A child having mass M holds her legs up as shown as she swings downward from rest at { θ }_{ 1 }θ1​. Her center of mass is located at point { G }_{ 1 }G1​. When she is at the bottom position θ = 0°, she suddenly lets her legs come down, shifting her center of mass to position { G }_{ 2 }G2​. Determine her speed at the beginning of the upswing, due to this sudden change in the position of her legs. Also, determine the maximum angle to which she will swing upwards. a) Solve the problem algebraically first b) Solve the problem for m = 50kg, using the data shown in the sketch

A uniform flat plate of metal is situated in the reference frame shown in the figure below. 5 4 3 2 1 0 + H 0 1 2 3 4 5 6 7 8 9 10 Y Calculate the coordinate of the center of mass of the metal plate.

A 0.400 kg hammer is moving horizontally at 4.00 m/s when it strikes a nail and comes to rest after driving it 1.00 cm into a board. (a) Calculate the duration of the impact in seconds.   s (b) What was the average force in newtons exerted on the nail?   N

She lies on a plank on two scales: one at her head, the other at her feet.  They are 1.71 meters apart.  Her head scale reads 386 N, and her foot scale reads 398 N. How far from her feet is her center of mass?

Two objects (m₁ = 4.95 kg and m2 = 3.25 kg) are connected by a light string passing over a light, frictionless pulley as in the figure below. The 4.95-kg object is released from rest at a point h = 4.00 m above the table. m2 m₁ (a) Determine the speed of each object when the two pass each other. m/s (b) Determine the speed of each object at the moment the 4.95-kg object hits the table. m/s (c) How much higher does the 3.25-kg object travel after the 4.95-kg object hits the table? m

In the instant of the figure, two particles move in an xy plane. Particle P₁ has mass 7.40 kg and speed v₁ = 1.91 m/s, and it is at distance d₁ = 9.52 m from point O (the figure is not drawn to scale). Particle P₂ has mass 2.73 kg and speed v2 = 2.37 m/s, and it is at distance d₂ = 8.89 m from point O. What is the magnitude of the net angular momentum of the two particles about O? P₁O Number i Units ས། ྋ P2

A body is traveling at 2.0 m/s along the positive direction of an x axis; no net force acts on the body. An internal explosion sepa-rates the body into two parts, each of 4.0 kg, and increases the total kinetic energy by 16 J. The forward part continues to move in the original direction of motion. What are the speeds of (a) the rear part and (b) the forward part?

Two objects are connected by a light string passing over a light, frictionless pulley as shown in the figure below. The object of mass m₁ kg is released from rest at a height h = 5.60 m above the table. = 7.00 m2 m1 (a) Using the isolated system model, determine the speed of the object of mass m2 3.00 kg just as the 7.00-kg object hits the table. m/s (b) Find the maximum height above the table to which the 3.00-kg object rises. m

A tourist is driving across Canada. They are currently in the rolling planes of Saskatchewan. They reach the peak of a hill. At the peak, they are travelling at 50 [ km/h]. They continue down the hill to a trough. At the bottom of the trough, they are driving at 100 [km/h]. The magnitude of the acceleration of the vehicle's mass center is the same at the peak and the trough. The vehicles mass center is 0.6 [m] from the road. It takes 10 seconds to travel from point A to B. Determine: a) The radius of curvature, PB, of the section of the road with the trough. Use the problem diagram below. 0.6 m Vrough PR Radius of Curvature at B V peak 40 m Radius of curvature at A

Two forces, F , = (-2,65î + 4.10ĵ) N and F, = (-4.50î + 7.10ĵ) N, act on a particle of mass 2.30 kg that is initially at rest at coordinates (+1.95 m, –4.20 m). (a) What are the components of the particle's velocity at t = 11.3 s? m/s (b) In what direction is the particle moving at t = 11.3 s? ° counterclockwise from the +x-axis (c) What displacement does the particle undergo during the first 11.3 s? AF = (d) What are the coordinates of the particle at t = 11.3 s? m