girl? (c) How far from the girl's initial position do they meet?A block with mass mb=7.75 kg is suspended on a string. You pull upwards on the string creating a tension force of magnitude TYb=79.2275 N. If the upward speed of the block is 2.25 m/s right now, then what is its speed 5.5 s later?Problem 2: In the Figure, three connected blocks are pulled to the right on a horizontal frictionless table by a force of magnitude T3 = 65 N. If m₁ = 12 kg, m₂ = 24 kg, and m3 = 31 kg, calculate: (a) The magnitude of the system's acceleration. Answer: 0.97 m/sec². (b) The tension T₁. Answer: 11.64 N. (c) The tension T₂. Answer: 34.92 N. m1 T₁ mq T2 mg T3
- A 124 kg crate is pushed at constant speed up a frictionless inclined plane of θ = 48 ° with the horizontal. Assuming one pushes with a horizontal force, what is the magnitude of the force F (in N) required to do this?From a standstill, a 77.0 kg basketball player bends their knees and pushes against the floor andextends legs vertically 30.0 cm before jumping vertically off the ground and reaches a maximumheight of 25.0 inches above the ground. Assume the force the floor exerts on the player is constant.What is the force the floor exerts on the player? Give answer in lbs. (Let 4.45 N = 1 lb., 1 inch = 2.54 cm)– 3. A 64.3 kg skydiver jumps out of an airplane with a parachute. She decides not to pull the rip cord until she reaches terminal velocity. If the resistive force proportionality constant is 2.35 kg/s, what is the magnitude of the velocity when she decides to pull the cord? (Assume the drag force is proportional to the speed.) - a. 16.4 m/s b. 268 m/s c. 151 m/s d. 9.80 m/s e. 27.4 m/s
- (optional) A skydiver is weighted 72.7 kg, together with his parachute. The acceleration of gravity is 9.80 m/sec². The air resistance force f to the parachute is proportional to the square of velocity, f = bv², with b = 30.0 Nt sec²/m². Find the expression for his falling speed and the numerical value for his landing speed. When he opens the parachute at t = 0, his falling speed is 10 m/s.A 112 kg crate is pushed at constant speed up a frictionless inclined plane of θ = 59 ° with the horizontal. Assuming one pushes with a horizontal force, what is the magnitude of the force F (in N) required to do this?3. A block of mass m = 2.00 kg rests on the left edge of a block of mass M = 8.00 kg. Thecoefficient of kinetic friction between the two blocks is 0.300, and the surface on which the 8.00kg block rests is frictionless. A constant horizontal force of magnitude F = 10.0 N is applied tothe 2.00-kg block, setting it in motion as shown in Figure. The distance L that the leading edge ofthe smaller block travels on the larger block is 3.00 m. (a) Draw a separate free-body diagram for each block. (b) In what time interval will the smaller block make it to the right side of the 8.00-kg block? as(Note: Both blocks are set into motion when the force is applied.) (c) How far does the 8.00-kg block move in the process?
- Two teams of nine members each engage in a tug of war. Each of the first team's members has an average mass of 72 kg and exerts an average force of 1350 N horizontally. Each of the second team's members has an average mass of 77 kg and exerts an average force of 1373 N horizontally. (a) What is the acceleration (in m/s2 in the direction the heavy team is pulling) of the two teams?Three forces acting on an object are given by F₁ = (-1.95î + 6.60ĵ) N, F₂ = (4.651 – 1.85ĵ) N, and F3 = (-43.51) N. The object experiences an acceleration of magnitude 3.65 m/s². (a) What is the direction of the acceleration? O (counterclockwise from the +x-axis) (b) What is the mass of the object? kg (c) If the object is initially at rest, what is its speed after 18.0 s? m/s (d) What are the velocity components of the object after 18.0 s? (Let the velocity be denoted by v.) î+ î) m/s7. A mass m₁ = 5.00 kg is connected by a light string that passes over a pulley of mass m3 = 8.0 kg to a mass m2 8.50 kg sliding on a frictionless inclined surface that makes an angle of 23° with the horizontal (see figure). The coefficient of kinetic friction between the mass m₁ and the horizontal surface is 0.19. There is no slippage between the string and the pulley. What is the magnitude of the acceleration of the system? (The moment of inertia of the pulley is 1/2Mr².) m/s² m₂ m3 = m₁