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A 2.00 [kg] frictionless block is attached to an ideal spring of force constant 300. [N/m]. At t = 0 the
block has velocity -4.00 [m/s] and displacement 0.200 [m]. Determine the following:
A.The amplitude of the oscillation
B. The position-time and velocity-time functions of the spring-mass system
Two identical uniform spheres A and B, with mass M = 1. 00 [kg], are
placed 0. 500 [m] away from another spherical mass C (m =
0. 300 [kg]) as shown. If mass C is released from rest, what is its net
acceleration? Assume that only the gravitational forces from spheres A
and B act on C.
Consider a “round” rigid body with moment of inertia I = BMR2, where M is the body’s mass, R is the body’s radius, and B is a constant depending on the type of the body.
The center of the “round” rigid body is attached to a spring of force constant k, and then the body is made to roll without slipping on a rough horizontal surface. Due to the spring, it is expected the body will oscillate by rolling back and forth from its resting position.
A. Determine the angular frequency and the period for small oscillations of the round rigid body. Express your answer in terms of B.
B. Among the four “round” rigid bodies shown at the table, for the same masses and radii, which among them will have the most number of cycles per second.
Two adults and a child want to push a wheeled cart in the +x direction. The two adults push with horizontal forces F1=100N at 60 degrees from +x anticlockwise and F2+140N at 30 degrees from the +x clockwise. (a) Find the magnitude and the direction of the small force that the child should exert, ignoring friction. (b) If the child exerts the minimum force in part (a), the cart accelerates at 2m/s^2 in the +x direction. What is the weight of the cart?
In a test on machine an effort of 50N was required to raise a load pf 250N. If the effort moves through 150 mm to raise the load by 25 mm, find the following:
i. The Mechanical Advantage
ii. The Velocity Ratio
iii. The efficiency
iv. The work done by the effort.
v. The work done in raising the load 25 mm.
vi. The power developed by the effort over a period of 5 seconds
a mass of 16 kg is attached to a spring of spring constant 2. the spring is attached to a frictionless surface. To make an oscillation,mass is extended to a distance of 3m and released. represent the displacement of mass from equilibrium as a position vs time graph
The efficiency of a wheel and axle system is 80% and the ratio of wheel to radius of axle is 4:1. In order to lift a mass of 20k, the effort required is?
A wheel with a radius of 1.95 m and a mass of 0.215 kg rolls without sliding down a plane that is inclined at an angle φ = 12.062 °. g = 9.806 m/s². Calculate the kinetic energy of the wheel after the time 0.923s if it has a moment of inertia 1.6 kg · m², starts from rest and a force acts on the wheel so that its angle of rotation varies with time according to θ(t) = 1.6 · t3 rad.
A disc with a mass of 1.21 kg rotates around an axis z with an initial angular velocity of 3.25 rad/s. On top of the disc (which has an inertia radius of 2.55m) is a rectangular disc with mass 1.21kg, base 3.163m and height 3.206m and rotates at the same angular velocity as the lower disc 3.25 rad/s. The axis of rotation passes through the center of mass of both discs. Calculate the total rotational energy of the discs.
1. A driver of an ambulance going 70 km/h suddenly sees another car 35.0 m ahead. It takes the driver 0.62 s before he applies the brakes. Once he does begin to brake, he reduces speed at a rate of 13.0 m/s².
1.1 Determine if the driver will hit the car or not. (6)
What would be the maximum speed at which the ambulance could travel and NOT hit the car 35.0m ahead?
