Round and Round we Go!
An object is moving in a circular path, the magnitude of velocity ___________ but the direction of velocity ________________
remains constant, is changing
A picture frame weighing 20 N hangs from a single nail on a wall. What is the tension in the string holding it?
T = 20 N
A 5 kg box is pushed with an applied force of 20 N on a level floor. If friction is 5 N, this is the net force acting on the box.
Fnet = 15 N
A crate slides down a frictionless ramp. If the ramp were made rough, how would the crate’s acceleration change, and why?
The acceleration would decrease because friction opposes motion, reducing the net force along the ramp.
A 10 kg box is placed on a frictionless ramp inclined at 30°. Calculate the acceleration of the box down the ramp.
a = 4.9m/s²
A car travels in a horizontal circle of 30 m; it completes 3 revolutions every 90 seconds. Calculate the Frequency and Time Period.
F = 0.033 Hz, T = 30s
An object in equilibrium has three forces acting on it. A 40 N force acts eastward, and a 55 N force acts 45° north of east. What is the magnitude and direction of the third force?
F3 = 87.95N (26.2° south of west)
A car located on a level highway has a mass of 400 kg. The frictional force on the car is 750 N. What acceleration will a force of 2.25 x 103 N produce on the car?
a = 3.75 m/s2
You swing a ball on a string in a horizontal circle. If the string breaks at some point, what path will the ball follow, and why?
The ball will move in a straight-line path tangent to the circle because no net force acts on it anymore, so it continues with its current velocity (Newton’s First Law).
A 5 kg crate is on a 25° ramp. The coefficient of kinetic friction between the crate and the ramp is 0.2. Find the acceleration of the crate down the ramp.
a = 1.7 m/s²
Determine the radius of a circle in which an airplane traveling at 95 m/s has a centripetal acceleration of 48 m/s2
r = 188.0 m
A 50 N sign hangs from two ropes, one at 30° to the horizontal and the other at 60° to the horizontal. Find the tension in each rope.
T1 = 25 N and T2 = 43.3 N
A dog sled with a mass of 80 kg is pulled by two dogs. The first dog pulls on the sled with a force of 37.5 N [NE] while the second pulls with a force of 45 N [21° S of E]. If the frictional force on the sled is 7.5 N, determine the acceleration of the sled.
a = 0.77 m/s2 [8.6° N of E]
Imagine you double the mass of an object but apply the same net force. How does this affect its acceleration, and why?
Acceleration is halved, because Newton’s Second Law (F=ma) shows that acceleration is inversely proportional to mass for a constant force.
A 12 kg block is pushed up a 40° frictionless ramp with a force of 80 N parallel to the ramp. Find the acceleration of the block.
a = 0.37 m/s²
A roller coaster car moves along a vertical circular loop with a radius of 8.0 m. It takes 6.0 seconds for the car to complete one full loop.
a) The speed of the roller coaster car as it moves around the loop.
b) The centripetal acceleration of the car at the top of the loop.
v = 8.38m/s and a = 8.78m/s²
A 10 kg chandelier is suspended by three cables arranged in a triangular pattern: two cables are attached at the ceiling at angles of 45° and 60° to the horizontal, and one cable hangs vertically. Find the tension in all three cables.
T1 = 40 N, T2 = 57 N, T3 = 20
An object is pulled by two forces, the first 40 N [NE] and the second 30 N [37° S of E]. If the acceleration of the object is 1.5 m/s2, what is the mass of the object?
m = 35.5 kg
Two objects with different masses fall freely in a vacuum. Which one hits the ground first, and why? What would change if air resistance were present?
In a vacuum, both hit at the same time because acceleration due to gravity is independent of mass.
A 15 kg block is on a 35° ramp. The coefficient of kinetic friction is 0.3. If a student pulls the block upward with a 100 N force parallel to the ramp, determine the acceleration of the block.
a = 1.49 m/s²
A satellite orbits the Earth in a circular path with a radius of 6.7×106 m. If the time period of the satellite’s orbit is 90 minutes, calculate the centripetal acceleration of the satellite.
ac = 9.1 m/s2
A lantern of mass m hangs from a ring at point B, where two ropes are attached. One rope runs horizontally to the left and is fastened to a wall at A. The second rope is fastened to the ceiling at point C, making a 40° angle above the horizontal.
The rope at A will detach if its tension exceeds 30 N.
What is the maximum mass of the lantern that can be safely supported without the rope at A detaching?
m = 2.57 kg
A 1000 kg barge is pulled upstream by ropes attached to two horses walking along the opposite sides of a canal. If each horse pulls with a force of 350 N at an angle of 45° with a line parallel to the shore and the resistance of the barge through the water is 50 N, determine the acceleration of the boat.
a = 0.44 m/s2
A person pushes a large box across a floor. Initially, the box doesn’t move. After some force, it starts sliding. Why does it require more force to start moving than to keep it moving?
Static friction is greater than kinetic friction. The maximum static friction must be overcome to start motion, after which kinetic friction (smaller) opposes motion.
Two blocks, m1=8 kg and m2=12 kg, are connected by a light rope over a frictionless pulley. m1 is on a 30° frictionless incline, and m2 hangs vertically. Find the acceleration of the system and the tension in the rope.
a = 3.92m/s²
T = 70.7 N