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Two forces
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Physics for Scientists and Engineers: Foundations and Connections
- A cart of mass 8.00 kg was moved by applying two constant forces. Force 1 is 28.0 N at 42.0°, and Force 2 is 13.0 N at 110°. Initially, the cart has a velocity of (3.50 i +2.20 j) m/s. a. Express the two forces in in unit-vector notation. Ans. F = (20.81 i + 18.74 j)N, F, = (-4.45 i + 12.22 j)N b. Find the total force exerted on the cart. Ans. EF = (16.36 i+ 30.96 j)N or 35.02 N c. Find the angle at which the total force is applied. Ans. 62.15°arrow_forwardA pendulum has a length l (the rope is massless). The mass of the object suspended from the pendulum is m. With rope horizontal θ = 90o When it makes an angle of degrees, we first leave the object at no speed. Any friction can be neglected. Gravitational acceleration g. Give your answers in terms of l, m and g. When = 0o, what is the tension in the rope?arrow_forwardThe dragster accelerates from rest down a road of length d = 400.0 m. In the absence of any friction the dragster has a constant acceleration of a = 21.1 m/s2 in the direction of motion, and its mass is m = 1175 kg. Assume the dragster is moving in the positive horizontal direction. a. What is the dragster's final speed, in meters per second, assuming Fr = 1000 N?arrow_forward
- a. A spacecraft that is initially at rest turns on its engine at t=0. If its mass is 3000 kg and the force from the engine is 111,111 N, what is the acceleration of the spacecraft? b. An ice skater moves without friction on a frozen pond. While traveling at 8.00 m/s, she finds that it takes 17.0 s to travel the length of the pond. How long is the pond?arrow_forwardA crate of mass m=66.2 kg is on a horizontal surface. Assume there is no friction between the crate and the surface. Two forces with magnitude F=11.2 N are applied to the crate, as shown. One force is horizontal, and the other makes and angle of φ = 37.4∘ with horizontal, as shown. A. Write an expression for the magnitude of the acceleration of the crate in terms of F, m, and φ. B. What is the magnitude of the acceleration of the crate in m/s2?arrow_forward2. a. Define displacement r, velocity v and acceleration a b. Use these parameters to derive a kinematic equation that expresses the final velocity vi of an object as a function of nitial velocity Vo, displacement r and position dependent acceleration a(r). C.Suppose the position dependent acceleration a(r) is given in Figure 2. Find the final velocity of the object d. Consider a sun bound asteroid of mass Ma. The mass of the sun, M,>>Ma. The asteroid is heading directly towards the sun. The attractive gravitational force Fs between the sun and the asteroid is: Fo IGM,M/r1l-r). The initial position of the asteroid is ro and its final position is r before reaching the sun. Express the final velocity of the asteroid as a function of ro, Vo, ri, and the known constants G and M 6 4. 2. 2arrow_forward
- Please show complete solution for letters d, e, f, g and harrow_forward9. a. An arrow is fired from a bow with a velocity of 69.2 m/s. The arrow has a mass of 0.082 kg. The arrow travels 0.855 m as it's being released/ while the force of the taunt string acts on it. What is the change in KE, AKE, of the arrow? 196.33 Previous submissions: b. What was the force of the bow string? 229.63 Previous submissions: J N V incorrect V incorrectarrow_forwardA crate of mass m = 1.27 kg is on a frictionless incline that makes an angle of θ = 29.3 degrees with horizontal. A force of magnitude P = 9.45 N is applied to the crate in a direction parallel and up the incline, as shown. a. Write an expression for the acceleration ax of the crate, where positive x is up the incline. Your answer should be in terms of m, P, θ, and g (9.80 m/s2). b. What is the acceleration of the crate in m/s2 in the x direction defined in part (a)? c. What is the direction of the net force on the crate? d. What is the direction of the velocity of the crate?arrow_forward
- Two masses m,=9 Kg and m,=9 Kg are connected with string and pulled with a force F=25 N that makes an angle of 53° with a smooth horizontal surface as shown in the figure. Find the tension in the string in a unit of Newton. F m2 A. 10.64 B. 7.523 C. None D. 15.05 E. 3.761 O d O O Uodouarrow_forward1.a. Two boxes with masses m1=1 kg and m2= 2 kg are connected by a cord running over a pulley. The coefficient of kinetic friction between the first box and the table is 0.20. Neglect the mass of the cord and the pulley, and any friction in the pulley. What is the acceleration of the system? b. What is the velocity obtained by the acceleration found in the previous part?arrow_forwardA 56-kg student runs at 4.2 m/s, grabs a hanging 10.0-m-long rope, and swings out over a lake (Figure 1). He releases the rope when his velocity is zero. a.)What is the angle θ when he releases the rope? Express your answer to two significant figures and include the appropriate units. b.)What is the tension in the rope just before he releases it? Express your answer to two significant figures and include the appropriate units. c.)What is the maximum tension in the rope during the swing? Express your answer to two significant figures and include the appropriate units.arrow_forward
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