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A object whose mass is 0.0050 kg is in simple harmonic motion with a period of 0.040 sec and
an amplitude of 10.0 mm. a) What is it’s maximum acceleration? b) What is the maximum force
on the object? c) What is it’s acceleration when it is 5.00 mm from it’s equilibrium position?
d) What is the objects total energy?
The mass of matts head is 5 kg and its centre of mass (A) is located LHead = 30 mm anterior to the axis of rotation (atlanto-occipital joint, B) acting at an angle of 90°. The neck extensors act LNeck = 52 mm posterior to the axis of rotation, at an angle of 𝜃
θ
= 128°. matt is currently holding his head still. How much force do the neck extensor muscles need to produce to keep the head from nodding (i.e. keep his head still). Assume gravity is 9.8 m.s-2?
Bruce and Dave are rugby players. Dave runs at Bruce, who has the ball (see figure below, bird’s eye view). Bruce is 95 kg and is running directly in the x direction at B = 6.2 m/s. Dave is 77 kg and runs towards Bruce at D = 5.2 m/s and a relative angle of 22°. When Dave tackles Bruce, they become entangled and lose their footing on the playing surface (i.e. moving together). How fast do Dave and Bruce travel directly after the impact of the tackle in the x direction (To the right and up on the page are considered positive directions for the purposes of calculations)?
A water is pumped at a rate of 24 cm^3/s through a 0.50 cm radius pipe on the main floor of a house to a 0.35 cm radius pipe in a solar hot water collector 4 m higher on the roof. If the pressure in the pipe on the roof is 1.2x10^5 Pa, what is the pressure in the larger pipe on the floor?
Courtney’s mass is 55kg. When she is in a tuck position her radius of gyration in the saggital plane is k= 0.35m and she rotates at an angular velocity of 9.9 rad/s. How fast would she rotate if she was able to bring her knees closer to her chest so reducing k to 0.28 m
Show that the equation y=2Asin(nπx/L)cos2πft for a standing wave is a solution of the wave equation
Show that V=(1+M/m)√2gh
VECTORS:
A ship was seen on a radar screen to be 10 km east of a particular location. Sometime later, the ship is at 12 km north of west. What is the displacement of the ship?
VECTORS:
An airplane flies northwest for 250 mi and then west for 150 mi. Find the resultant (or sum) displacement vector by a) graphical method and b) the component method.
Leo and Christian are twins. At the age of 30, Leo left for a round trip to a distance star in a spaceship with a speed of 0.95c relative to Earth. The whole trip took 20 years according to the shipboard clock. Find the ages when Leo returns
With solution
