Mechanics | Relativity Answers

A body vibrating with simple harmonic motion has a frequency of 4hz and an a amplitude of 0.15m.Calculate the maximum values of the acceleration and velocity
The acceleration and velocity at a point 0.09 from the equilibrium position of motion

An object of mass 20 kg is pulled up with a force of 150 N on an inclined plane for a
distance of 3.0 m. The plane makes an angle of 30º with the horizontal and the
coefficient of kinetic friction between the object and the plane is 0.3. Draw the free
body diagram and calculate the work done by each force. (Take g = 10 ms−2
)

Assuming that the skater has a speed of zero at position A, (Top of half pipe) which is 3.5m above the bottom of the half pipe.

Calculate the speed of the skater at position B (The middle bottom of the half pipe)

A falling stone takes 0.250 s to travel past a window 1.9 m tall. From what height above the top of the window did the stone fall?

A mass m, free to move along a line is attracted towards a given point on the line with a force proportional to its distance from the given point. If the mass starts from rest at a distance Xo from the given point, show that the mass moves in a simple harmonic motion.

While driving along a road an overloaded truck traveling at 79 km h−1 passes a stationary police car at the side of the road.
The police car begins to accelerate at a constant rate until it catches up and passes the truck 2.8 km down the road.
What is the acceleration required for the the police car to catch the truck in this distance? (in m s−2 to 2 s.f)

A model car is moving around a circular track of radius 3.0 m at a speed of 1.5 m s−1 as shown in the figure. It takes the car 12.6 s to complete one full lap.
What is the magnitude of the average acceleration of the car (a) between point A and point B? (in m s−2 to 2 s.f)

A rabbit and a dog catch sight of each other when they are 2.7 m apart. The dog begins to chase the rabbit as the rabbit runs directly towards its burrow. The rabbit starts of 11 m from its burrow.

Both the dog and the rabbit move along the same straight line and both start from rest and accelerate at a constant rate. If the dog can accelerate at a rate of 3.3 m s−2 then at what rate is the rabbit required to accelerate in order to prevent being caught? (in m s−2 to 2 s.f)

A uniform rod AB of length 4.6 m and mass M = 3.8 kg is hinged at A and held in equilibrium by a light cord. A load W = 22 N hangs from the rod at a distance d so that the tension in the cord is 94 N .
A = 53 degrees
B = 37 degrees
Part B
Determine the vertical force on the rod exerted by the hinge.
Express your answer to two significant figures and include the appropriate units. Enter positive value if the force is upward and negative value if the force is downward.
Part C
Determine the horizontal force on the rod exerted by the hinge.
Express your answer to two significant figures and include the appropriate units. Enter positive value if the force is directed to the right and negative value if the force is directed to the left.
Part D
Determine d from the appropriate torque equation.
Express your answer to two significant figures and include the appropriate units.

Suppose David puts a 0.60 kg rock into a sling of length 1.6 m and begins whirling the rock in a nearly horizontal circle, accelerating it from rest to a rate of 120 rpm after 5.7 s .
Part A
What is the torque required to achieve this feat?
Express your answer using three significant figures and include the appropriate units.
Part B
Where does the torque come from?