Motor M draws in the cable with an acceleration of 4 ft/s?, measured relative to the 200 -lb mine car.(Figure 1) Determine the acceleration of the car. Neglect the mass of the pulleys. Express your answer with the appropriate units. Value ft/s acar = Determine the tension in the cable. Express your answer with the appropriate units. ? T = Value lb apie -4 ft/s?

Learning Goal: In 1687, Isaac Newton presented three basic laws that describe the motion of a particle: • First law: A particle originally at rest, or moving in a straight line with a constant velocity, will remain in this state provided that the particle is not subjected to an unbalanced force. Second law: A particle acted upon by an unbalanced force, F experiences an acceleration, a, that has the same direction as the force and a magnitude that is directly proportional to the force. Figure 1 1 1 V 1 of 2

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Figure 6.35 shows a proposed roller-coaster track. Each car starts from rest atpoint A, where ya = 21 mand it will roll freely without friction along the track.It is important that there be at least some small normal force exerted by thetrack on the car at all points; otherwise, the car will leave the track. What is the minimum safe value for the radius of the curvature at point B?

5. A simple pendulum at the UCR department of physics and astronomy has a length of 20 m, and the acceleration due to gravity at this location is measured to be 9.803 m/s². Calculate the period of the pendulum.

a.) What is the angle, measured relative to the positive x-axis, of the load's acceleration? (The correct answer is: -10.219 degrees) Just need the steps to get there  b.) Three horses pull and guide a 132 kg payload down a river, exerting the forces shown in the figure, with F1 = 29 N, F2 = 38 N, F3 = 58 N, θ1 = 30°, and θ2 = 60°. What is the magnitude of the payload's acceleration? (The correct answer is: 0.7861 m/s^2)Just need the correct steps to get there

Consider the given pulley system. The rope is drawn towards the motor with a speed of 3 m/s. What is the speed of mass A and in what direction is it moving?

1. Two blocks are connected by a pulley system shown in the figure below. Neglect friction between the block on the left and the ramp sloped at angle 0. Suppose that the block on the left has mass m, and that the block on the right is moving downward at a constant speed v. m Given m, 0, and v, answer the questions below. (a) Find the mass of the block on the right? (b) Find the velocity of the block on the left. (c) If the block on the right was moving at a constant speed v upward, instead of downward, how would your answer to Question la change?

KOREK a "la KOREK + HW2 SOLUTION: Write the kinematic relationships for the dependent motions and accelerations of the blocks. • Write the equations of motion for the blocks and pulley. 300 kg B Combine the kinematic relationships with the equations of motion to solve for the The two blocks shown start accelerations and cord tension. from rest. The horizontal plane and the pulley are frictionless, and the pulley is assumed to be of negligible mass. Determine the acceleration of each block and the tension in the cord. 12 12

A small box of mass m is placed on top of a larger box of mass 2m as shown in Figure. When a force is applied to the large box, both boxes accelerate to the right with the same acceleration. If the coefficient of friction (static/kinetic) between all surfaces is µ, what would be the magnitude of the force and what would be the acceleration ? 2m F O 1. The information given in the problem is insufficient. O 2. 3m( µ+ g), g O 3. 3µmg, µg O 4. 6µmg, µg