There is a block that is moving along on a wooden plank that moves and follows simple harmonic motion with a frequency of 15 oscillations per minute. In one oscillation, the motion of the center of mass of the object spans 3 m along the x-axis. Please determine the minimum value of the static friction coefficient that stops the block from slipping? Please determine the position, velocity and acceleration of the block 0.5 second after going through the center of the trajectory in the negative x-direction?

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

rigid body statics

A skateboard of mass m rests on the top of a hemispheric dome of radius R. After giving the skateboard a small kick, imparting an initial speed of vo, it begins rolling down the dome. Let the angle 0 indicate the location of the skateboard as it rolls down the surface of the dome. R 1. Eventually, the skateboard will lose contact with the dome. Given m, R, vo, and g, find the angle 0. at which the skateboard loses contact. Express your answer symbolically (i.e. without numbers). Check your work. Suppose you choose m = 1.5 kg, vo = g = 9.81 m/s. In this case, your answer should evaluate to 0. = 34.2°. 4.5 m/s, R = 4.3 m, and 2. Given m, R, and g, determine the range of speeds for which it is impossible to remain in contact with the wall at all.

A hammer is made of a solid sphere and a solid rod of negligible mass attached to the sphere. The radius of the sphere is R=25.0 cm and its mass is m=0.100 kg. The distance from the center of the sphere to the pivot is l=1.00 m. The hammer is released from it is initial position at the angle ϕ=30° with the vertical direction (see Figure below). Find the velocity of its center of mass at the lowest point. The moment of inertia of a solid sphere is 2mR2/5 about the axis through any diameter.

A physical pendulum consists of a vertical board of of mass 5.8 kg, length 172 cm, and width 5 cm hanging from a horizontal, frictionless axle. A bullet of mass 145 g and a purely horizontal speed v impacts the pendulum at the bottom edge of the board. The board then makes a complete circle. (a) If the bullet embedded itself in the board, what is the minimum speed the bullet could have to make this so? (b) If the bullet passed through the board, reducing its speed by 1/5 its original value, what is the minimum speed of the bullet? (c) If the bullet is made of rubber and rebounds elastically, what is the minimum speed the bullet could have? (d) What is the rebound speed of the bullet?

Objects with a uniform mass distribution and a symmetric shape have a center of mass at the center of the object. For non-uniform objects, the center of mass needs to be determined experimentally. To measure the center of mass of such an object, a pivot is placed in the middle of a board and the top of the non-uniform object is placed to the right of the pivot. When a uniform 10.0 kg mass has its center placed 60.0 cm to the left of the pivot the system balances perfectly (as shown below). The mass of the non-uniform object is measured with an electronic scale in the lab and found to beM = 39.8 kg . Top of non-uniform object 10.0 kg M 60.0 cm Part A Where is the center of mass of the non-uniform object? (report the location from the top of the object, and in cm) ΑΣΦ ? dCM = ст

It's a beautiful sunny day and you decide to go fishing for small crappies. Instead a very large curious carp takes your bait and accelerates at a rate of 4.2 m/s^2 when it realizes that it is hooked. You only used fishing line that guarantees a max tensile strength of 25 pounds. What is the maximum weight (kg) of the carp you could catch without snapping the line?

Among the elderly population, a sideway fall is a most frequent cause of hip fracture. An old man of mass 65 kg and height 1.7m was sent to Prince of Wales Hospital due to sideway fall. He slipped and fell laterally down with a straight body. Before falling, his centre of mass was 0.9 m above ground. His centre of mass was on the ground at the end of the fall. The radius of gyration about the anterior-posterior axis at his centre of mass was 0.55 m. (a) Calculate the initial potential energy before his fall. (b) Assuming his potential energy would be converted to linear kinetic energy of his centre of mass and rotational kinetic energy about his centre of mass, calculate the impact velocity v of his centre of mas right before he hit the ground. C. M. 1.7m 0.9m

The cylindrical plug A of mass mA = 2.7 kg is released from rest at B and slides down the smooth circular guide. The plug strikes the block C of mass mc = 2.1 kg and becomes embedded in it. Calculate the distances which the block and plug slide before coming to rest. The coefficient of kinetic friction between the block and the horizontal surface is uk = 0.38 and the distance r = 2.08 m. Hk Answer: s= i mc A MA B m