1. A ball hanging from the ceiling by a string swings in a circle. If the...

1. A ball hanging from the ceiling by a string swings in a circle. If the radius of the circle it traces is 2 meters and its distance from the ceiling is 5 meters, what is the velocity of the ball?

2. Assuming an iced over road (no friction), if a car is going 25 m/s around a curve in the road of radius 75 meters, what is the perfect angle to bank the road so that the car stays on the road?

3. A block starts at rest and slides down a 3 meter long incline plane at 30 degrees in 3 seconds. Calculate the coefficient of kinetic friction between the block and the incline plane. Hint: use kinematics to find the acceleration, then use a force diagram to solve for the coefficient of kinetic friction.

4. A block of mass 10kg slides on an incline plane of 30 degrees while attached to a second mass of 2kg by a rope. The rope runs through a pulley and the second mass is hanging from the top of the ramp (as the problem we worked in class). Define the positive direction such that the first mass slides down the ramp. The coefficient of kinetic friction between the first mass and the incline plane is 0.1. Calculate the acceleration of the two mass system.

5. A block slides down an incline plane of 20 degrees. The coefficient of kinetic friction between the block and incline is 0.25. Calculate the resulting acceleration.

Expert Solution

genius_generous answered 2 years ago

A 3.9 kg ball swings from a string in a vertical circle such that it has...

A 3.9 kg ball swings from a string in a vertical circle such that it has constant mechanical energy. Ignore any friction from the air or in the string. What is the difference in the tension between the lowest and highest points on the circle? Give a positive answer in N.

A charged polystyrene ball of mass m = 10.0 g is hanging from the ceiling by...

A charged polystyrene ball of mass m = 10.0 g is hanging from the ceiling by a piece of string with negligible mass. The ball hangs between two charged, parallel plates which create a uniform electric field of magnitude E = 10.00 N/C directed from left to right, as shown in the figure. When the ball is in equilibrium between the plates, the string makes an angle of 20° to the vertical. Calculate how many electrons have been added or...

An athlete swings a ball, connected to the end of a chain, in a horizontal circle....

An athlete swings a ball, connected to the end of a chain, in a horizontal circle. The athlete is able to rotate the ball at the rate of 8rev/s when the length of the chain is 0.600m. when he increases the length to 0.900 m, he is able to rotate the ball 6.00 rev/s. (a) which rate of rotation gives the greater speed for the ball? (b) what is the centripetal acceleration of the ball at 8.00 rev/s? (c) what...

An ideal spring is in equilibrium, hanging from a ceiling with a 1 kg mass at...

An ideal spring is in equilibrium, hanging from a ceiling with a 1 kg mass at the end. At rest, the length of the hanging spring is 10 cm. Then, an additional 5 kg block is added to the spring, causing its length at rest to increase to 13 cm. The 5 kg block is then removed. Starting from rest, when the 5 kg block is removed, the spring begins to oscillate. What will the spring’s velocity be, the third...

A ball is attached to a string and swung in a horizontal circle at a constant...

A ball is attached to a string and swung in a horizontal circle at a constant speed. Assume air resistance is negligible. If the string tripled in length but the speed of the ball remained the same, show mathematically how the inward force on the ball would change.

A ball is tied to a string and whirled in a horizontal circle at a constant...

A ball is tied to a string and whirled in a horizontal circle at a constant 4 revolutions per second. Categorize the following according to whether they are constant and zero in value, constant and non-zero in value, or non-constant in value: linear speed (scalar) linear velocity (vector) radial (centripetal) acceleration (scalar) radial (centripetal) acceleration (vector) angular speed (scalar) angular velocity (vector) angular acceleration (scalar) angular acceleration (vector)

A spring is hanging motionless from the ceiling of a room on the earth. You attach...

A spring is hanging motionless from the ceiling of a room on the earth. You attach a mass to the end of the spring and after releasing the mass, you observe that the spring extends a distance before momentarily coming to a halt. What then must be the distance below just the spring's equilibrium position to the new equilibrium position of the spring-mass system? A. B. C. D. A spring is hanging downward from the ceiling of a room on the...

A mass weighing 8 lb is attached to a spring hanging from the ceiling, and comes...

A mass weighing 8 lb is attached to a spring hanging from the ceiling, and comes to rest at its equilibrium position. The spring constant is 4 lb/ft and there is no damping. A. How far (in feet) does the mass stretch the spring from its natural length? L= B. What is the resonance frequency for the system? ω0= C. At time t=0 seconds, an external force F(t)=3cos(ω0t) is applied to the system (where ω0 is the resonance frequency from...

An 8-pound weight is attached to a spring hanging from a ceiling. The weight stretches the...

An 8-pound weight is attached to a spring hanging from a ceiling. The weight stretches the spring 9.6 inches, coming to rest at its stretched equilibrium position. The weight is displaced 8 inches below this stretched equilibrium position, and at time t = 0 the mass is released. At the same instant, an external force of F(t)= 2cos(2t) pounds is applied to the system. The damping constant is 1 lb/(ft/sec). Find the function that gives the displacement of the mass...

An 7-kg mass is attached to a spring hanging from the ceiling and allowed to come...

An 7-kg mass is attached to a spring hanging from the ceiling and allowed to come to rest. Assume that the spring constant is 50 N/m and the damping constant is 4 N-sec/m At time t=0, an external force of 8sin(3t)cos(3t) is applied to the system. Determine the amplitude and frequency of the steady-state solution.

Question