A metal plate has a horizontal width of 3 m and a vertical height of 2 m. The density of the plate is uniform, meaning that the mass is evenly distributed. Let’s consider the origin to be the bottom left of the plate. That means the center of mass of the plate is _____x + _________ym.

A woman weighing 61.5 kg stands at one end of a 120-kg raft that is 6.00 m long. The other end of the raft is 0.500 m from a pier. So, before the woman moves, she is at a total distance of 6.50 m away from the pier. The woman walks toward the pier until she gets to the other end of the uniform raft and stops there. What is the distance between the uniform raft and the pier?

A rod of length 24.00 cm has linear density (mass per length) given by 2 = 50.0 + 19.5x where x is the distance from one end, and A is measured in grams/meter. (a) What is its mass? (b) How far from the x = 0 end is its center of mass?

a shape is on an x-y axis, beginning at x = 0.  The bottom of the shape is 25 cm long and it reaches a height of 20 cm.  The shape weights 450 g.   The shape has a triangular form, like a wedge.    If shape has a uniform density and a uniform width in the z-direction, find the x-component of the center-of-mass.

A rod of length 23.00 cm has linear density (mass per length) given by 1 = 50.0 + 17.5x where x is the distance from one end, and 2 is measured in grams/meter. (a) What is its mass? (b) How far from the x = 0 end is its center of mass? m

The figure shows a composite slab with dimensions d₁ = 11.9 cm, d₂ = 2.94 cm, and d3 = 12.8 cm. Half the slab consists of aluminum (density = 2.70 g/cm³) and half consists of iron (density = 7.85 g/cm³). What are (a) the x coordinate, (b) the y coordinate, and (c) the z coordinate of the slab's center of mass? (a) Number (b) Number (c) Number dy Iron Units Units Units 2d₁ -Midpoint Aluminum dy 11

You have been chosen as the test subject for the newest attraction at Canada’s Wonderland. This attraction is a single-person roller coaster ride that has a 25.0 m drop followed by a plunger/piston device that brings the ride to rest. The plunger/piston is connected to a cylinder that contains 250 kg of water. The cart has a mass of 75.0 kg and starts at rest from the top of the track. To determine the total mass of the cart during the ride you must add your mass. As the cart moves down the track it has been determined that friction in the wheels and axles results in the production of 2750 J of thermal and sound energy combined. The plunger/piston at the bottom of the device has been designed to stop the cart with a maximum acceleration of 5.00 g’s (i.e. 49.0 m/s2). My Mass = 50kg   Problem 3: In order to stop the ride, the cart collides with the plunger/piston system applying a force to it. According to Newton’s 3rd law, the piston will apply the same force back on the cart. This…

You have been chosen as the test subject for the newest attraction at Canada’s Wonderland. This attraction is a single-person roller coaster ride that has a 25.0 m drop followed by a plunger/piston device that brings the ride to rest. The plunger/piston is connected to a cylinder that contains 250 kg of water. The cart has a mass of 75.0 kg and starts at rest from the top of the track. To determine the total mass of the cart during the ride you must add your mass. As the cart moves down the track it has been determined that friction in the wheels and axles results in the production of 2750 J of thermal and sound energy combined. The plunger/piston at the bottom of the device has been designed to stop the cart with a maximum acceleration of 5.00 g’s (i.e. 49.0 m/s2). MASS: 146 lb = 66.2kg Problem 1: The cart with you inside of it starts from rest at the top of the ride. Determine the gravitational potential energy of the cart with you as the single passenger at the top of the ride.…

The figure below shows a slab with dimensions d1=10.2 cm, d2= 2.8 cm, and d3= 13.0 cm.  Half the slab is aluminum (density = 2.70 g/cm3) and half is iron (density = 7.85 g/cm3).  Determine the y coordinate of the slab's center of mass (in cm).

rigid body statics